From d501b00249543b536dbf6db017e7247e67a445c6 Mon Sep 17 00:00:00 2001 From: nils Date: Wed, 3 Oct 2018 23:18:55 +0200 Subject: [PATCH] initial commit of the technical specification document --- LICENSE.md | 175 ++ README.md | 22 +- actus-techspecs.tex | 4113 +++++++++++++++++++++++++++++++++++++ bibliography.bib | 1 + build.sh | 37 + media/bdc-interface.png | Bin 0 -> 34971 bytes media/dcc-interface.png | Bin 0 -> 41963 bytes media/model-interface.png | Bin 0 -> 33831 bytes media/rf-interface.png | Bin 0 -> 60299 bytes media/taxonomy.png | Bin 0 -> 46997 bytes 10 files changed, 4346 insertions(+), 2 deletions(-) create mode 100644 LICENSE.md create mode 100644 actus-techspecs.tex create mode 100644 bibliography.bib create mode 100644 build.sh create mode 100644 media/bdc-interface.png create mode 100644 media/dcc-interface.png create mode 100644 media/model-interface.png create mode 100644 media/rf-interface.png create mode 100644 media/taxonomy.png diff --git a/LICENSE.md b/LICENSE.md new file mode 100644 index 0000000..22dc42e --- /dev/null +++ b/LICENSE.md @@ -0,0 +1,175 @@ +## creative commons + +# Attribution-ShareAlike 4.0 International + +Creative Commons Corporation (“Creative Commons”) is not a law firm and does not provide legal services or legal advice. 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For the avoidance of doubt, this paragraph does not form part of the public licenses. + +Creative Commons may be contacted at [creativecommons.org](http://creativecommons.org/). +``` diff --git a/README.md b/README.md index a90c718..cd20dc3 100644 --- a/README.md +++ b/README.md @@ -1,2 +1,20 @@ -# actus-techspecs -The ACTUS technical specifications +# ACTUS Technical Specification Document + +[![License: CC BY-SA 4.0](https://img.shields.io/badge/License-CC%20BY--SA%204.0-lightgrey.svg)](https://creativecommons.org/licenses/by-sa/4.0/) + +The ACTUS Technical Specification Document provides a formal specification of the ACTUS standard for the algorithmic representation of financial contracts. + +It comes as a single ``latex`` file ``actus-techspecs.tex``. The latest version is generally available as a PDF at https://actusfrf.org/actus-techspecs.pdf. + +The ACTUS Technical Specification Document is freely available and licensed under Creative Commons Attribution Share-Alike (CC-BY-SA) version 4.0. + +## How to build + +The ACTUS Technical Specification Document can be built as a PDF as follows: + +``` +git clone https://github.com/actusfrf/actus-techspecs.git +cd actus-techspecs +./build.sh +``` +Building will create a (number of) config-file(s) used for compiling the ``latex`` file and a PDF version of the ACTUS Technical Specifications Document. Standard `pdflatex` tools like http://latex.informatik.uni-halle.de/latex-online/latex.php can be used for compiling/preview once the White Paper is built. diff --git a/actus-techspecs.tex b/actus-techspecs.tex new file mode 100644 index 0000000..04e022e --- /dev/null +++ b/actus-techspecs.tex @@ -0,0 +1,4113 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%% THIS IS THE %%%%%%%%%%%%%% +%%%%%%%%%%%% ACTUS TECHNICAL SPECIFICATION DOCUMENT %%%%%%%%%%%%%% +%%%%%%%%%%%% v1.0 %%%%%%%%%%%%%% +%%%%%%%%%%%% ---------------- %%%%%%%%%%%%%% +%%%%%%%%%%%% Copyright (C) 2016 - present by %%%%%%%%%%%%%% +%%%%%%%%%%%% ACTUS Financial Research Foundation %%%%%%%%%%%%%% +%%%%%%%%%%%% ----------------- %%%%%%%%%%%%%% +%%%%%%%%%%%% Please see distribution for license %%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\documentclass[9pt,oneside]{amsart} +\usepackage{multicol} +\usepackage[a4paper, + width=170mm, + top=18mm, + bottom=22mm, + includeheadfoot]{geometry} +\usepackage[bookmarks=true, + unicode=true, + pdftitle={ACTUS Technical Specification}, + pdfauthor={ACTUS Financial Research Foundation}, + pdfkeywords={ACTUS, Financial Contracts, Algorithmic Contracts, Technical Specification}, + pdfborder={0 0 0.5 [1 3]}]{hyperref} + + +% ---------------------- Language -------------------------------- +\usepackage[english]{babel} + + +% ---------------------- floats and figures -------------------------------- +\usepackage{graphicx} +\usepackage{float} +\usepackage{longtable} + + +% ---------------------- math -------------------------------- +\usepackage{amsmath} +\usepackage{amssymb} +\usepackage{amsthm} % for theorem-style environments +\newtheorem{example}{Example} + + +% ------------------- special tables ----------------------------- +\newenvironment{states}[1]{ + \begin{longtable}[H]{| p{0.5\textwidth} | p{0.45\textwidth} |} + \multicolumn{2}{c}{\textbf{#1: State Variables Initialization}}\\ + \hline + \textbf{Initialization per $t_0$} & \textbf{Comments} \\ + \hline + \endfirsthead + \multicolumn{2}{c}{\textit{Continued from previous page}} \\ + \hline + \textbf{Initialization per $t_0$} & \textbf{Comments} \\ + \hline + \endhead + \hline \multicolumn{2}{r}{\textit{Continued on next page}} \\ + \endfoot + \hline + \endlastfoot +}{% + \end{longtable} +} + +\newenvironment{schedule}[1]{ + \begin{longtable}[H]{| p{0.06\textwidth} | p{0.49\textwidth} | p{0.4\textwidth} |} + \multicolumn{3}{c}{\textbf{#1: Contract Schedule}}\\ + \hline + \textbf{Event} & \textbf{Schedule} & \textbf{Comments} \\ + \hline + \endfirsthead + \multicolumn{2}{c}{\textit{Continued from previous page}} \\ + \hline + \textbf{Event} & \textbf{Schedule} & \textbf{Comments} \\ + \hline + \endhead + \hline \multicolumn{2}{r}{\textit{Continued on next page}} \\ + \endfoot + \hline + \endlastfoot +}{% + \end{longtable} +} + +\newenvironment{functions}[1]{ + \begin{longtable}[H]{| p{0.06\textwidth} | p{0.42\textwidth} | p{0.47\textwidth} |} + \multicolumn{3}{c}{\textbf{#1: State Transition Functions and Pay Off Functions}}\\ + \hline + \textbf{Event} & \textbf{Pay Off Function} & \textbf{State Transition Function}\\ + \hline + \endfirsthead + \multicolumn{2}{c}{\textit{Continued from previous page}} \\ + \hline + \textbf{Event} & \textbf{Pay Off Function} & \textbf{State Transition Function}\\ + \hline + \endhead + \hline \multicolumn{2}{r}{\textit{Continued on next page}} \\ + \endfoot + \hline + \endlastfoot +}{% + \end{longtable} +} + +% ---------------------- misc -------------------------------- +\usepackage{verbatim} +\usepackage{natbib} +\setlength\parindent{0pt} +\newcommand{\svar}[2]{\textbf{#1}_{#2}} +\newcommand{\attr}[1]{\texttt{#1}} +\newcommand{\stf}[2]{STF\_#1\_#2()} +\newcommand{\pof}[2]{POF\_#1\_#2()} +\newcommand{\dfl}[1]{D(\textbf{Prf}_{#1})} +\newcommand{\sgn}{R(\attr{CNTRL})} +\newcommand{\sdl}[3]{S(#1,#2,#3)} +\newcommand{\yfr}[2]{Y(#1,#2)} +\newcommand{\undef}{\varnothing} + + +% ---------------------- Input options -------------------------------- +\newcommand{\VersionNumber}{unknown revision} +\IfFileExists{build_options.tex}{\input{build_options.tex}} + + +%%%%%%%%%%%%%%%%%%%% Titlepage %%%%%%%%%%%%%%%%%%%% + +\title{ACTUS: The algorithmic representation of financial contracts \\ + {\smaller \textbf{Version \VersionNumber}}} + +\author{ + ACTUS Financial Research Foundation\\ + info@actusfrf.org +} + +%%%%%%%%%%%%%%%%%%%% Document code starts here %%%%%%%%%%%%%%%%%%%% + +\begin{document} + +%\begin{abstract} +% +%\end{abstract} + +\maketitle + + + +%%%%%%%%%%%%%%%%%%% About %%%%%%%%%%%%%%%%%%%% + +\section*{About this document}\label{sec:about} + +This Document defines provides high-level documentation regarding the Algorithmic Contract Types Unified Standards (ACTUS). It is provided to the ACTUS Users Association by the ACTUS Financial Research Foundation under the terms of the open source, public good contribution of the ACTUS body of work by the ACTUS Financial Research Foundation. + + +%%%%%%%%%%%%%%%%%%%% Versions %%%%%%%%%%%%%%%%%%%% + +\section*{Versions}\label{sec:version} + +The version of this document (cf. titlepage) has following format: [major].[minor]-[revision]-[date] where [major] and [minor] are integers marking major and minor release, [revision] indicates an unreleased revision in form of the short form of the respective git commit hash, and [date] the respective date of the revision. Releases are recorded in the following table with minor releases increasing the version number by 0.1; major releases by 1.0. + +\begin{table}[H] + \centering + \begin{tabular}{| p{0.1\textwidth} | p{0.1\textwidth} | p{0.75\textwidth} |} + \hline + Date & Version & Description \\ + \hline + 2016-06-17 & 0.1 & Initial Draft of the ACTUS High Level Description \\ + \hline + 2017-04-06 & 0.2 & Various conceptual refinements, introduced PP (Principal Prepayment), and PY (Penalty Payment) event types, introduced Contract Types Call Money (CLM), Cash (CSH), Commodity (COM), Foreign Exchange Outright (FXOUT) \\ + \hline + 2018-09-30 & 1.0 & General overhaul of the specifications including introduction of various interfaces, additional rate-reset related attributes and Undefined Maturity Profile (UMP) Contract Type.\\ + \hline + \end{tabular} +\end{table} + + +%%%%%%%%%%%% Starting new page here %%%%%%%%%%%%%% + +\newpage + + +%%%%%%%%%%%% Table Of Contents %%%%%%%%%%%%%% + +\tableofcontents + + +%%%%%%%%%%%% Starting new page here %%%%%%%%%%%%%% + +\newpage + + +%%%%%%%%%%%%%%%%%%%% 2-columns starts here %%%%%%%%%%%%%%%%%%%% +\setlength{\columnsep}{20pt} +\begin{multicols}{2} + + +%%%%%%%%%%%%%%%%%%%% Introduction %%%%%%%%%%%%%%%%%%%% + +\section{Introduction}\label{sec:intro} + +Financial contracts are legal agreements between two (or more) counterparties on the exchange of future cash flows. Such legal agreements are defined unambiguously by means of a set of contractual terms and logic. As a result, financial contracts can be described mathematically and represented as computer readable algorithms. + +The exchange of cash flows between counterparties follows certain patterns. Each pattern is called ContractType (CT) within the ACTUS framework. A typical CT or exchange pattern of cash flows is what we could call the bond pattern where principal is exchanged initially followed by a period of cyclical interest payments and finally the principal is reversed at maturity date. Interest rates could be fixed or variable with certain interest rate reset cycles. This pattern is used also for many types of loans. Within ACTUS this CT is called PrincipalAtMaturity or PAM for short. + +Another popular pattern is used for mortgages in many countries. Principal is also exchanged initially followed however by regular payments which combine interest and principal redemption at the same time. Since the total payment is given, the split between the principal portion and the interest portion varies over time. This CT is called Annuity or ANN. PAM and ANN are two examples of CT´s. As we will see below, there are about thirty CT´s to describe the overwhelming bulk of all cash flow exchange patterns found in the financial world. + +Financial contracts represent the deterministic part of finance. This offers a strict definition for what belongs to a contract and what not. It especially excludes any stochastic element which are called risk factors within the ACTUS framework. ACTUS has a clearly defined interface to these risk factor (see the specific chapter below) but it does not model these risk factors. The link between ACTUS and the risk factors can best be explained with the variable side of a swap or any variable rate instrument that resets its rate periodically. + +A variable rate instrument has a current coupon that is known and therefore part of the contract attributes. It also has a rule, how to derive new rates such as \textit{Libor plus x basis points}. These rules are contract terms and therefore also part of the contract attributes. However, ACTUS is agnostic towards the external market link (or Risk Factor) from which the new rate is fed upon a rate reset. + + +%%%%%%%%%%%%%%%%%%%% Taxonomy %%%%%%%%%%%%%%%%%%%% + +\section{Financial contract taxonomy} + +Below an overview of the ACTUS Contract Types taxonomy. + + +%%%%%%%%%%%%%%%%%%%% Figure/Image No: 2 starts here %%%%%%%%%%%%%%%%%%%% + +\begin{figure}[H] + \centering + \includegraphics[width=0.45\textwidth]{./media/taxonomy.png} + \caption{An overview of the ACTUS Contract Types Taxonomy.} + \label{fig:taxonomy} +\end{figure} + + +%%%%%%%%%%%%%%%%%%%% Figure/Image No: 2 Ends here %%%%%%%%%%%%%%%%%%%% + + +Table \ref{tbl:taxonomy} provides further details on the ACTUS Taxonomy including the real-world financial contracts covered through the various ACTUS Contract Types. + + +\end{multicols} + +%%%%%%%%%%%%%%%%%%%% Table No: 3 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{longtable}{| p{0.07\textwidth}p{0.07\textwidth}p{0.1\textwidth}p{0.45\textwidth}p{0.2\textwidth} |} + \hline + \textbf{Family} & \textbf{Class} & \textbf{Type} & \textbf{Description} & \textbf{Covered contracts} \\ + \hline + \endfirsthead + \multicolumn{4}{c}{\textit{Continued from previous page}} \\ + \hline + \textbf{Family} & \textbf{Class} & \textbf{Type} & \textbf{Description} & \textbf{Covered contracts} \\ + \hline + \endhead + \hline \multicolumn{4}{r}{\textit{Continued on next page}} \\ + \endfoot + \hline + \endlastfoot + Basic CT & Maturity & PAM: Principal at Maturity & Principal payment fully at Initial Exchange Date (IED) and repaid at Maturity Date (MD). Fixed and variable rates. & All kind of bonds, term deposits, bullet loans and mortgages etc. \\ + \hline + & & ANN: Annuity & Principal payment fully at IED and interest plus principal repaid periodically in constant amounts till MD. If variable rate, total amount for interest and principal is recalculated to be fully matured at MD. & Classical level payment mortgages, leasing contracts etc. \\ + \hline + & & NAM: Negative Amortizer & Similar as ANN. However when resetting rate, total amount (interest plus principal) stay constant. MD shifts. Only variable rates. & Special class of ARM´s (adjustable rate mortgages), Certain loans. \\ + \hline + & & LAM: Linear Amortizer & Principal payment fully at IED. Principal repaid periodically in constant amounts till MD. Interest gets reduced accordingly. If variable rate, only interest payment is recalculated. Fixed and variable rates. & Many amortizing loans \\ + \hline + & & ANX: Exotic Annuity & Exotic version of ANN However step ups with respect to (i) Principal, (ii) Interest rates are possible. Highly flexible to match totally irregular principal payments. Principal can also be paid out in steps. & A special version of this kind are teaser rate loans and mortgages with annuity features \\ + \hline + & & LAX: Exotic Linear Amortizer & Exotic version of LAM. However step ups with respect to (i) Principal, (ii) Interest rates are possible. Highly flexible to match totally irregular principal payments. Principal can also be paid out in steps. & A special version of this kind are teaser rate loans and mortgages \\ + \hline + & & NAX: Exotic Negative Amortizer & Exotic version of NAM However step ups with respect to (i) Principal, (ii) Interest rates are possible. Highly flexible to match totally irregular principal payments. Principal can also be paid out in steps. & A special version of this kind are teaser rate loans and mortgages with variable MD \\ + \hline + & & CLM: Call Money & Loans that are rolled over as long as they are not called. Once called it has to be paid back after the stipulated notice period. & Interbank loans with call features \\ + \hline + & & PBN: Perpetual Bonds & Bonds without any maturity date. Interest is paid into eternity if is not terminated. & Consoles, war loans \\ + \hline + & Non-Maturity & UMP: Undefined Maturity Profile & Principal paid in and out at any point in time without prefixed schedule. Interest calculated on outstanding and capitalized periodically. Needs link to a behavioral function describing expected flows. & Saving products of all kind, current accounts. In some countries even variable rate mortgages can be represented with this CT \\ + \hline + & & CSH: Cash & Cash or cash equivalent position & Cash, deposits at central bank \\ + \hline + & & STK: Stock & Any instrument which is bought at a certain amount (market price normally) and then follows an index. & All straight stocks \\ + \hline + & & COM: Commodity & This is not a financial contract in its proper sense. However it tracks movements of commodities such as oil, gas or even houses. Such commodities can serve as underlyings of commodity futures, guarantees or simply asset positions. & Oil, gas, electricity, houses etc. \\ + \hline + Combined & Swap and Option like & SWAPS: Swap & Exchange of two basic CT´s (PAM, ANN etc.). Normally one is fixed, the other variable. However all variants possible including different currencies for cross currency swaps, basic swaps or even different principal exchange programs. & All kind of swaps. The variety is defined by the underlying CT´s which currently are PAM and ANN in all tis flavors. With each new basic CT the variety rises \\ + \hline + & & SWPPV: Plain Vanilla Swap & Plain vanilla swaps where the underlying is always a PAM and one leg is fixed, the other variable. Plain vanilla cross currency swaps also covered. & More than 90\% of all interest rate swaps follow this simple pattern. \\ + \hline + & & FXOUT: Foreign Ex-change Outright & Two parties agree to exchange two fixed cash flows in different currencies at a certain point in time in future. & Any FX-outright transaction. This is also the underlying of FX-options and FX futures \\ + \hline + & & CAPFL: Cap Floors & Interest rate option expressed in a maximum or minimum interest rate & Caps and Floor options \\ + \hline + & & CFXOP: Exotic Cap Floor & Exotic variants of caps and floors & \\ + \hline + & Securiti-zation & SCRMR: Securitized Instruments Market Risk & Instruments bundled and traded in tranches without any specific credit risk feature & MBS, ABS, Principal only, Interest only instruments \\ + \hline + & & SCRCR: Securitized instrument Credit Risk Feature & Instruments bundled and traded in tranches that include specific credit risk feature & CDOs \\ + \hline + & Symmetric & MRGNG & A generic margining contract governing the agreement of margining usually present at central clearing houses & \\ + \hline + & & FUTUR: Future & Keeps track of value changes for any basic CT as underlying (PAM, ANN etc. but also FXOUT, STK, COM). Handles margining calls. & Standard interest rate, FX, stock and commodity futures. \\ + \hline + & Options & OPTNS: Option & Calculates straight option pay-off for any basic CT as underlying (PAM, ANN etc.) but also SWAPS, FXOUT, STK and COM. Single, periodic and continuous strike is supported. & European, American and Bermudan options with Interest rate, FX and stock futures as underlying instruments \\ + \hline + & & BNDCP: Callable or puttable maturity contract & Bonds with a call or put option. If option is exercised, underlying bond ceases to exist. & Callable and puttable bonds or loans \\ + \hline + & & BNDWR: Bond with warrant & Bonds with a warrant. If option is exercised, underlying bond continues to exist. & Warrants \\ + \hline + & & IRXOP: Exotic Interest Rate Option & Exotic interest rate options & \\ + \hline + & & STXOP: Stock Option & Exotic stock options & \\ + \hline + & & CMXOP: Exotic Commodity Option & Exotic commodity options & \\ + \hline + & & FXXOP: Exotic FX Option & Exotic FX options & \\ + \hline + & Credit Risk & CEG: Guarantees & Guarantee is a credit enhancement contract. It creates a relationship between a guarantor, an obligee and a debtor, moving the exposure from the debtor to the guarantor. & Personal guarantee. Government guarantee. Underlyings of CDOs. \\ + \hline + & & CEC: Collateral & Collateral is a credit enhancement contract. It creates a relationship between a collateral an obligee and a debtor, covering the exposure from the debtor with the collateral. & Mortgages include a collateral contract. Any coverage with financial or physical collateral \\ + \hline + & & CDSWP: Credit Default Swap & All sorts of credit default swaps & \\ + \hline + & & CRSWP: Total Return Swap & All sorts of total return swaps & \\ + \hline + & & CLNTE: Credit Linked Note & All sorts of credit linked notes & \\ + \hline + \caption{Financial contract taxonomy} + \label{tbl:taxonomy} +\end{longtable} + +%%%%%%%%%%%%%%%%%%%% Table No: 3 ends here %%%%%%%%%%%%%%%%%%%% + + +%%%%%%%%%%%%%%%%%%%% 2-columns starts here %%%%%%%%%%%%%%%%%%%% +\setlength{\columnsep}{20pt} +\begin{multicols}{2} + + +%%%%%%%%%%%%%%%%%%%% Notations %%%%%%%%%%%%%%%%%%%% + +\section{Notations}\label{sec:notations} + +\subsection{Contract Attributes } + +Contract Attributes represent the legal contractual terms that define the exchange of cash-flows of a financial contract. Contract Attributes are introduced by the ACTUS data standard and described in the ACTUS Data Dictionary (DD). Throughout this document Contract Attributes are written in the short form and expressed in capitals (not bold). + +\begin{example}[Contract Attribute] +The ACTUS attribute \textit{Initial Exchange Date} is represented in short form \attr{IED}. +\end{example} + + +\subsection{$\undef$-Operator} + +The $\undef$-operator is used to indicate that a certain property is undefined or, in other words, that no value has been assigned to the respective property. In particular, for optional contract attributes it means that the attribute is not defined and for schedule times (see section \ref{sec:schedules}) it means that the respective schedule is empty, i.e. no schedule time defined. + +\begin{example}[Undefined Attribute] +$\attr{IPANX}=\undef$ indicates that attribute \attr{IPANX} is undefined. +\end{example} + +\begin{example}[Empty Schedule] +$\vec{t}^{IP}=\undef$ means the same as $\vec{t}^{IP}=\{\}$, with $\{\}$ the empty set, and states that the IP schedule $\vec{t}^{IP}$ does not contain a schedule time. +\end{example} + + +\subsection{$t_0$-Time} + +$t_0$ marks the time as per which the state of a contract is represented in form of the respective set of attributes. Status Date \attr{SD} itself is an attribute of the contract. In general, from the contractual logic we are able to derive any contractual events and contract states for any time $t>t_0$. + + +\subsection{State Variables} + +State Variables describe the inner state of a financial contract at a certain point in time $t$ during its lifetime such as (outstanding) Nominal Value, applicable Interest Rate, or the contract performance through Contract Status. State Variables are written in the short form as defined in table \ref{tbl:statevars} with first letter capitalized, printed in bold, and indexed with time. + +\begin{example}[State Variables] +$\svar{Nvl}{t}$ refers to the State Variable \textit{Nominal Value} observed at per time $t$. +\end{example} + + +\subsection{Contract Events} + +Contract Events mark specific points in time during the lifetime of a financial contract at which a cash flow is being exchanged or the State Variables of the contract are being updated. Contract Events are written in the short form as defined in table \ref{tbl:events} and printed in bold capitals. + +\begin{example}[Contract Events] +The \textit{Initial Exchange Date} event of a contract is written as \textbf{IED}. +\end{example} + + +\subsection{State Transition Functions} + +State Transition Functions (STF) define how the State Variables are being updated when a certain Contract Event applies from a pre-event state indexed $t^-$ to a post-event state indexed $t^+$. These functions are specific to a certain Contract Event and Contract Type. STFs are written according to the following pattern \stf{[event type]}{[contract type]} where [event type] and [contract type] refer to the respective event type and contract type to which the STF belongs. + +\begin{example}[State Transition Functions] +The STF for an IP event and PAM contract is written as \stf{IP}{PAM} and maps e.g. state variable \textit{Nominal Accrued} from a pre-event state $\svar{Nac}{t^-}$ to post-event state $\svar{Nac}{t^+}$. +\end{example} + + +\subsection{Pay Off Functions} + +Pay Off Functions (POF) define how the cash flow for a certain Contract Event is being derived from current State Variables and Contract Attributes. These functions are specific to a certain Contract Event and Contract Type. POFs are written according to the following pattern \pof{[event type]}{[contract type]} where [event type] and [contract type] refer to the respective event type and contract type to which the STF belongs. + +\begin{example}[Pay Off Functions] +The POF for an IP event and PAM contract is written as \pof{IP}{PAM}. +\end{example} + + +\subsection{Date/Time} + +ACTUS builds on the ISO 8601 date/time format. Hence, dates are generally expressed in the following format: [YYYY]-[MM]-[DD]T[hh]:[mm]:[ss]. + +Time zone information is currently not supported. + +A special case is \textit{midnight}. ISO 8601 recognizes both times 00:00:00 and 24:00:00 each referring to midnight. Yet, while 24:00:00 refers to the end of one day, 00:00:00 refers to the beginning of the following day. In ACTUS the interpretation is the same why the time period (measured in any time unit) between the two points in time will always be zero. + +For brevity, we use the term \textit{time} for a specific date-time variable and in particular abbreviation Tev for the date of a Contract Event. + + +\subsection{Event Sequence} + +Contract Events of different types may occur at the same time, i.e. exactly the same point in time. In this case, the sequence of evaluating their State Transition and Pay Off Functions is decisive for the resulting cash flows and state updates. The Event Sequence given for all events in table \ref{tbl:events} defines the order in which these functions are evaluated for the respective event types. + + +\subsection{Contract Lifetime} + +The lifetime of an ACTUS contract is the time period of its existence from the perspective of the analyzing user. For every point in time during its lifetime, an ACTUS contract can be analyzed in terms of current State Variables and future cash flows.\\ + +The lifetime of a contract starts with its \attr{SD} and ends with $\min(MD, AMD, PR^*, STD, TD,$\verb'MAX_LIFETIME'$)$.\\ + +Note that $PR^*$ refers to the PR event of a maturity contract after which \textbf{Nvl}=0.0 (i.e. at which the remaining outstanding principal is redeemed). Further, \attr{MD}, \attr{AMD}, and PR(\textbf{Nvl}=0.0) in the definition above do only apply for maturity contracts but have to be considered infinity in all other cases. Similarly, \attr{STD} only applies for certain contracts and is considered infinity for all others. Finally, \verb'MAX_LIFETIME' is a parameter that may be used to restrict the considered lifetime in an analysis. In particular, this parameter is used for contracts that do not have a \textit{natural} end to their lifetime such as STK. + + +%%%%%%%%%%%%%%%%%%%% Utility Functions %%%%%%%%%%%%%%%%%%%% + +\section{Utility Functions} + +\subsection{Schedules}\label{sec:schedules} + +A schedule is a function $S$ mapping times $s,T$ with $s0$:] $x$ flows from \attr{LEICP} to \attr{LEIRC} + + \item[$x<0$:] $x$ flows from \attr{LEIRC} to \attr{LEICP} +\end{itemize} + +Table \ref{tbl:cntrl} defines the domain of the Contract Role Sign function, i.e. the range of attribute \attr{CNTRL}, with meaning and Contract Role Sign to which the function maps. + + +%%%%%%%%%%%%%%%%%%%% Table No: 4 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \centering + \begin{tabular}{| p{0.5in}p{1.5in}p{0.2in} |} + \hline + \textbf{Value} & \textbf{Meaning} & $\textbf{R}$ \\ + \hline + RPA & Real position asset & +1 \\ + \hline + RPL & Real position liability & -1 \\ + \hline + CLO & Role of a collateral & +1 \\ + \hline + CNO & Role of a close-out-netting & +1 \\ + \hline + COL & Role of an underlying to a collateral & +1 \\ + \hline + LG & Long position & +1 \\ + \hline + ST & Short position & -1 \\ + \hline + BUYER & Protection buyer & +1 \\ + \hline + SELLER & Protection seller & -1 \\ + \hline + RFL & Receive first leg & +1 \\ + \hline + PFL & Pay first leg & -1 \\ + \hline + RF & Receive fix leg & +1 \\ + \hline + PF & Pay fix leg & -1 \\ + \hline + \end{tabular} + \caption{Contract Role definitions.} + \label{tbl:cntrl} +\end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 4 ends here %%%%%%%%%%%%%%%%%%%% + + +\subsection{Contract Default Convention} + +Performance of a contract indicates whether as per a certain time all parties involved adhere to their obligations arising from the contract. Attribute \attr{CTS} captures a contract's performance as per $t_0$. For any time $t>t_0$ and depending on the behavior of the parties involved the contract can migrate into different contract (performance) statuses from \textit{'performing'} to \textit{'default'}. State variable $\svar{Prf}{t}$ (cf. table \ref{tbl:statevars}) captures these dynamics and the performance as per any time $t>t_0$.\\ + +The Contract Default Convention is a function $D$ that maps the $\svar{Prf}{t}$ state variable into $+1$ indicating that the contract is performing or $0$ which reflext default and, from an analytical perspective, means that future cash flows \textit{cancel out}: + +\[ +\dfl{t} = \begin{cases} 1 & \text{if} \quad \svar{Prf}{t}\neq \text{'D'} \\ + 0 & \text{else} \end{cases} +\] + + + +%%%%%%%%%%%%%%%%%%%% Contract State Variables %%%%%%%%%%%%%%%%%%%% + +\section{Contract State Variables}\label{sec:statevars} + +Driven by Contract Events (see section \ref{sec:events}) certain contractual dimensions, state variables, of financial contracts may change during the lifetime of a financial contract. Thereby, the set of State Variables varies for different CTs. Table \ref{tbl:statevars} represents the set of all covered State Variables throughout the universe of CTs.\\ + +By definition, State Variables are updated through Contract Events only. The value of State Variables always shows the state of the contract \textbf{after} the respective Contract Event. + + + +%%%%%%%%%%%%%%%%%%%% Table No: 5 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \centering + \begin{tabular}{| p{0.8in}p{0.4in}p{1.6in} |} + \hline + \textbf{Name} & \textbf{Abbrv.} & \textbf{Explanation} \\ + \hline + Performance & $\svar{Prf}{t}$ & Contract performance \\ + \hline + Last Event Date & $\svar{Led}{t}$ & The date of the most recent Contract Event \\ + \hline + Nominal Value & $\svar{Nvl}{t}$ & The outstanding nominal value \\ + \hline + Secondary Nominal Value & $\svar{Nv2}{t}$ & The outstanding nominal value of the second leg \\ + \hline + Nominal Rate & $\svar{Nrt}{t}$ & The applicable nominal rate \\ + \hline + Nominal Accrued & $\svar{Nac}{t}$ & The current value of nominal accrued interest at the Nominal Rate \\ + \hline + Interest Calculation Base & $\svar{Icb}{t}$ & The basis at which interest is being accrued if different from $\svar{Nvl}{t}$ \\ + \hline + Notional Scaling Multiplier & $\svar{Nsc}{t}$ & The multiplier being applied to Notional/Principal related + cash-flows \\ + \hline + Interest Scaling Multiplier & $\svar{Isc}{t}$ & The multiplier being applied to Interest related cash-flows \\ + \hline + Next Principal Redemption Payment & $\svar{Npr}{t}$ & The value at which $\svar{Nvl}{t}$ is being repaid. This may be including or excluding of interest depending on the instrument\\ + \hline + \end{tabular} + \caption{State variables} + \label{tbl:statevars} +\end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 5 ends here %%%%%%%%%%%%%%%%%%%% + + +%%%%%%%%%%%%%%%%%%%% Contract Model %%%%%%%%%%%%%%%%%%%% + +\section{Contract Model}\label{sec:model} + +A Contract Model is a structured representation of the various Contract Attributes a CT is based on. The set of Contract Attributes is different for each CT which has to be reflected in the Contract Model (or model as we will refer to henceforth for brevity). The ACTUS DD defines the set of Contract Attributes by CT which provides the content of a Model. On the other hand, ACTUS does not define the model in terms of data structure used on the Software-level but only a Contract Model Interface which any model-implementation has to implement. + + +%%%%%%%%%%%%%%%%%%%% Figure/Image No: 5 starts here %%%%%%%%%%%%%%%%%%%% + +\begin{figure}[H] + \centering + \includegraphics[width=0.45\textwidth]{./media/model-interface.png} + \caption{Contract Model Interface.} + \label{fig:model-interface} +\end{figure} + + +%%%%%%%%%%%%%%%%%%%% Figure/Image No: 5 Ends here %%%%%%%%%%%%%%%%%%%% + + +As shown in figure \ref{fig:model-interface}, the Model interface requires from any implementation to implement method getAs which returns for an attribute’s Long Name it’s value in the specified value type. When requesting from the Model the value of a specific attribute, the value has to be type-casted to the required target-type as indicated in the data dictionary. If this type conversion fails an AttributeConversionException must be thrown. + +Hence, the respective function has the following form \par + +getAs[T](Par1) throw AttributeConversionException \par + +where + +\begin{itemize} + \item T: the respective variable type + + \item Par1: a string representing the Long-Name of the attribute to be returned +\end{itemize} + + + +%%%%%%%%%%%%%%%%%%%% Risk Factor Provider %%%%%%%%%%%%%%%%%%%% + +\section{Risk Factor Model}\label{rfmodel} + +The payoff of financial instruments always depends on the context in which it is evaluated. That is, financial instruments are always embedded in a context of counterparties, markets, and behavioral factors which drive future payoffs. We refer to these as the risk factors to which financial instruments are exposed to because they are the only source of uncertainty in the ACTUS framework. Obviously, evaluating the future payoff of financial instruments requires an assumption about the future state of the risk factors. However, such assumptions are purely subjective which is why they cannot be embedded in the ACTUS standard. Instead, these assumptions must be collected in an external \textit{Risk Factor Model} against which ACTUS contracts may be evaluated. Therefore, ACTUS provides a standardized interface that allows ACTUS contracts to \textit{communicate} with an external model. The general data flow through this interface is represented in figure \ref{fig:rf-interface}. As the figure shows, the Risk Factor Model interface has two main purposes, it forces any implementation of an external market model to provide certain methods and it assures to the ACTUS contract that these methods will be available. Thereby, the Risk Factor Model interface allows an ACTUS contract to demand the state of the risk factors at any future point in time (or the context to be evaluated in). + + +%%%%%%%%%%%%%%%%%%%% Figure/Image No: 7 starts here %%%%%%%%%%%%%%%%%%%% + +\begin{figure}[H] + \centering + \includegraphics[width=0.45\textwidth]{./media/rf-interface.png} + \caption{Risk Factor Model Interface data flow} + \label{fig:rf-interface} +\end{figure} + + +%%%%%%%%%%%%%%%%%%%% Figure/Image No: 7 Ends here %%%%%%%%%%%%%%%%%%%% + + +On the other hand, the design and implementation of a specific Risk Factor Model is left to the user of ACTUS. This gives the user community the necessary flexibility to account for their specific needs in terms of modeling assumptions. Hence, the structure of the Risk Factor Model consisting of a \textit{connecting} element implementing the Risk Factor Model Interface and multiple sub-models implementing the dynamics of various specific risk factors (such as interest rates, stock prices, prepayment rates, etc.) is just illustrative and an actual implementation may look different. + +In this document we will generally refer to the Risk Factor Model function call by\par + +RF(Par1, Par2, Par3, Par4)\par + +where + +\begin{itemize} + \item Par1: the unique ID of the risk factor whose state should be returned + + \item Par2: the future date for which the risk factor’s state should be returned + + \item Par3: the inner states of the contract at the future date + + \item Par4: the contract terms of the contract +\end{itemize} + + +%%%%%%%%%%%%%%%%%%%% Contract Events %%%%%%%%%%%%%%%%%%%% + +\section{Contract Events}\label{sec:events} + +Find an overview of event types below. + + +%%%%%%%%%%%%%%%%%%%% Table No: 6 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \begin{tabular}{| p{0.23in}p{0.7in}p{1.4in}p{0.2in} |} + \hline + \textbf{Type} & \textbf{Name} & \textbf{Explanation} & \textbf{Seq.} \\ + \hline + STD & Settlement Date & Date when payment for derivatives is settled & 1 \\ + \hline + IED & Initial Exchange Date & Date of first principal event, start of accrual calculation & 2 \\ + \hline + IPCI & Interest Capitalization & Periodic interest payment, however capitalized & 3 \\ + \hline + IP & Interest Payment & Periodic interest payment & 4 \\ + \hline + FP & Fee Payment & (Periodic) fee payment & 5 \\ + \hline + PR & Principal Redemption & (Periodic) principal redemption payment & 6 \\ + \hline + PY & Penalty Payment & Payment of a penalty (e.g. due to early repayment of principal outstanding) & 7 \\ + \hline + PP & Principal Prepayment & Early repayment of principal outstanding & 8 \\ + \hline + CD & Credit Default & Indicates whether a contract is in its default state or not & 9 \\ + \hline + RRY & Next Rate Reset & Rate reset event where new rate is already known & 10 \\ + \hline + RR & Rate Reset & Interest rate is reset periodically & 11 \\ + \hline + DV & Dividend Payment & Periodic dividend payment & 12 \\ + \hline + PRD & Purchase Date & Purchase date of a contract bought in the secondary market & 13 \\ + \hline + MR & Margin Call Date & Margin call event & 14 \\ + \hline + TD & Termination Date & Sell date of a contract sold in the secondary market & 15 \\ + \hline + SC & Scaling Index Revision & & 16 \\ + \hline + IPCB & Interest Payment Calculation Base & Updates the calculation base for IP accruing & 17 \\ + \hline + AD & Analysis Event & Retrieves current contract states without alter these & 18 \\ + \hline + \end{tabular} + \caption{Contract Events Definitions.} + \label{tbl:events} +\end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 6 ends here %%%%%%%%%%%%%%%%%%%% + + + + +%%%%%%%%%%%%%%%%%%%% End first part here %%%%%%%%%%%%%%%%%%%% + +\end{multicols} +\newpage + + + +%%%%%%%%%%%%%%%%%%%% Start Contract Types here %%%%%%%%%%%%%%%%%%%% + +\section{Contract Types} + + +\subsection{PAM: Principal At Maturity} + + +%%%%%%%%%%%%%%%%%%%% Table No: 7 starts here %%%%%%%%%%%%%%%%%%%% + +\begin{schedule}{PAM} + AD & $\vec{t}^{AD} = \left(t_0,t_1,...,t_n\right)$ & With $t_i,i=1,2,...$ a custom input \\ + \hline + IED & $t^{IED} = \attr{IED}$ & \\ + \hline + PR & $t^{PR} = \attr{MD}$ & \\ + \hline + PP & $\vec{t}^{PP} = \begin{cases} \undef & \text{if} \quad \attr{PPEF}=\text{'N'} \\ + (\vec{u},\vec{v}) & \text{else} \end{cases}$ + \par where \par + {$\begin{aligned} \vec{u} &= \sdl{s}{\attr{OPCL}}{T^{MD}} \\ + \vec{v} &= RF(\attr{PPMO}) \end{aligned}$} + & with\par $s = \begin{cases} \undef & \text{if} \quad \attr{OPANX}=\undef \land \attr{OPCL}=\undef\\ + \attr{IED}+\attr{OPCL} & \text{else if} \quad \attr{OPANX} = \undef \\ + \attr{OPANX} & \text{else} \end{cases}$ \\ + \hline + PY & $\vec{t}^{PY} = \begin{cases} \undef & \text{if} \quad \attr{PYTP}=\text{'O'} \\ + \vec{t}^{PP} & \text{else} \end{cases}$ & \\ + \hline + FP & $\vec{t}^{FP} = \begin{cases} \undef & \text{if} \quad \attr{FER}=\undef \lor \attr{FER}=0 \\ + \sdl{s}{\attr{FPCL}}{T^{MD}} & \text{else} \end{cases}$ + & with\par $s = \begin{cases} \undef & \text{if} \quad \attr{FPANX}=\undef \land \attr{FPCL}=\undef\\ + \attr{IED}+\attr{FPCL} & \text{else if} \quad \attr{FPANX} = \undef \\ + \attr{FPANX} & \text{else} \end{cases}$ \\ + \hline + PRD & $t^{PRD}= \attr{PRD}$ & \\ + \hline + TD & $t^{TD}= \attr{TD}$ & \\ + \hline + IP & $\vec{t}^{IP} = \begin{cases} \undef & \text{if} \quad \attr{IPNR}=\text{'O'} \\ + \sdl{s}{\attr{IPCL}}{T} & \text{else} \end{cases}$ + & with\par {$\begin{aligned} s &= \begin{cases} \undef & \text{if} \quad \attr{IPANX}=\undef \land \attr{IPCL}=\undef\\ + \attr{IED}+\attr{IPCL} & \text{else if} \quad \attr{IPANX} = \undef \\ + \attr{IPANX} & \text{else} \end{cases} \\ + T &= \begin{cases} T^{MD} & \text{if} \quad \attr{IPCED}=\undef \\ + \attr{IPCED} & \text{else} \end{cases} \end{aligned}$} \\ + \hline + IPCI & $\vec{t}^{IPCI} = \begin{cases} \undef & \text{if} \quad \attr{IPCED}=\undef \\ + \sdl{s}{\attr{IPCL}}{\attr{IPCED}} & \text{else} \end{cases}$ + & with\par $s = \begin{cases} \undef & \text{if} \quad \attr{IPANX}=\undef \land \attr{IPCL}=\undef\\ + \attr{IED}+\attr{IPCL} & \text{else if} \quad \attr{IPANX} = \undef \\ + \attr{IPANX} & \text{else} \end{cases}$ \\ + \hline + RR & $\vec{t}^{RR} = \begin{cases} \undef & \text{if} \quad \attr{RRANX}=\undef \land \attr{RRCL}=\undef \\ + \vec{t} \setminus t^{RRY} & \text{else if} \attr{RRNXT} \neq \undef \\ + \vec{t} & \text{else} \end{cases}$ \par + where $\vec{t}=\sdl{s}{\attr{RRCL}}{T^{MD}}$ + & with\par {$\begin{aligned} s &= \begin{cases} \attr{IED}+\attr{RRCL} & \text{if} \quad \attr{RRANX} = \undef \\ + \attr{RRANX} & \text{else} \end{cases} \\ + t^{RRY} &= \inf{t}, t \in \vec{t}, t>\attr{SD} \end{aligned}$} \\ + \hline + RRY & $t^{RRY} = \begin{cases} \undef & \text{if} \quad \attr{RRANX}=\undef \land \attr{RRCL}=\undef \\ + \inf{t}, t \in \vec{t}, t>\attr{SD} & \text{else} \end{cases}$ \par + where $\vec{t}=\sdl{s}{\attr{RRCL}}{T^{MD}}$ + & with\par $s = \begin{cases} \attr{IED}+\attr{RRCL} & \text{if} \quad \attr{RRANX} = \undef \\ + \attr{RRANX} & \text{else} \end{cases}$ \\ + \hline + SC & $\vec{t}^{SC} = \begin{cases} \undef & \text{if} \quad \attr{SCEF}=\text{'000'} \\ + \sdl{s}{\attr{SCCL}}{T^{MD}} & \text{else} \end{cases}$ + & with\par $s = \begin{cases} \undef & \text{if} \quad \attr{SCANX}=\undef \land \attr{SCCL}=\undef\\ + \attr{IED}+\attr{SCCL} & \text{else if} \quad \attr{SCANX} = \undef \\ + \attr{SCANX} & \text{else} \end{cases}$ \\ + \hline + CD & $t^{CD} = RF(LEICP)$ & \\ + \hline +\end{schedule} + + +%%%%%%%%%%%%%%%%%%%% Table No: 7 ends here %%%%%%%%%%%%%%%%%%%% + + + + +%%%%%%%%%%%%%%%%%%%% Table No: 8 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{states}{PAM} + $\svar{Tmd}{t_0} = \attr{MD}$ & \\ + \hline + $\svar{Nvl}{t_0} = \begin{cases} 0.0 & \text{if} \quad \attr{IED} > t_0 \\ + \sgn\times\attr{NT} & \text{else} \end{cases}$ & \\ + \hline + $\svar{Nrt}{t_0} = \begin{cases} 0.0 & \text{if} \quad \attr{IED} > t_0 \\ + \attr{IPNR} & \text{else} \end{cases}$ & \\ + \hline + $\svar{Nac}{t_0} = \begin{cases} 0.0 & \text{if} \quad \attr{IPNR}=\undef \\ + \attr{IPAC} & \text{else if} \quad \attr{IPAC} \neq \undef \\ + \yfr{t^-}{t_0}\times\svar{Nvl}{t_0}\times\svar{Nrt}{t_0} & \text{else} \end{cases}$ & + with $t^- = \sup{t}, t \in t^{IP}, tt_0 \end{aligned}$} \\ + \hline + $\svar{Nsc}{t_0} = \begin{cases} \attr{SCIXSD} & \text{if} \quad \attr{SCEF}=\text{'[x]N[x]'} \\ + 1.0 & \text{else} \end{cases}$ & \\ + \hline + $\svar{Isc}{t_0} = \begin{cases} \attr{SCIXSD} & \text{if} \quad \attr{SCEF}=\text{'I[x][x]'} \\ + 1.0 & \text{else} \end{cases}$ & \\ + \hline + $\svar{Prf}{t_0} = \attr{CTS}$ & \\ + \hline + $\svar{Led}{t_0} = t_0$ & \\ + \hline +\end{states} + + +%%%%%%%%%%%%%%%%%%%% Table No: 8 ends here %%%%%%%%%%%%%%%%%%%% + + + +%%%%%%%%%%%%%%%%%%%% Table No: 9 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{functions}{PAM} + AD & 0.0 & {$\begin{aligned} + \svar{Nac}{t^+} &= \svar{Nac}{t^-} + \yfr{\svar{Led}{t^-1}}{Tev}\svar{Nrt}{t^-}\svar{Nvl}{t^-}\\ + \svar{Led}{t^+} &= Tev + \end{aligned}$} \\ + \hline + IED & $\dfl{t^-}\sgn(-1)(\attr{NT}+\attr{PDIED})$ + & {$\begin{aligned} + \svar{Nvl}{t^+} &=\sgn\attr{NT} \\ + \svar{Nrt}{t^+} &= \begin{cases} 0.0 & \text{if} \quad \attr{IPNR}=\undef \\ + \attr{IPNR} & \text{else} \end{cases} \\ + \svar{Nac}{t^+} &= \begin{cases} \attr{IPAC} & \text{if} \quad \attr{IPAC} \neq \undef \\ + y\svar{Nvl}{t^+}\svar{Nrt}{t^+} & \text{if} \quad \attr{IPANX} \neq \undef \land \attr{IPANX}t_0\\ + \attr{IED}+\attr{PRCL} & \text{else if}\quad \attr{PRANX} = \undef \land \attr{IED}+\attr{PRCL}>t_0 \\ + t^- & \text{else} \end{cases}$\par + and where $t^- = \sup{t}, t \in t^{PR}, t= SD \par } & +\multicolumn{1}{|p{2.49in}|}{} \\ +\hhline{---} +%row no:5 +\multicolumn{1}{|p{0.34in}}{PP} & +\multicolumn{1}{|p{3.05in}}{Same as PAM} & +\multicolumn{1}{|p{2.49in}|}{Same as PAM} \\ +\hhline{---} +%row no:6 +\multicolumn{1}{|p{0.34in}}{PY} & +\multicolumn{1}{|p{3.05in}}{Same as PAM} & +\multicolumn{1}{|p{2.49in}|}{Same as PAM} \\ +\hhline{---} +%row no:7 +\multicolumn{1}{|p{0.34in}}{FP} & +\multicolumn{1}{|p{3.05in}}{Same as PAM} & +\multicolumn{1}{|p{2.49in}|}{Same as PAM} \\ +\hhline{---} +%row no:8 +\multicolumn{1}{|p{0.34in}}{PRD} & +\multicolumn{1}{|p{3.05in}}{same as PAM} & +\multicolumn{1}{|p{2.49in}|}{same as PAM} \\ +\hhline{---} +%row no:9 +\multicolumn{1}{|p{0.34in}}{TD} & +\multicolumn{1}{|p{3.05in}}{same as PAM} & +\multicolumn{1}{|p{2.49in}|}{same as PAM} \\ +\hhline{---} +%row no:10 +\multicolumn{1}{|p{0.34in}}{IP} & +\multicolumn{1}{|p{3.05in}}{if IPANX != NULL Then Tstrt = IPANX \par Else Tstrt = IED+IPCL \par Sdl(Tstrt, IPCL, IPCED, EOMC, BDC) >= SD \par Sdl(Tstrt, IPCL, PRANX-1PRCL, EOMC, BDC) >= SD \par Sdl(PRANX, PRCL, Tmd, EOMC, BDC) >= SD \par } & +\multicolumn{1}{|p{2.49in}|}{IPCED != NULL And Tstrt< IPCED \par IPCED != NULL And Tstrt < PRANX-1PRCL \par } \\ +\hhline{---} +%row no:11 +\multicolumn{1}{|p{0.34in}}{IPCI} & +\multicolumn{1}{|p{3.05in}}{same as PAM} & +\multicolumn{1}{|p{2.49in}|}{IPCED <= PRANX-1PRCL} \\ +\hhline{---} +%row no:12 +\multicolumn{1}{|p{0.34in}}{RR} & +\multicolumn{1}{|p{3.05in}}{same as PAM} & +\multicolumn{1}{|p{2.49in}|}{Same as PAM} \\ +\hhline{---} +%row no:13 +\multicolumn{1}{|p{0.34in}}{RRY} & +\multicolumn{1}{|p{3.05in}}{same as PAM} & +\multicolumn{1}{|p{2.49in}|}{same as PAM} \\ +\hhline{---} +%row no:14 +\multicolumn{1}{|p{0.34in}}{SC} & +\multicolumn{1}{|p{3.05in}}{same as PAM} & +\multicolumn{1}{|p{2.49in}|}{same as PAM} \\ +\hhline{---} +%row no:15 +\multicolumn{1}{|p{0.34in}}{CD} & +\multicolumn{1}{|p{3.05in}}{same as PAM} & +\multicolumn{1}{|p{2.49in}|}{same as PAM} \\ +\hhline{---} +%row no:16 +\multicolumn{1}{|p{0.34in}}{IPCB} & +\multicolumn{1}{|p{3.05in}}{no event \par if IPCBANX != NULL Then Tstrt = IPCBANX \par Else Tstrt = IED+IPCBCL \par Sdl(Tstrt, IPCBCL, Tmd, EOMC, BDC) >= SD \par } & +\multicolumn{1}{|p{2.49in}|}{if IPCB == NULL OR IPCB==NT OR IPCB==NTIED \par Else (i.e. if IPCB == NTL) \par } \\ +\hhline{---} + +\end{longtable}} + +%%%%%%%%%%%%%%%%%%%% Table No: 10 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsubsection{State Variables Initialization} + + +%%%%%%%%%%%%%%%%%%%% Table No: 11 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \centering +\begin{tabular}{p{0.48in}p{2.79in}p{2.63in}} +\hline +%row no:1 +\multicolumn{1}{|p{0.48in}}{State Variable} & +\multicolumn{1}{|p{2.79in}}{Contract Attribute} & +\multicolumn{1}{|p{2.63in}|}{Comments} \\ +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.48in}}{\textbf{Nvl}} & +\multicolumn{1}{|p{2.79in}}{same as PAM} & +\multicolumn{1}{|p{2.63in}|}{same as PAM} \\ +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.48in}}{\textbf{Nrt}} & +\multicolumn{1}{|p{2.79in}}{same as PAM} & +\multicolumn{1}{|p{2.63in}|}{same as PAM} \\ +\hhline{---} +%row no:4 +\multicolumn{1}{|p{0.48in}}{\textbf{Nac}} & +\multicolumn{1}{|p{2.79in}}{same as PAM} & +\multicolumn{1}{|p{2.63in}|}{same as PAM} \\ +\hhline{---} +%row no:5 +\multicolumn{1}{|p{0.48in}}{\textbf{Fac}} & +\multicolumn{1}{|p{2.79in}}{Same as PAM} & +\multicolumn{1}{|p{2.63in}|}{Same as PAM} \\ +\hhline{---} +%row no:6 +\multicolumn{1}{|p{0.48in}}{\textbf{Led}} & +\multicolumn{1}{|p{2.79in}}{same as PAM} & +\multicolumn{1}{|p{2.63in}|}{same as PAM} \\ +\hhline{---} +%row no:7 +\multicolumn{1}{|p{0.48in}}{\textbf{Nsc}} & +\multicolumn{1}{|p{2.79in}}{same as PAM} & +\multicolumn{1}{|p{2.63in}|}{same as PAM} \\ +\hhline{---} +%row no:8 +\multicolumn{1}{|p{0.48in}}{\textbf{Isc}} & +\multicolumn{1}{|p{2.79in}}{Same as PAM} & +\multicolumn{1}{|p{2.63in}|}{Same as PAM} \\ +\hhline{---} +%row no:9 +\multicolumn{1}{|p{0.48in}}{\textbf{Pod}} & +\multicolumn{1}{|p{2.79in}}{Same as PAM} & +\multicolumn{1}{|p{2.63in}|}{Same as PAM} \\ +\hhline{---} +%row no:10 +\multicolumn{1}{|p{0.48in}}{\textbf{Npr}} & +\multicolumn{1}{|p{2.79in}}{Sign(CNTRL) $\ast$ PRNXT \par Sign(CNTRL) $\ast$ NT / ceil(Yfr(PRANX,Tmd)/Yfr(PRANX, PRANX+1PRCL)) \par Sign(CNTRL) $\ast$ NT / ceil(Yfr(IED+1PRCL,Tmd)/Yfr(IED+1PRCL, IED+2PRCL)) \par Sign(CNTRL) $\ast$ NT / ceil(Yfr(Lpr,Tmd)/Yfr(Lpr, Lpr+1PRCL)) \par } & +\multicolumn{1}{|p{2.63in}|}{if PRNXT != NULL \par Else \par if PRANX != NULL And PRANX > SD \par Else if PRANX == NULL And IED + 1PRCL > SD \par Else \par } \\ +\hhline{---} +%row no:11 +\multicolumn{1}{|p{0.48in}}{\textbf{Icb}} & +\multicolumn{1}{|p{2.79in}}{If SD < IED Then 0.0 \par Else \par if IPCB==NT then Sgn(CNTRL)$\ast$ NT \par Else Sgn(CNTRL)$\ast$ IPCBA \par } & +\multicolumn{1}{|p{2.63in}|}{contains either the initial NT (IPCB=NTIED) or the state of the interest calculation base since its last change (IPCB=NTL) \par } \\ +\hhline{---} + +\end{tabular} + \end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 11 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsubsection{Contract Events, State Transition Functions and Pay Off Functions} + + +%%%%%%%%%%%%%%%%%%%% Table No: 12 starts here %%%%%%%%%%%%%%%%%%%% + + +{ +\setlength\extrarowheight{3pt} +\begin{longtable}{p{0.48in}p{2.8in}p{-0.45in}p{0.26in}p{0.12in}p{0.37in}p{0.06in}p{0.09in}} + +\endfirsthead +\multicolumn{8}{c}{\textit{continued from previous page}}\hline +\endhead\hline +\multicolumn{8}{r}{\textit{continued on next page}} \\ +\endfoot +\hline +\endlastfoot\hline +%row no:1 +\multicolumn{1}{|p{0.48in}}{\textbf{Event Type}} & +\multicolumn{1}{|p{2.8in}}{\textbf{Pay Off Function}} & +\multicolumn{1}{|p{-0.45in}}{\textbf{State Transition Function}} & + +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.48in}}{AD} & +\multicolumn{1}{|p{2.8in}}{Same as PAM} & +\multicolumn{1}{|p{-0.45in}}{Same as PAM} & + +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.48in}}{IED} & +\multicolumn{1}{|p{2.8in}}{same as PAM} & +\multicolumn{1}{|p{-0.45in}}{\textbf{Nvl }= Sgn(CNTRL) $\ast$ NT \par \textbf{Nac }= 0.0 \par \textbf{Fac }= 0.0 \par \textbf{Nrt }= IPNR \par \textbf{Led }= Tev \par If IPCB==NT then \par \textbf{Icb }= Sgn(CNTRL)$\ast$ NT \par Else \par \textbf{Icb }= Sgn(CNTRL)$\ast$ IPCBA} & + +\hhline{---} +%row no:4 +\multicolumn{1}{|p{0.48in}}{PR} & +\multicolumn{1}{|p{2.8in}}{= (1-\textbf{Pod}) $\ast$ \textbf{Nsc $\ast$ } \textbf{Npr}} & +\multicolumn{1}{|p{-0.45in}}{\textbf{Nvl }= \textbf{Nvl }- \textbf{Npr} \par If IPCB == NT then \textbf{Icb }= \textbf{Nvl} \par \textbf{Nac }= \textbf{Nac }+ Yfr(\textbf{Led},Tev) $\ast$ \textbf{Nrt }$\ast$ \textbf{Icb} \par \textbf{Fac }= \textbf{Fac} + Yfr(\textbf{Led},Tev) $\ast$ FER\textbf{ }$\ast$ \textbf{Nvl} \par \textbf{Led }= Tev } & + +\hhline{---} +%row no:5 +\multicolumn{1}{|p{0.48in}}{PP} & +\multicolumn{1}{|p{2.8in}}{Same as PAM} & +\multicolumn{1}{|p{-0.45in}}{\textbf{Nac }= \textbf{Nac} + Yfr(\textbf{Led},Tev) $\ast$ \textbf{Nrt }$\ast$ \textbf{Icb} \par \textbf{Fac }= \textbf{Fac} + Yfr(\textbf{Led},Tev) $\ast$ FER\textbf{ }$\ast$ \textbf{Nvl} \par \textbf{Nvl }= ( 1 - RF(OPMO, Tev) ) $\ast$ \textbf{Nvl} \par If IPCB == NT then \textbf{Icb }= \textbf{Nvl} \par \textbf{Led }= Tev} & + +\hhline{---} +%row no:6 +\multicolumn{1}{|p{0.48in}}{PY} & +\multicolumn{1}{|p{2.8in}}{Same as PAM} & +\multicolumn{1}{|p{-0.45in}}{\textbf{Nac }= \textbf{Nac} + Yfr(\textbf{Led},Tev) $\ast$ \textbf{Nrt }$\ast$ \textbf{Icb} \par \textbf{Fac }= \textbf{Fac} + Yfr(\textbf{Led},Tev) $\ast$ FER\textbf{ }$\ast$ \textbf{Nvl} \par \textbf{Led }= Tev} & + +\hhline{---} +%row no:7 +\multicolumn{1}{|p{0.48in}}{FP} & +\multicolumn{1}{|p{2.8in}}{Same as PAM} & +\multicolumn{1}{|p{-0.45in}}{\textbf{Nac }= \textbf{Nac} + Yfr(\textbf{Led},Tev) $\ast$ \textbf{Nrt }$\ast$ \textbf{Icb} \par \textbf{Fac }= 0.0 \par \textbf{Led }= Tev} & + +\hhline{---} +%row no:8 +\multicolumn{1}{|p{0.48in}}{PRD} & +\multicolumn{1}{|p{2.8in}}{= (1-\textbf{Pod}) $\ast$ Sgn(CNTRL) $\ast$ (-1) $\ast$ (PPRD +\textbf{Nac + }Yfr(\textbf{Led},Tev) $\ast$ \textbf{Nrt }$\ast$ \textbf{Icb})} & +\multicolumn{1}{|p{-0.45in}}{\textbf{Nac }= \textbf{Nac }+ Yfr(\textbf{Led},Tev) $\ast$ \textbf{Nrt }$\ast$ \textbf{Icb} \par \textbf{Fac }= \textbf{Fac} + Yfr(\textbf{Led},Tev) $\ast$ FER\textbf{ }$\ast$ \textbf{Nvl} \par \textbf{Led }= Tev} & + +\hhline{---} +%row no:9 +\multicolumn{1}{|p{0.48in}}{TD } & +\multicolumn{1}{|p{2.8in}}{= (1-\textbf{Pod}) $\ast$ ( Sgn(CNTRL) $\ast$ (PTD +\textbf{Nac + }Yfr(\textbf{Led},Tev) $\ast$ \textbf{Nrt }$\ast$ \textbf{Icb}) )} & +\multicolumn{1}{|p{-0.45in}}{same as PAM} & + +\hhline{---} +%row no:10 +\multicolumn{1}{|p{0.48in}}{IP} & +\multicolumn{1}{|p{2.8in}}{= (1-\textbf{Pod}) $\ast$ \textbf{Isc} $\ast$ ( \textbf{Nac + }Yfr(\textbf{Led},Tev) $\ast$ \textbf{Nrt }$\ast$ \textbf{Icb })} & +\multicolumn{1}{|p{-0.45in}}{same as PAM} & + +\hhline{---} +%row no:11 +\multicolumn{1}{|p{0.48in}}{IPCI} & +\multicolumn{1}{|p{2.8in}}{same as PAM} & +\multicolumn{1}{|p{-0.45in}}{\textbf{Nvl }= \textbf{Nvl }+ \textbf{Nac }+ Yfr(\textbf{Led},Tev) $\ast$ \textbf{Nrt }$\ast$ \textbf{Icb} \par If IPCB == NT then \textbf{Icb }= \textbf{Nvl} \par \textbf{Nac }= 0.0 \par \textbf{Fac }= \textbf{Fac} + Yfr(\textbf{Led},Tev) $\ast$ FER\textbf{ }$\ast$ \textbf{Nvl} \par \textbf{Led }= Tev} & + +\hhline{---} +%row no:12 +\multicolumn{1}{|p{0.48in}}{RR} & +\multicolumn{1}{|p{2.8in}}{same as PAM} & +\multicolumn{1}{|p{-0.45in}}{\textbf{Nac }= \textbf{Nac }+ Yfr(\textbf{Led},Tev) $\ast$ \textbf{Nrt }$\ast$ \textbf{Icb} \par \textbf{Fac }= \textbf{Fac} + Yfr(\textbf{Led},Tev) $\ast$ FER\textbf{ }$\ast$ \textbf{Nvl} \par rate = RF(RRMO, Tev)$\ast$ RRMT+RRSP \par deltaRate= min(max(rate-\textbf{Nrt},RRPF),RRPC) \par \textbf{Nrt }= min(max(\textbf{Nrt}+deltaRate,RRLF),RRLC) \par \textbf{Led }= Tev} & + +\hhline{---} +%row no:13 +\multicolumn{1}{|p{0.48in}}{RRY} & +\multicolumn{1}{|p{2.8in}}{same as PAM} & +\multicolumn{1}{|p{-0.45in}}{\textbf{Nac }= \textbf{Nac }+ Yfr(\textbf{Led},Tev) $\ast$ \textbf{Nrt }$\ast$ \textbf{Icb} \par \textbf{Fac }= \textbf{Fac} + Yfr(\textbf{Led},Tev) $\ast$ FER\textbf{ }$\ast$ \textbf{Nvl} \par \textbf{Nrt }= RRNXT \par \textbf{Led }= Tev} & + +\hhline{---} +%row no:14 +\multicolumn{1}{|p{0.48in}}{SC} & +\multicolumn{1}{|p{2.8in}}{same as PAM} & +\multicolumn{1}{|p{-0.45in}}{\textbf{Nac }= \textbf{Nac }+ Yfr(\textbf{Led},Tev) $\ast$ \textbf{Nrt }$\ast$ \textbf{Icb} \par \textbf{Fac }= \textbf{Fac} + Yfr(\textbf{Led},Tev) $\ast$ FER\textbf{ }$\ast$ \textbf{Nvl} \par if SCEF == [x]N[x] \par \textbf{Nsc }= (RF(SCMO, Tev) - SCIED) / SCIED \par if SCEF == I[x][x] \par \textbf{Isc }= (RF(SCMO, Tev) - SCIED) / SCIED \par \textbf{Led }= Tev} & + +\hhline{---} +%row no:15 +\multicolumn{1}{|p{0.48in}}{CD} & +\multicolumn{1}{|p{2.8in}}{same as PAM} & +\multicolumn{1}{|p{-0.45in}}{\textbf{Pod }= RF(LEICP, Tev) \par \textbf{Nac} = \textbf{Nac }+ Yfr(\textbf{Led},Tev) $\ast$ \textbf{Nrt }$\ast$ \textbf{Icb} \par \textbf{Fac }= \textbf{Fac} + Yfr(\textbf{Led},Tev) $\ast$ FER\textbf{ }$\ast$ \textbf{Nvl} \par \textbf{Led }= Tev} & + +\hhline{---} +%row no:16 +\multicolumn{1}{|p{0.48in}}{IPCB} & +\multicolumn{1}{|p{2.8in}}{= 0.0} & +\multicolumn{1}{|p{-0.45in}}{\textbf{Icb }= \textbf{Nvl} \par \textbf{Nac }= \textbf{Nac }+ Yfr(\textbf{Led},Tev) $\ast$ \textbf{Nrt }$\ast$ \textbf{Icb} \par \textbf{Fac }= \textbf{Fac} + Yfr(\textbf{Led},Tev) $\ast$ FER\textbf{ }$\ast$ \textbf{Nvl} \par \textbf{Led }= Tev} & + +\hhline{---} + +\end{longtable}} + +%%%%%%%%%%%%%%%%%%%% Table No: 12 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsection{Negative Amortizer (NAM)} +\subsubsection{Maturity Determination} +If MD != NULL Then Tmd=MD + +Else if RRCL == NULL And IPCB == NT Then Tmd=NT/(\textbf{Npr}-\textbf{Nvl}$\ast$ \textbf{Nrt}$\ast$ Yfr(PRANX,PRANX+PRCL)\par + +Else Tmd = MAX\_Lifetime + +\subsubsection{Contract Events Generation} + + +%%%%%%%%%%%%%%%%%%%% Table No: 13 starts here %%%%%%%%%%%%%%%%%%%% + + +{ +\setlength\extrarowheight{3pt} +\begin{longtable}{p{0.34in}p{3.05in}p{2.49in}} + +\endfirsthead +\multicolumn{3}{c}{\textit{continued from previous page}}\hline +\endhead\hline +\multicolumn{3}{r}{\textit{continued on next page}} \\ +\endfoot +\hline +\endlastfoot\hline +%row no:1 +\multicolumn{1}{|p{0.34in}}{Event Type} & +\multicolumn{1}{|p{3.05in}}{Schedule} & +\multicolumn{1}{|p{2.49in}|}{Conditions} \\ +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.34in}}{AD} & +\multicolumn{1}{|p{3.05in}}{Same as PAM} & +\multicolumn{1}{|p{2.49in}|}{Same as PAM} \\ +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.34in}}{IED} & +\multicolumn{1}{|p{3.05in}}{same as PAM} & +\multicolumn{1}{|p{2.49in}|}{same as PAM} \\ +\hhline{---} +%row no:4 +\multicolumn{1}{|p{0.34in}}{PR} & +\multicolumn{1}{|p{3.05in}}{Same as LAM} & +\multicolumn{1}{|p{2.49in}|}{Same as LAM} \\ +\hhline{---} +%row no:5 +\multicolumn{1}{|p{0.34in}}{PP} & +\multicolumn{1}{|p{3.05in}}{Same as PAM} & +\multicolumn{1}{|p{2.49in}|}{Same as PAM} \\ +\hhline{---} +%row no:6 +\multicolumn{1}{|p{0.34in}}{PY} & +\multicolumn{1}{|p{3.05in}}{Same as PAM} & +\multicolumn{1}{|p{2.49in}|}{Same as PAM} \\ +\hhline{---} +%row no:7 +\multicolumn{1}{|p{0.34in}}{FP} & +\multicolumn{1}{|p{3.05in}}{Same as PAM} & +\multicolumn{1}{|p{2.49in}|}{Same as PAM} \\ +\hhline{---} +%row no:8 +\multicolumn{1}{|p{0.34in}}{PRD} & +\multicolumn{1}{|p{3.05in}}{same as PAM} & +\multicolumn{1}{|p{2.49in}|}{same as PAM} \\ +\hhline{---} +%row no:9 +\multicolumn{1}{|p{0.34in}}{TD} & +\multicolumn{1}{|p{3.05in}}{same as PAM} & +\multicolumn{1}{|p{2.49in}|}{same as PAM} \\ +\hhline{---} +%row no:10 +\multicolumn{1}{|p{0.34in}}{IP} & +\multicolumn{1}{|p{3.05in}}{Same as LAM} & +\multicolumn{1}{|p{2.49in}|}{Same as LAM \par } \\ +\hhline{---} +%row no:11 +\multicolumn{1}{|p{0.34in}}{IPCI} & +\multicolumn{1}{|p{3.05in}}{same as PAM} & +\multicolumn{1}{|p{2.49in}|}{Same as LAM} \\ +\hhline{---} +%row no:12 +\multicolumn{1}{|p{0.34in}}{RR} & +\multicolumn{1}{|p{3.05in}}{same as PAM} & +\multicolumn{1}{|p{2.49in}|}{Same as PAM} \\ +\hhline{---} +%row no:13 +\multicolumn{1}{|p{0.34in}}{RRY} & +\multicolumn{1}{|p{3.05in}}{same as PAM} & +\multicolumn{1}{|p{2.49in}|}{same as PAM} \\ +\hhline{---} +%row no:14 +\multicolumn{1}{|p{0.34in}}{SC} & +\multicolumn{1}{|p{3.05in}}{same as PAM} & +\multicolumn{1}{|p{2.49in}|}{same as PAM} \\ +\hhline{---} +%row no:15 +\multicolumn{1}{|p{0.34in}}{CD} & +\multicolumn{1}{|p{3.05in}}{same as PAM} & +\multicolumn{1}{|p{2.49in}|}{same as PAM} \\ +\hhline{---} +%row no:16 +\multicolumn{1}{|p{0.34in}}{IPCB} & +\multicolumn{1}{|p{3.05in}}{Same as LAM} & +\multicolumn{1}{|p{2.49in}|}{Same as LAM \par } \\ +\hhline{---} + +\end{longtable}} + +%%%%%%%%%%%%%%%%%%%% Table No: 13 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsubsection{State Variables Initialization} + + +%%%%%%%%%%%%%%%%%%%% Table No: 14 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \centering +\begin{tabular}{p{0.48in}p{2.79in}p{2.63in}} +\hline +%row no:1 +\multicolumn{1}{|p{0.48in}}{State Variable} & +\multicolumn{1}{|p{2.79in}}{Contract Attribute} & +\multicolumn{1}{|p{2.63in}|}{Comments} \\ +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.48in}}{\textbf{Nvl}} & +\multicolumn{1}{|p{2.79in}}{same as PAM} & +\multicolumn{1}{|p{2.63in}|}{same as PAM} \\ +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.48in}}{\textbf{Nrt}} & +\multicolumn{1}{|p{2.79in}}{same as PAM} & +\multicolumn{1}{|p{2.63in}|}{same as PAM} \\ +\hhline{---} +%row no:4 +\multicolumn{1}{|p{0.48in}}{\textbf{Nac}} & +\multicolumn{1}{|p{2.79in}}{same as PAM} & +\multicolumn{1}{|p{2.63in}|}{same as PAM} \\ +\hhline{---} +%row no:5 +\multicolumn{1}{|p{0.48in}}{\textbf{Fac}} & +\multicolumn{1}{|p{2.79in}}{Same as PAM} & +\multicolumn{1}{|p{2.63in}|}{Same as PAM} \\ +\hhline{---} +%row no:6 +\multicolumn{1}{|p{0.48in}}{\textbf{Led}} & +\multicolumn{1}{|p{2.79in}}{same as PAM} & +\multicolumn{1}{|p{2.63in}|}{same as PAM} \\ +\hhline{---} +%row no:7 +\multicolumn{1}{|p{0.48in}}{\textbf{Nsc}} & +\multicolumn{1}{|p{2.79in}}{same as PAM} & +\multicolumn{1}{|p{2.63in}|}{same as PAM} \\ +\hhline{---} +%row no:8 +\multicolumn{1}{|p{0.48in}}{\textbf{Isc}} & +\multicolumn{1}{|p{2.79in}}{Same as PAM} & +\multicolumn{1}{|p{2.63in}|}{Same as PAM} \\ +\hhline{---} +%row no:9 +\multicolumn{1}{|p{0.48in}}{\textbf{Pod}} & +\multicolumn{1}{|p{2.79in}}{Same as PAM} & +\multicolumn{1}{|p{2.63in}|}{Same as PAM} \\ +\hhline{---} +%row no:10 +\multicolumn{1}{|p{0.48in}}{\textbf{Npr}} & +\multicolumn{1}{|p{2.79in}}{Sign(CNTRL) $\ast$ PRNXT} & +\multicolumn{1}{|p{2.63in}|}{PRNXT is an NN attribute for NAM} \\ +\hhline{---} +%row no:11 +\multicolumn{1}{|p{0.48in}}{\textbf{Icb}} & +\multicolumn{1}{|p{2.79in}}{Same as LAM} & +\multicolumn{1}{|p{2.63in}|}{Same as LAM} \\ +\hhline{---} + +\end{tabular} + \end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 14 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsubsection{Contract Events, State Transition Functions and Pay Off Functions} + + +%%%%%%%%%%%%%%%%%%%% Table No: 15 starts here %%%%%%%%%%%%%%%%%%%% + + +{ +\setlength\extrarowheight{3pt} +\begin{longtable}{p{0.4in}p{2.8in}p{-0.59in}p{0.15in}p{0.04in}p{0.23in}p{-0.01in}p{0.02in}} + +\endfirsthead +\multicolumn{8}{c}{\textit{continued from previous page}}\hline +\endhead\hline +\multicolumn{8}{r}{\textit{continued on next page}} \\ +\endfoot +\hline +\endlastfoot\hline +%row no:1 +\multicolumn{1}{|p{0.4in}}{\textbf{Event Type}} & +\multicolumn{1}{|p{2.8in}}{\textbf{Pay Off Function}} & +\multicolumn{1}{|p{-0.59in}}{\textbf{State Transition Function}} & + +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.4in}}{AD} & +\multicolumn{1}{|p{2.8in}}{Same as PAM} & +\multicolumn{1}{|p{-0.59in}}{Same as PAM} & + +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.4in}}{IED} & +\multicolumn{1}{|p{2.8in}}{same as PAM} & +\multicolumn{1}{|p{-0.59in}}{Same as LAM} & + +\hhline{---} +%row no:4 +\multicolumn{1}{|p{0.4in}}{PR} & +\multicolumn{1}{|p{2.8in}}{= (1 - \textbf{Pod}) $\ast$ \textbf{Nsc} $\ast$ ( \textbf{Npr }- \textbf{Nac }- Yfr(\textbf{Led},Tev) $\ast$ \textbf{Nrt }$\ast$ \textbf{Icb }) )} & +\multicolumn{1}{|p{-0.59in}}{\textbf{Nac }= \textbf{Nac }+ Yfr(\textbf{Led},Tev) $\ast$ \textbf{Nrt }$\ast$ \textbf{Icb} \par \textbf{Fac }= \textbf{Fac} + Yfr(\textbf{Led},Tev) $\ast$ FER\textbf{ }$\ast$ \textbf{Nvl} \par \textbf{Nvl }= \textbf{Nvl} - (\textbf{Npr} - \textbf{Nac}) \par If IPCB == NT then \textbf{Icb }= \textbf{Nvl} \par \textbf{Led }= Tev } & + +\hhline{---} +%row no:5 +\multicolumn{1}{|p{0.4in}}{PP} & +\multicolumn{1}{|p{2.8in}}{Same as PAM} & +\multicolumn{1}{|p{-0.59in}}{Same as LAM} & + +\hhline{---} +%row no:6 +\multicolumn{1}{|p{0.4in}}{PY} & +\multicolumn{1}{|p{2.8in}}{Same as PAM} & +\multicolumn{1}{|p{-0.59in}}{Same as LAM} & + +\hhline{---} +%row no:7 +\multicolumn{1}{|p{0.4in}}{FP} & +\multicolumn{1}{|p{2.8in}}{Same as PAM} & +\multicolumn{1}{|p{-0.59in}}{Same as LAM} & + +\hhline{---} +%row no:8 +\multicolumn{1}{|p{0.4in}}{PRD} & +\multicolumn{1}{|p{2.8in}}{Same as LAM} & +\multicolumn{1}{|p{-0.59in}}{Same as LAM} & + +\hhline{---} +%row no:9 +\multicolumn{1}{|p{0.4in}}{TD } & +\multicolumn{1}{|p{2.8in}}{Same as LAM} & +\multicolumn{1}{|p{-0.59in}}{same as PAM} & + +\hhline{---} +%row no:10 +\multicolumn{1}{|p{0.4in}}{IP} & +\multicolumn{1}{|p{2.8in}}{Same as LAM} & +\multicolumn{1}{|p{-0.59in}}{same as PAM} & + +\hhline{---} +%row no:11 +\multicolumn{1}{|p{0.4in}}{IPCI} & +\multicolumn{1}{|p{2.8in}}{same as PAM} & +\multicolumn{1}{|p{-0.59in}}{Same as LAM} & + +\hhline{---} +%row no:12 +\multicolumn{1}{|p{0.4in}}{RR} & +\multicolumn{1}{|p{2.8in}}{same as PAM} & +\multicolumn{1}{|p{-0.59in}}{Same as LAM} & + +\hhline{---} +%row no:13 +\multicolumn{1}{|p{0.4in}}{RRY} & +\multicolumn{1}{|p{2.8in}}{same as PAM} & +\multicolumn{1}{|p{-0.59in}}{Same as LAM} & + +\hhline{---} +%row no:14 +\multicolumn{1}{|p{0.4in}}{SC} & +\multicolumn{1}{|p{2.8in}}{same as PAM} & +\multicolumn{1}{|p{-0.59in}}{Same as LAM} & + +\hhline{---} +%row no:15 +\multicolumn{1}{|p{0.4in}}{CD} & +\multicolumn{1}{|p{2.8in}}{same as PAM} & +\multicolumn{1}{|p{-0.59in}}{Same as LAM} & + +\hhline{---} +%row no:16 +\multicolumn{1}{|p{0.4in}}{IPCB} & +\multicolumn{1}{|p{2.8in}}{Same as LAM} & +\multicolumn{1}{|p{-0.59in}}{Same as LAM} & + +\hhline{---} + +\end{longtable}} + +%%%%%%%%%%%%%%%%%%%% Table No: 15 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsection{Annuity (ANN)} +\subsubsection{Maturity Determination} +If MD != NULL Then Tmd=MD + +Else if AMD != NULL Then Tmd=AMD + +Else if RRCL == NULL And IPCB == NT Then Tmd=NT/(\textbf{Npr}-\textbf{Nvl}$\ast$ \textbf{Nrt}$\ast$ Yfr(PRANX,PRANX+PRCL)\par + +Else Tmd = MAX\_Lifetime + +\subsubsection{Contract Events Generation} + + +%%%%%%%%%%%%%%%%%%%% Table No: 16 starts here %%%%%%%%%%%%%%%%%%%% + + +{ +\setlength\extrarowheight{3pt} +\begin{longtable}{p{0.34in}p{3.05in}p{2.49in}} + +\endfirsthead +\multicolumn{3}{c}{\textit{continued from previous page}}\hline +\endhead\hline +\multicolumn{3}{r}{\textit{continued on next page}} \\ +\endfoot +\hline +\endlastfoot\hline +%row no:1 +\multicolumn{1}{|p{0.34in}}{Event Type} & +\multicolumn{1}{|p{3.05in}}{Schedule} & +\multicolumn{1}{|p{2.49in}|}{Conditions} \\ +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.34in}}{AD} & +\multicolumn{1}{|p{3.05in}}{Same as PAM} & +\multicolumn{1}{|p{2.49in}|}{Same as PAM} \\ +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.34in}}{IED} & +\multicolumn{1}{|p{3.05in}}{same as PAM} & +\multicolumn{1}{|p{2.49in}|}{same as PAM} \\ +\hhline{---} +%row no:4 +\multicolumn{1}{|p{0.34in}}{PR} & +\multicolumn{1}{|p{3.05in}}{Same as LAM} & +\multicolumn{1}{|p{2.49in}|}{Same as LAM} \\ +\hhline{---} +%row no:5 +\multicolumn{1}{|p{0.34in}}{PP} & +\multicolumn{1}{|p{3.05in}}{Same as PAM} & +\multicolumn{1}{|p{2.49in}|}{Same as PAM} \\ +\hhline{---} +%row no:6 +\multicolumn{1}{|p{0.34in}}{PY} & +\multicolumn{1}{|p{3.05in}}{Same as PAM} & +\multicolumn{1}{|p{2.49in}|}{Same as PAM} \\ +\hhline{---} +%row no:7 +\multicolumn{1}{|p{0.34in}}{FP} & +\multicolumn{1}{|p{3.05in}}{Same as PAM} & +\multicolumn{1}{|p{2.49in}|}{Same as PAM} \\ +\hhline{---} +%row no:8 +\multicolumn{1}{|p{0.34in}}{PRD} & +\multicolumn{1}{|p{3.05in}}{same as PAM} & +\multicolumn{1}{|p{2.49in}|}{same as PAM} \\ +\hhline{---} +%row no:9 +\multicolumn{1}{|p{0.34in}}{TD} & +\multicolumn{1}{|p{3.05in}}{same as PAM} & +\multicolumn{1}{|p{2.49in}|}{same as PAM} \\ +\hhline{---} +%row no:10 +\multicolumn{1}{|p{0.34in}}{IP} & +\multicolumn{1}{|p{3.05in}}{Same as LAM} & +\multicolumn{1}{|p{2.49in}|}{Same as LAM} \\ +\hhline{---} +%row no:11 +\multicolumn{1}{|p{0.34in}}{IPCI} & +\multicolumn{1}{|p{3.05in}}{same as PAM} & +\multicolumn{1}{|p{2.49in}|}{Same as LAM} \\ +\hhline{---} +%row no:12 +\multicolumn{1}{|p{0.34in}}{RR} & +\multicolumn{1}{|p{3.05in}}{same as PAM} & +\multicolumn{1}{|p{2.49in}|}{Tstrt must be in-line with PR-Schedule \par RRCL must be a multiple of PRCL \par } \\ +\hhline{---} +%row no:13 +\multicolumn{1}{|p{0.34in}}{RRY} & +\multicolumn{1}{|p{3.05in}}{same as PAM} & +\multicolumn{1}{|p{2.49in}|}{same as PAM} \\ +\hhline{---} +%row no:14 +\multicolumn{1}{|p{0.34in}}{SC} & +\multicolumn{1}{|p{3.05in}}{same as PAM} & +\multicolumn{1}{|p{2.49in}|}{same as PAM} \\ +\hhline{---} +%row no:15 +\multicolumn{1}{|p{0.34in}}{CD} & +\multicolumn{1}{|p{3.05in}}{same as PAM} & +\multicolumn{1}{|p{2.49in}|}{same as PAM} \\ +\hhline{---} +%row no:16 +\multicolumn{1}{|p{0.34in}}{IPCB} & +\multicolumn{1}{|p{3.05in}}{Same as LAM} & +\multicolumn{1}{|p{2.49in}|}{Same as LAM} \\ +\hhline{---} + +\end{longtable}} + +%%%%%%%%%%%%%%%%%%%% Table No: 16 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsubsection{State Variables Initialization} + + +%%%%%%%%%%%%%%%%%%%% Table No: 17 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \centering +\begin{tabular}{p{0.48in}p{2.79in}p{2.63in}} +\hline +%row no:1 +\multicolumn{1}{|p{0.48in}}{State Variable} & +\multicolumn{1}{|p{2.79in}}{Contract Attribute} & +\multicolumn{1}{|p{2.63in}|}{Comments} \\ +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.48in}}{\textbf{Nvl}} & +\multicolumn{1}{|p{2.79in}}{same as PAM} & +\multicolumn{1}{|p{2.63in}|}{same as PAM} \\ +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.48in}}{\textbf{Nrt}} & +\multicolumn{1}{|p{2.79in}}{same as PAM} & +\multicolumn{1}{|p{2.63in}|}{same as PAM} \\ +\hhline{---} +%row no:4 +\multicolumn{1}{|p{0.48in}}{\textbf{Nac}} & +\multicolumn{1}{|p{2.79in}}{same as PAM} & +\multicolumn{1}{|p{2.63in}|}{same as PAM} \\ +\hhline{---} +%row no:5 +\multicolumn{1}{|p{0.48in}}{\textbf{Fac}} & +\multicolumn{1}{|p{2.79in}}{Same as PAM} & +\multicolumn{1}{|p{2.63in}|}{Same as PAM} \\ +\hhline{---} +%row no:6 +\multicolumn{1}{|p{0.48in}}{\textbf{Led}} & +\multicolumn{1}{|p{2.79in}}{same as PAM} & +\multicolumn{1}{|p{2.63in}|}{same as PAM} \\ +\hhline{---} +%row no:7 +\multicolumn{1}{|p{0.48in}}{\textbf{Nsc}} & +\multicolumn{1}{|p{2.79in}}{same as PAM} & +\multicolumn{1}{|p{2.63in}|}{same as PAM} \\ +\hhline{---} +%row no:8 +\multicolumn{1}{|p{0.48in}}{\textbf{Isc}} & +\multicolumn{1}{|p{2.79in}}{Same as PAM} & +\multicolumn{1}{|p{2.63in}|}{Same as PAM} \\ +\hhline{---} +%row no:9 +\multicolumn{1}{|p{0.48in}}{\textbf{Pod}} & +\multicolumn{1}{|p{2.79in}}{Same as PAM} & +\multicolumn{1}{|p{2.63in}|}{Same as PAM} \\ +\hhline{---} +%row no:10 +\multicolumn{1}{|p{0.48in}}{\textbf{Npr}} & +\multicolumn{1}{|p{2.79in}}{PRNXT \par \( \left( Nvl+Nac \right) \frac{ \prod_{i=1}^{N-1} \left( 1+Nrt \times Yfr \left( Tev_{i},Tev_{i+1}_{i} \right) }{1+ \sum _{i=1}^{N-1} \prod_{j=i}^{N-1} \left( 1+Nrt \times Yfr \left( Tev_{j},Tev_{j+1} \right) \right) } \) \par where \par \( N \) := number of IP/PR Events \( ev_{i} \) with \( T_{ev_{i}}>SD, \forall i \) \par \( T_{ev_{i}} \) := date of the \( i \) ’th future IP/PR Event \( ev_{i} \) \par } & +\multicolumn{1}{|p{2.63in}|}{if PRNXT != NULL \par Else \par } \\ +\hhline{---} +%row no:11 +\multicolumn{1}{|p{0.48in}}{\textbf{Icb}} & +\multicolumn{1}{|p{2.79in}}{Same as LAM} & +\multicolumn{1}{|p{2.63in}|}{Same as LAM} \\ +\hhline{---} + +\end{tabular} + \end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 17 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsubsection{Contract Events, State Transition Functions and Pay Off Functions} + + +%%%%%%%%%%%%%%%%%%%% Table No: 18 starts here %%%%%%%%%%%%%%%%%%%% + + +{ +\setlength\extrarowheight{3pt} +\begin{longtable}{p{0.4in}p{2.8in}p{-0.59in}p{0.15in}p{0.04in}p{0.23in}p{-0.01in}p{0.02in}} + +\endfirsthead +\multicolumn{8}{c}{\textit{continued from previous page}}\hline +\endhead\hline +\multicolumn{8}{r}{\textit{continued on next page}} \\ +\endfoot +\hline +\endlastfoot\hline +%row no:1 +\multicolumn{1}{|p{0.4in}}{\textbf{Event Type}} & +\multicolumn{1}{|p{2.8in}}{\textbf{Pay Off Function}} & +\multicolumn{1}{|p{-0.59in}}{\textbf{State Transition Function}} & + +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.4in}}{AD} & +\multicolumn{1}{|p{2.8in}}{Same as PAM} & +\multicolumn{1}{|p{-0.59in}}{Same as PAM} & + +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.4in}}{IED} & +\multicolumn{1}{|p{2.8in}}{same as PAM} & +\multicolumn{1}{|p{-0.59in}}{Same as LAM} & + +\hhline{---} +%row no:4 +\multicolumn{1}{|p{0.4in}}{PR} & +\multicolumn{1}{|p{2.8in}}{Same as NAM} & +\multicolumn{1}{|p{-0.59in}}{Same as NAM} & + +\hhline{---} +%row no:5 +\multicolumn{1}{|p{0.4in}}{PP} & +\multicolumn{1}{|p{2.8in}}{Same as PAM} & +\multicolumn{1}{|p{-0.59in}}{Same as LAM} & + +\hhline{---} +%row no:6 +\multicolumn{1}{|p{0.4in}}{PY} & +\multicolumn{1}{|p{2.8in}}{Same as PAM} & +\multicolumn{1}{|p{-0.59in}}{Same as LAM} & + +\hhline{---} +%row no:7 +\multicolumn{1}{|p{0.4in}}{FP} & +\multicolumn{1}{|p{2.8in}}{Same as PAM} & +\multicolumn{1}{|p{-0.59in}}{Same as LAM} & + +\hhline{---} +%row no:8 +\multicolumn{1}{|p{0.4in}}{PRD} & +\multicolumn{1}{|p{2.8in}}{Same as LAM} & +\multicolumn{1}{|p{-0.59in}}{Same as LAM} & + +\hhline{---} +%row no:9 +\multicolumn{1}{|p{0.4in}}{TD } & +\multicolumn{1}{|p{2.8in}}{Same as LAM} & +\multicolumn{1}{|p{-0.59in}}{same as PAM} & + +\hhline{---} +%row no:10 +\multicolumn{1}{|p{0.4in}}{IP} & +\multicolumn{1}{|p{2.8in}}{Same as LAM} & +\multicolumn{1}{|p{-0.59in}}{same as PAM} & + +\hhline{---} +%row no:11 +\multicolumn{1}{|p{0.4in}}{IPCI} & +\multicolumn{1}{|p{2.8in}}{same as PAM} & +\multicolumn{1}{|p{-0.59in}}{Same as LAM} & + +\hhline{---} +%row no:12 +\multicolumn{1}{|p{0.4in}}{RR} & +\multicolumn{1}{|p{2.8in}}{same as PAM} & +\multicolumn{1}{|p{-0.59in}}{\textbf{Nac }= \textbf{Nac }+ Yfr(\textbf{Led},Tev) $\ast$ \textbf{Nrt }$\ast$ \textbf{Icb} \par \textbf{Fac }= \textbf{Fac} + Yfr(\textbf{Led},Tev) $\ast$ FER\textbf{ }$\ast$ \textbf{Nvl} \par rate = RF(RRMO, Tev)$\ast$ RRMT+RRSP \par deltaRate= min(max(rate-\textbf{Nrt},RRPF),RRPC) \par \textbf{Nrt }= min(max(\textbf{Nrt}+deltaRate,RRLF),RRLC) \par \textbf{Npr }= \( \left( Nvl+Nac \right) \frac{ \prod_{i=1}^{N-1} \left( 1+Nrt \times Yfr \left( Tev_{i},Tev_{i+1}_{i} \right) }{1+ \sum _{i=1}^{N-1} \prod_{j=i}^{N-1} \left( 1+Nrt \times Yfr \left( Tev_{j},Tev_{j+1} \right) \right) } \) \par where \par \( N \) := number of IP/PR Events \( ev_{i} \) with \( T_{ev_{i}}>SD, \forall i \) \par \( T_{ev_{i}} \) := date of the \( i \) ’th future IP/PR Event \( ev_{i} \) \par \textbf{Led }= Tev} & + +\hhline{---} +%row no:13 +\multicolumn{1}{|p{0.4in}}{RRY} & +\multicolumn{1}{|p{2.8in}}{same as PAM} & +\multicolumn{1}{|p{-0.59in}}{\textbf{Nac }= \textbf{Nac }+ Yfr(\textbf{Led},Tev) $\ast$ \textbf{Nrt }$\ast$ \textbf{Icb} \par \textbf{Fac }= \textbf{Fac} + Yfr(\textbf{Led},Tev) $\ast$ FER\textbf{ }$\ast$ \textbf{Nvl} \par \textbf{Nrt }= RRNXT \par \textbf{Npr }= \( \left( Nvl+Nac \right) \frac{ \prod_{i=1}^{N-1} \left( 1+Nrt \times Yfr \left( Tev_{i},Tev_{i+1}_{i} \right) }{1+ \sum _{i=1}^{N-1} \prod_{j=i}^{N-1} \left( 1+Nrt \times Yfr \left( Tev_{j},Tev_{j+1} \right) \right) } \) \par where \par \( N \) := number of IP/PR Events \( ev_{i} \) with \( T_{ev_{i}}>SD, \forall i \) \par \( T_{ev_{i}} \) := date of the \( i \) ’th future IP/PR Event \( ev_{i} \) \par \textbf{Led }= Tev} & + +\hhline{---} +%row no:14 +\multicolumn{1}{|p{0.4in}}{SC} & +\multicolumn{1}{|p{2.8in}}{same as PAM} & +\multicolumn{1}{|p{-0.59in}}{Same as LAM} & + +\hhline{---} +%row no:15 +\multicolumn{1}{|p{0.4in}}{CD} & +\multicolumn{1}{|p{2.8in}}{same as PAM} & +\multicolumn{1}{|p{-0.59in}}{Same as LAM} & + +\hhline{---} +%row no:16 +\multicolumn{1}{|p{0.4in}}{IPCB} & +\multicolumn{1}{|p{2.8in}}{Same as LAM} & +\multicolumn{1}{|p{-0.59in}}{Same as LAM} & + +\hhline{---} + +\end{longtable}} + +%%%%%%%%%%%%%%%%%%%% Table No: 18 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsection{Call Money (CLM)} +\subsubsection{Maturity Determination} +If MD != NULL: Tmd=MD + +Else Tmd=AD0+XDN + +\subsubsection{Contract Events Generation} + + +%%%%%%%%%%%%%%%%%%%% Table No: 19 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \centering +\begin{tabular}{p{0.34in}p{3.05in}p{2.49in}} +\hline +%row no:1 +\multicolumn{1}{|p{0.34in}}{Event Type} & +\multicolumn{1}{|p{3.05in}}{Schedule} & +\multicolumn{1}{|p{2.49in}|}{Conditions} \\ +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.34in}}{AD} & +\multicolumn{1}{|p{3.05in}}{Same as PAM} & +\multicolumn{1}{|p{2.49in}|}{} \\ +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.34in}}{IED} & +\multicolumn{1}{|p{3.05in}}{same as PAM} & +\multicolumn{1}{|p{2.49in}|}{same as PAM} \\ +\hhline{---} +%row no:4 +\multicolumn{1}{|p{0.34in}}{PR} & +\multicolumn{1}{|p{3.05in}}{Single event at Tmd} & +\multicolumn{1}{|p{2.49in}|}{} \\ +\hhline{---} +%row no:5 +\multicolumn{1}{|p{0.34in}}{FP} & +\multicolumn{1}{|p{3.05in}}{Same as PAM} & +\multicolumn{1}{|p{2.49in}|}{Same as PAM} \\ +\hhline{---} +%row no:6 +\multicolumn{1}{|p{0.34in}}{IP} & +\multicolumn{1}{|p{3.05in}}{Single event at Tmd} & +\multicolumn{1}{|p{2.49in}|}{} \\ +\hhline{---} +%row no:7 +\multicolumn{1}{|p{0.34in}}{IPCI} & +\multicolumn{1}{|p{3.05in}}{no event \par if IPANX != NULL Then Tstrt = IPANX \par Else Tstrt = IED+IPCL \par Sdl(Tstrt, IPCL, Tmd, EOMC, BDC) >= SD \par } & +\multicolumn{1}{|p{2.49in}|}{if IPCL == NULL \par if IPCL != NULL \par } \\ +\hhline{---} +%row no:8 +\multicolumn{1}{|p{0.34in}}{RR} & +\multicolumn{1}{|p{3.05in}}{same as PAM} & +\multicolumn{1}{|p{2.49in}|}{Same as PAM} \\ +\hhline{---} +%row no:9 +\multicolumn{1}{|p{0.34in}}{RRY} & +\multicolumn{1}{|p{3.05in}}{same as PAM} & +\multicolumn{1}{|p{2.49in}|}{same as PAM} \\ +\hhline{---} +%row no:10 +\multicolumn{1}{|p{0.34in}}{CD} & +\multicolumn{1}{|p{3.05in}}{same as PAM} & +\multicolumn{1}{|p{2.49in}|}{same as PAM} \\ +\hhline{---} + +\end{tabular} + \end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 19 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsubsection{State Variables Initialization} + + +%%%%%%%%%%%%%%%%%%%% Table No: 20 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \centering +\begin{tabular}{p{0.48in}p{2.79in}p{2.63in}} +\hline +%row no:1 +\multicolumn{1}{|p{0.48in}}{State Variable} & +\multicolumn{1}{|p{2.79in}}{Contract Attribute} & +\multicolumn{1}{|p{2.63in}|}{Comments} \\ +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.48in}}{\textbf{Nvl}} & +\multicolumn{1}{|p{2.79in}}{same as PAM} & +\multicolumn{1}{|p{2.63in}|}{same as PAM} \\ +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.48in}}{\textbf{Nrt}} & +\multicolumn{1}{|p{2.79in}}{same as PAM} & +\multicolumn{1}{|p{2.63in}|}{same as PAM} \\ +\hhline{---} +%row no:4 +\multicolumn{1}{|p{0.48in}}{\textbf{Nac}} & +\multicolumn{1}{|p{2.79in}}{same as PAM} & +\multicolumn{1}{|p{2.63in}|}{same as PAM} \\ +\hhline{---} +%row no:5 +\multicolumn{1}{|p{0.48in}}{\textbf{Fac}} & +\multicolumn{1}{|p{2.79in}}{Same as PAM} & +\multicolumn{1}{|p{2.63in}|}{Same as PAM} \\ +\hhline{---} +%row no:6 +\multicolumn{1}{|p{0.48in}}{\textbf{Led}} & +\multicolumn{1}{|p{2.79in}}{same as PAM} & +\multicolumn{1}{|p{2.63in}|}{same as PAM} \\ +\hhline{---} +%row no:7 +\multicolumn{1}{|p{0.48in}}{\textbf{Pod}} & +\multicolumn{1}{|p{2.79in}}{Same as PAM} & +\multicolumn{1}{|p{2.63in}|}{Same as PAM} \\ +\hhline{---} + +\end{tabular} + \end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 20 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsubsection{Contract Events, State Transition Functions and Pay Off Functions} + + +%%%%%%%%%%%%%%%%%%%% Table No: 21 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \centering +\begin{tabular}{p{0.48in}p{2.8in}p{-0.45in}p{0.26in}p{0.12in}p{0.37in}p{0.06in}p{0.09in}} +\hline +%row no:1 +\multicolumn{1}{|p{0.48in}}{\textbf{Event Type}} & +\multicolumn{1}{|p{2.8in}}{\textbf{Pay Off Function}} & +\multicolumn{1}{|p{-0.45in}}{\textbf{State Transition Function}} & + +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.48in}}{AD} & +\multicolumn{1}{|p{2.8in}}{Same as PAM} & +\multicolumn{1}{|p{-0.45in}}{Same as PAM} & + +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.48in}}{IED} & +\multicolumn{1}{|p{2.8in}}{= (1-\textbf{Pod}) $\ast$ Sgn(CNTRL) $\ast$ (-1) $\ast$ NT} & +\multicolumn{1}{|p{-0.45in}}{Same as PAM} & + +\hhline{---} +%row no:4 +\multicolumn{1}{|p{0.48in}}{PR} & +\multicolumn{1}{|p{2.8in}}{Same as PAM} & +\multicolumn{1}{|p{-0.45in}}{Same as PAM} & + +\hhline{---} +%row no:5 +\multicolumn{1}{|p{0.48in}}{FP} & +\multicolumn{1}{|p{2.8in}}{Same as PAM} & +\multicolumn{1}{|p{-0.45in}}{Same as PAM} & + +\hhline{---} +%row no:6 +\multicolumn{1}{|p{0.48in}}{IP} & +\multicolumn{1}{|p{2.8in}}{= (1-\textbf{Pod})\textbf{ }$\ast$ ( \textbf{Nac + }Yfr(\textbf{Led},Tev) $\ast$ \textbf{Nrt }$\ast$ \textbf{Nvl })} & +\multicolumn{1}{|p{-0.45in}}{\textbf{Nac }= 0.0 \par \textbf{Fac }= 0.0 \par \textbf{Led }= Tev} & + +\hhline{---} +%row no:7 +\multicolumn{1}{|p{0.48in}}{IPCI} & +\multicolumn{1}{|p{2.8in}}{same as PAM} & +\multicolumn{1}{|p{-0.45in}}{Same as PAM} & + +\hhline{---} +%row no:8 +\multicolumn{1}{|p{0.48in}}{RR} & +\multicolumn{1}{|p{2.8in}}{same as PAM} & +\multicolumn{1}{|p{-0.45in}}{Same as PAM} & + +\hhline{---} +%row no:9 +\multicolumn{1}{|p{0.48in}}{RRY} & +\multicolumn{1}{|p{2.8in}}{same as PAM} & +\multicolumn{1}{|p{-0.45in}}{Same as PAM} & + +\hhline{---} +%row no:10 +\multicolumn{1}{|p{0.48in}}{CD} & +\multicolumn{1}{|p{2.8in}}{same as PAM} & +\multicolumn{1}{|p{-0.45in}}{Same as PAM} & + +\hhline{---} + +\end{tabular} + \end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 21 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsection{Undefined Maturity Profile (UMP)} +\subsubsection{Maturity Determination} +Else Tmd=max(Tev) where Tev the sequence of times of events in RF(CID)\par + +\subsubsection{Contract Events Generation} + + +%%%%%%%%%%%%%%%%%%%% Table No: 22 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \centering +\begin{tabular}{p{0.34in}p{3.05in}p{2.49in}} +\hline +%row no:1 +\multicolumn{1}{|p{0.34in}}{Event Type} & +\multicolumn{1}{|p{3.05in}}{Schedule} & +\multicolumn{1}{|p{2.49in}|}{Conditions} \\ +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.34in}}{AD} & +\multicolumn{1}{|p{3.05in}}{Same as PAM} & +\multicolumn{1}{|p{2.49in}|}{} \\ +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.34in}}{IED} & +\multicolumn{1}{|p{3.05in}}{same as PAM} & +\multicolumn{1}{|p{2.49in}|}{same as PAM} \\ +\hhline{---} +%row no:4 +\multicolumn{1}{|p{0.34in}}{PR} & +\multicolumn{1}{|p{3.05in}}{un-scheduled events according to RF(CID)} & +\multicolumn{1}{|p{2.49in}|}{un-scheduled events only} \\ +\hhline{---} +%row no:5 +\multicolumn{1}{|p{0.34in}}{FP} & +\multicolumn{1}{|p{3.05in}}{same as PAM} & +\multicolumn{1}{|p{2.49in}|}{same as PAM} \\ +\hhline{---} +%row no:6 +\multicolumn{1}{|p{0.34in}}{TD} & +\multicolumn{1}{|p{3.05in}}{Same as PAM} & +\multicolumn{1}{|p{2.49in}|}{Same as PAM} \\ +\hhline{---} +%row no:7 +\multicolumn{1}{|p{0.34in}}{IPCI} & +\multicolumn{1}{|p{3.05in}}{no event \par single event at IPANX \par if IPANX != NULL Then Tstrt = IPANX \par Else Tstrt = IED+IPCL \par Sdl(Tstrt, IPCL, Tmd, EOMC, BDC) >= SD \par } & +\multicolumn{1}{|p{2.49in}|}{if IPCL == NULL And IPANX == NULL \par If IPCL == NULL And IPANX != NULL \par if IPCL != NULL \par } \\ +\hhline{---} +%row no:8 +\multicolumn{1}{|p{0.34in}}{RR} & +\multicolumn{1}{|p{3.05in}}{same as PAM} & +\multicolumn{1}{|p{2.49in}|}{Same as PAM} \\ +\hhline{---} +%row no:9 +\multicolumn{1}{|p{0.34in}}{RRY} & +\multicolumn{1}{|p{3.05in}}{same as PAM} & +\multicolumn{1}{|p{2.49in}|}{same as PAM} \\ +\hhline{---} +%row no:10 +\multicolumn{1}{|p{0.34in}}{CD} & +\multicolumn{1}{|p{3.05in}}{same as PAM} & +\multicolumn{1}{|p{2.49in}|}{same as PAM} \\ +\hhline{---} + +\end{tabular} + \end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 22 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsubsection{State Variables Initialization} + + +%%%%%%%%%%%%%%%%%%%% Table No: 23 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \centering +\begin{tabular}{p{0.48in}p{2.79in}p{2.63in}} +\hline +%row no:1 +\multicolumn{1}{|p{0.48in}}{State Variable} & +\multicolumn{1}{|p{2.79in}}{Contract Attribute} & +\multicolumn{1}{|p{2.63in}|}{Comments} \\ +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.48in}}{\textbf{Nvl}} & +\multicolumn{1}{|p{2.79in}}{same as PAM} & +\multicolumn{1}{|p{2.63in}|}{same as PAM} \\ +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.48in}}{\textbf{Nrt}} & +\multicolumn{1}{|p{2.79in}}{same as PAM} & +\multicolumn{1}{|p{2.63in}|}{same as PAM} \\ +\hhline{---} +%row no:4 +\multicolumn{1}{|p{0.48in}}{\textbf{Nac}} & +\multicolumn{1}{|p{2.79in}}{same as PAM} & +\multicolumn{1}{|p{2.63in}|}{same as PAM} \\ +\hhline{---} +%row no:5 +\multicolumn{1}{|p{0.48in}}{\textbf{Fac}} & +\multicolumn{1}{|p{2.79in}}{Same as PAM} & +\multicolumn{1}{|p{2.63in}|}{Same as PAM} \\ +\hhline{---} +%row no:6 +\multicolumn{1}{|p{0.48in}}{\textbf{Led}} & +\multicolumn{1}{|p{2.79in}}{same as PAM} & +\multicolumn{1}{|p{2.63in}|}{same as PAM} \\ +\hhline{---} + +\end{tabular} + \end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 23 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} + +\vspace{\baselineskip} +\subsubsection{Contract Events, State Transition Functions and Pay Off Functions} + + +%%%%%%%%%%%%%%%%%%%% Table No: 24 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \centering +\begin{tabular}{p{0.48in}p{2.8in}p{-0.45in}p{0.26in}p{0.12in}p{0.37in}p{0.06in}p{0.09in}} +\hline +%row no:1 +\multicolumn{1}{|p{0.48in}}{\textbf{Event Type}} & +\multicolumn{1}{|p{2.8in}}{\textbf{Pay Off Function}} & +\multicolumn{1}{|p{-0.45in}}{\textbf{State Transition Function}} & + +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.48in}}{AD} & +\multicolumn{1}{|p{2.8in}}{Same as PAM} & +\multicolumn{1}{|p{-0.45in}}{Same as PAM} & + +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.48in}}{IED} & +\multicolumn{1}{|p{2.8in}}{Same as CLM} & +\multicolumn{1}{|p{-0.45in}}{Same as PAM} & + +\hhline{---} +%row no:4 +\multicolumn{1}{|p{0.48in}}{PR} & +\multicolumn{1}{|p{2.8in}}{= Vev} & +\multicolumn{1}{|p{-0.45in}}{\textbf{Nac }= \textbf{Nac }+ Yfr(\textbf{Led},Tev) $\ast$ \textbf{Nrt }$\ast$ \textbf{Icb} \par \textbf{Fac }= \textbf{Fac} + Yfr(\textbf{Led},Tev) $\ast$ FER\textbf{ }$\ast$ \textbf{Nvl} \par \textbf{Nvl = Nvl - }Vev \par \textbf{Led = }Tev} & + +\hhline{---} +%row no:5 +\multicolumn{1}{|p{0.48in}}{FP} & +\multicolumn{1}{|p{2.8in}}{Same as PAM} & +\multicolumn{1}{|p{-0.45in}}{Same as PAM} & + +\hhline{---} +%row no:6 +\multicolumn{1}{|p{0.48in}}{TD} & +\multicolumn{1}{|p{2.8in}}{Same as PAM} & +\multicolumn{1}{|p{-0.45in}}{Same as PAM} & + +\hhline{---} +%row no:7 +\multicolumn{1}{|p{0.48in}}{IPCI} & +\multicolumn{1}{|p{2.8in}}{Same as PAM} & +\multicolumn{1}{|p{-0.45in}}{Same as PAM} & + +\hhline{---} +%row no:8 +\multicolumn{1}{|p{0.48in}}{RR} & +\multicolumn{1}{|p{2.8in}}{same as PAM} & +\multicolumn{1}{|p{-0.45in}}{Same as CLM} & + +\hhline{---} +%row no:9 +\multicolumn{1}{|p{0.48in}}{RRY} & +\multicolumn{1}{|p{2.8in}}{same as PAM} & +\multicolumn{1}{|p{-0.45in}}{Same as PAM} & + +\hhline{---} +%row no:10 +\multicolumn{1}{|p{0.48in}}{CD} & +\multicolumn{1}{|p{2.8in}}{same as PAM} & +\multicolumn{1}{|p{-0.45in}}{Same as PAM} & + +\hhline{---} + +\end{tabular} + \end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 24 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsection{Cash (CSH)} +\subsubsection{Contract Events Generation} + + +%%%%%%%%%%%%%%%%%%%% Table No: 25 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \centering +\begin{tabular}{p{0.34in}p{3.05in}p{2.49in}} +\hline +%row no:1 +\multicolumn{1}{|p{0.34in}}{Event Type} & +\multicolumn{1}{|p{3.05in}}{Schedule} & +\multicolumn{1}{|p{2.49in}|}{Conditions} \\ +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.34in}}{AD} & +\multicolumn{1}{|p{3.05in}}{Same as PAM} & +\multicolumn{1}{|p{2.49in}|}{Same as STK} \\ +\hhline{---} + +\end{tabular} + \end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 25 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsubsection{State Variables Initialization} + + +%%%%%%%%%%%%%%%%%%%% Table No: 26 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \centering +\begin{tabular}{p{0.48in}p{2.79in}p{2.63in}} +\hline +%row no:1 +\multicolumn{1}{|p{0.48in}}{State Variable} & +\multicolumn{1}{|p{2.79in}}{Contract Attribute} & +\multicolumn{1}{|p{2.63in}|}{Comments} \\ +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.48in}}{\textbf{Led}} & +\multicolumn{1}{|p{2.79in}}{Same as STK} & +\multicolumn{1}{|p{2.63in}|}{Same as STK} \\ +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.48in}}{\textbf{Nvl}} & +\multicolumn{1}{|p{2.79in}}{Sgn(CNTRL) $\ast$ NT} & +\multicolumn{1}{|p{2.63in}|}{} \\ +\hhline{---} + +\end{tabular} + \end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 26 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsubsection{Contract Events, State Transition Functions and Pay Off Functions} + + +%%%%%%%%%%%%%%%%%%%% Table No: 27 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \centering +\begin{tabular}{p{0.4in}p{2.8in}p{-0.58in}p{0.15in}p{0.05in}p{0.23in}p{0.01in}p{0.02in}} +\hline +%row no:1 +\multicolumn{1}{|p{0.4in}}{\textbf{Event Type}} & +\multicolumn{1}{|p{2.8in}}{\textbf{Pay Off Function}} & +\multicolumn{1}{|p{-0.58in}}{\textbf{State Transition Function}} & + +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.4in}}{AD} & +\multicolumn{1}{|p{2.8in}}{Same as PAM} & +\multicolumn{1}{|p{-0.58in}}{\textbf{Led }= Tev} & + +\hhline{---} + +\end{tabular} + \end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 27 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsection{Stock (STK)} +\subsubsection{Contract Events Generation} + + +%%%%%%%%%%%%%%%%%%%% Table No: 28 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \centering +\begin{tabular}{p{0.34in}p{3.05in}p{2.49in}} +\hline +%row no:1 +\multicolumn{1}{|p{0.34in}}{Event Type} & +\multicolumn{1}{|p{3.05in}}{Schedule} & +\multicolumn{1}{|p{2.49in}|}{Conditions} \\ +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.34in}}{AD} & +\multicolumn{1}{|p{3.05in}}{Same as PAM} & +\multicolumn{1}{|p{2.49in}|}{} \\ +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.34in}}{PRD} & +\multicolumn{1}{|p{3.05in}}{single event at PRD} & +\multicolumn{1}{|p{2.49in}|}{if PRD >= SD} \\ +\hhline{---} +%row no:4 +\multicolumn{1}{|p{0.34in}}{TD} & +\multicolumn{1}{|p{3.05in}}{single event at TD} & +\multicolumn{1}{|p{2.49in}|}{if TD >= SD} \\ +\hhline{---} +%row no:5 +\multicolumn{1}{|p{0.34in}}{DV} & +\multicolumn{1}{|p{3.05in}}{no event \par Sdl(DVANX, DVCL, MAX\_LIFETIME, EOMC, BDC) >= SD \par } & +\multicolumn{1}{|p{2.49in}|}{if DVCL== NULL \par Else \par } \\ +\hhline{---} +%row no:6 +\multicolumn{1}{|p{0.34in}}{CD} & +\multicolumn{1}{|p{3.05in}}{Same as PAM} & +\multicolumn{1}{|p{2.49in}|}{Same as PAM} \\ +\hhline{---} + +\end{tabular} + \end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 28 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsubsection{State Variables Initialization} + + +%%%%%%%%%%%%%%%%%%%% Table No: 29 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \centering +\begin{tabular}{p{0.48in}p{2.79in}p{2.63in}} +\hline +%row no:1 +\multicolumn{1}{|p{0.48in}}{State Variable} & +\multicolumn{1}{|p{2.79in}}{Contract Attribute} & +\multicolumn{1}{|p{2.63in}|}{Comments} \\ +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.48in}}{\textbf{Nvl}} & +\multicolumn{1}{|p{2.79in}}{0.0} & +\multicolumn{1}{|p{2.63in}|}{Nominal value remains 0.0 throughout the CT’s lifetime} \\ +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.48in}}{\textbf{Nac}} & +\multicolumn{1}{|p{2.79in}}{0.0} & +\multicolumn{1}{|p{2.63in}|}{Nominal accrued remains 0.0 throughout the CT’s lifetime} \\ +\hhline{---} +%row no:4 +\multicolumn{1}{|p{0.48in}}{\textbf{Led}} & +\multicolumn{1}{|p{2.79in}}{SD} & +\multicolumn{1}{|p{2.63in}|}{} \\ +\hhline{---} +%row no:5 +\multicolumn{1}{|p{0.48in}}{\textbf{Pod}} & +\multicolumn{1}{|p{2.79in}}{Same as PAM} & +\multicolumn{1}{|p{2.63in}|}{Same as PAM} \\ +\hhline{---} + +\end{tabular} + \end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 29 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsubsection{Contract Events, State Transition Functions and Pay Off Functions} + + +%%%%%%%%%%%%%%%%%%%% Table No: 30 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \centering +\begin{tabular}{p{0.4in}p{2.8in}p{-0.58in}p{0.15in}p{0.05in}p{0.23in}p{0.01in}p{0.02in}} +\hline +%row no:1 +\multicolumn{1}{|p{0.4in}}{\textbf{Event Type}} & +\multicolumn{1}{|p{2.8in}}{\textbf{Pay Off Function}} & +\multicolumn{1}{|p{-0.58in}}{\textbf{State Transition Function}} & + +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.4in}}{AD} & +\multicolumn{1}{|p{2.8in}}{Same as PAM} & +\multicolumn{1}{|p{-0.58in}}{\textbf{Led }= Tev} & + +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.4in}}{PRD} & +\multicolumn{1}{|p{2.8in}}{= Sgn(CNTRL) $\ast$ (-1) $\ast$ (1-\textbf{Pod}) $\ast$ QT $\ast$ PPRD} & +\multicolumn{1}{|p{-0.58in}}{\textbf{Led }= Tev} & + +\hhline{---} +%row no:4 +\multicolumn{1}{|p{0.4in}}{TD } & +\multicolumn{1}{|p{2.8in}}{= Sgn(CNTRL) $\ast$ (1-\textbf{Pod}) $\ast$ QT $\ast$ PTD} & +\multicolumn{1}{|p{-0.58in}}{\textbf{Led }= Tev} & + +\hhline{---} +%row no:5 +\multicolumn{1}{|p{0.4in}}{DV} & +\multicolumn{1}{|p{2.8in}}{= Sgn(CNTRL) $\ast$ (1-\textbf{Pod}) $\ast$ Yfr(Tev - DVCL, Tev, A/AISDA) $\ast$ RF(DVMO, Tev, DVCL) $\ast$ MVO} & +\multicolumn{1}{|p{-0.58in}}{\textbf{Led }= Tev} & + +\hhline{---} +%row no:6 +\multicolumn{1}{|p{0.4in}}{CD} & +\multicolumn{1}{|p{2.8in}}{Same as PAM} & +\multicolumn{1}{|p{-0.58in}}{\textbf{Pod }= RF(LEICP, Tev) \par \textbf{Led }= Tev} & + +\hhline{---} + +\end{tabular} + \end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 30 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsection{Commodity (COM)} +\subsubsection{Contract Events Generation} + + +%%%%%%%%%%%%%%%%%%%% Table No: 31 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \centering +\begin{tabular}{p{0.34in}p{3.05in}p{2.49in}} +\hline +%row no:1 +\multicolumn{1}{|p{0.34in}}{Event Type} & +\multicolumn{1}{|p{3.05in}}{Schedule} & +\multicolumn{1}{|p{2.49in}|}{Conditions} \\ +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.34in}}{AD} & +\multicolumn{1}{|p{3.05in}}{Same as PAM} & +\multicolumn{1}{|p{2.49in}|}{Same as STK} \\ +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.34in}}{PRD} & +\multicolumn{1}{|p{3.05in}}{Same as STK} & +\multicolumn{1}{|p{2.49in}|}{Same as STK} \\ +\hhline{---} +%row no:4 +\multicolumn{1}{|p{0.34in}}{TD} & +\multicolumn{1}{|p{3.05in}}{Same as STK} & +\multicolumn{1}{|p{2.49in}|}{Same as STK} \\ +\hhline{---} + +\end{tabular} + \end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 31 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsubsection{State Variables Initialization} + + +%%%%%%%%%%%%%%%%%%%% Table No: 32 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \centering +\begin{tabular}{p{0.48in}p{2.79in}p{2.63in}} +\hline +%row no:1 +\multicolumn{1}{|p{0.48in}}{State Variable} & +\multicolumn{1}{|p{2.79in}}{Contract Attribute} & +\multicolumn{1}{|p{2.63in}|}{Comments} \\ +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.48in}}{\textbf{Nvl}} & +\multicolumn{1}{|p{2.79in}}{0.0} & +\multicolumn{1}{|p{2.63in}|}{Nominal value remains 0.0 throughout the CT’s lifetime} \\ +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.48in}}{\textbf{Nac}} & +\multicolumn{1}{|p{2.79in}}{0.0} & +\multicolumn{1}{|p{2.63in}|}{Nominal accrued remains 0.0 throughout the CT’s lifetime} \\ +\hhline{---} +%row no:4 +\multicolumn{1}{|p{0.48in}}{\textbf{Led}} & +\multicolumn{1}{|p{2.79in}}{Same as STK} & +\multicolumn{1}{|p{2.63in}|}{Same as STK} \\ +\hhline{---} + +\end{tabular} + \end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 32 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsubsection{Contract Events, State Transition Functions and Pay Off Functions} + + +%%%%%%%%%%%%%%%%%%%% Table No: 33 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \centering +\begin{tabular}{p{0.4in}p{2.8in}p{-0.58in}p{0.15in}p{0.05in}p{0.23in}p{0.01in}p{0.02in}} +\hline +%row no:1 +\multicolumn{1}{|p{0.4in}}{\textbf{Event Type}} & +\multicolumn{1}{|p{2.8in}}{\textbf{Pay Off Function}} & +\multicolumn{1}{|p{-0.58in}}{\textbf{State Transition Function}} & + +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.4in}}{AD} & +\multicolumn{1}{|p{2.8in}}{Same as PAM} & +\multicolumn{1}{|p{-0.58in}}{Same as STK} & + +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.4in}}{PRD} & +\multicolumn{1}{|p{2.8in}}{Same as STK} & +\multicolumn{1}{|p{-0.58in}}{Same as STK} & + +\hhline{---} +%row no:4 +\multicolumn{1}{|p{0.4in}}{TD } & +\multicolumn{1}{|p{2.8in}}{Same as STK} & +\multicolumn{1}{|p{-0.58in}}{Same as STK} & + +\hhline{---} + +\end{tabular} + \end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 33 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsection{Combined contract types} +The class of Combined CTs refers to real-world financial instruments for which their payoff depends on the payoff or the market price of an underlying instrument. The underlying instrument can either be a Basic CT or Combined CT. \par + +\subsection{Foreign Exchange Outright (FXOUT)} +\subsubsection{Settlement determination} +If STD == NULL: Tstd = MD + +Else Tsd = STD + +\subsubsection{Contract Events Generation} + + +%%%%%%%%%%%%%%%%%%%% Table No: 34 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \centering +\begin{tabular}{p{0.34in}p{3.05in}p{2.49in}} +\hline +%row no:1 +\multicolumn{1}{|p{0.34in}}{Event Type} & +\multicolumn{1}{|p{3.05in}}{Schedule} & +\multicolumn{1}{|p{2.49in}|}{Conditions} \\ +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.34in}}{AD} & +\multicolumn{1}{|p{3.05in}}{Same as PAM} & +\multicolumn{1}{|p{2.49in}|}{} \\ +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.34in}}{PRD} & +\multicolumn{1}{|p{3.05in}}{Same as PAM} & +\multicolumn{1}{|p{2.49in}|}{Same as PAM} \\ +\hhline{---} +%row no:4 +\multicolumn{1}{|p{0.34in}}{TD} & +\multicolumn{1}{|p{3.05in}}{Same as PAM} & +\multicolumn{1}{|p{2.49in}|}{Same as PAM} \\ +\hhline{---} +%row no:5 +\multicolumn{1}{|p{0.34in}}{\multirowcell{2}{}{\begin{tabular}{p{0.34in}}STD\\STD\textsuperscript{1}, STD\textsuperscript{2}\\\end{tabular}}} & +\multicolumn{1}{|p{3.05in}}{\multirowcell{3}{}{\begin{tabular}{p{3.05in}}single event at Tstd\\two events at Tstd\\\end{tabular}}} & +\multicolumn{1}{|p{2.49in}|}{\multirowcell{3}{}{\begin{tabular}{p{2.49in}}if TD == NULL $\&$ DS == ‘S’\\else if TD == NULL\\\end{tabular}}} \\ + +\hhline{~~~} +%row no:6 +\multicolumn{1}{|p{0.34in}}{\multirow{1}{*}{\begin{tabular}{p{0.34in}}CD\\\end{tabular}}} & +\multicolumn{1}{|p{3.05in}}{\multirowcell{3}{}{\begin{tabular}{p{3.05in}}no event\\dates of RF(LEICP)\\\end{tabular}}} & +\multicolumn{1}{|p{2.49in}|}{\multirowcell{5}{}{\begin{tabular}{p{2.49in}}if RF(LEICP) == $ \{ $ $ \} $ $\ast$ \\if RF(LEICP) != $ \{ $ $ \} $ $\ast$ \\$\ast$ credit default risk factor for LEICP is an empty (==$ \{ $ $ \} $ ) or non-empty (!=$ \{ $ $ \} $ ), respectively, set of Date/Value pairs\\\end{tabular}}} \\ + +\hhline{~~~} +%row no:7 +\multicolumn{1}{|p{0.34in}}{\multirow{1}{*}{\begin{tabular}{p{0.34in}}\end{tabular}}} & +\multicolumn{1}{|p{3.05in}}{\multirow{1}{*}{\begin{tabular}{p{3.05in}}\end{tabular}}} & +\multicolumn{1}{|p{2.49in}|}{\multirow{1}{*}{\begin{tabular}{p{2.49in}}\end{tabular}}} \\ + +\hhline{~~~} +%row no:8 +\multicolumn{1}{|p{0.34in}}{CD} & +\multicolumn{1}{|p{3.05in}}{Same as PAM} & +\multicolumn{1}{|p{2.49in}|}{Same as PAM} \\ +\hhline{---} + +\end{tabular} + \end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 34 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsubsection{State Variables Initialization} + + +%%%%%%%%%%%%%%%%%%%% Table No: 35 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \centering +\begin{tabular}{p{0.48in}p{2.79in}p{2.63in}} +\hline +%row no:1 +\multicolumn{1}{|p{0.48in}}{State Variable} & +\multicolumn{1}{|p{2.79in}}{Contract Attribute} & +\multicolumn{1}{|p{2.63in}|}{Comments} \\ +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.48in}}{\textbf{Nvl}} & +\multicolumn{1}{|p{2.79in}}{0.0} & +\multicolumn{1}{|p{2.63in}|}{Nominal value remains 0.0 throughout the CT’s lifetime} \\ +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.48in}}{\textbf{Nac}} & +\multicolumn{1}{|p{2.79in}}{0.0} & +\multicolumn{1}{|p{2.63in}|}{Nominal accrued remains 0.0 throughout the CT’s lifetime} \\ +\hhline{---} +%row no:4 +\multicolumn{1}{|p{0.48in}}{\textbf{Led}} & +\multicolumn{1}{|p{2.79in}}{SD} & +\multicolumn{1}{|p{2.63in}|}{} \\ +\hhline{---} +%row no:5 +\multicolumn{1}{|p{0.48in}}{\textbf{Pod}} & +\multicolumn{1}{|p{2.79in}}{Same as PAM} & +\multicolumn{1}{|p{2.63in}|}{Same as PAM} \\ +\hhline{---} + +\end{tabular} + \end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 35 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsubsection{Contract Events, State Transition Functions and Pay Off Functions} + + +%%%%%%%%%%%%%%%%%%%% Table No: 36 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \centering +\begin{tabular}{p{0.46in}p{2.81in}p{2.59in}p{0.08in}p{0.01in}p{0.15in}p{-0.03in}p{-0.02in}} +\hline +%row no:1 +\multicolumn{1}{|p{0.46in}}{\textbf{Event Type}} & +\multicolumn{1}{|p{2.81in}}{\textbf{Pay Off Function}} & +\multicolumn{1}{|p{2.59in}}{\textbf{State Transition Function}} & + +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.46in}}{AD} & +\multicolumn{1}{|p{2.81in}}{Same as PAM} & +\multicolumn{1}{|p{2.59in}}{Same as STK} & + +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.46in}}{PRD} & +\multicolumn{1}{|p{2.81in}}{= Sgn(CNTRL) $\ast$ (-1) $\ast$ (1-\textbf{Pod}) $\ast$ PPRD} & +\multicolumn{1}{|p{2.59in}}{\textbf{Led }= Tev} & + +\hhline{---} +%row no:4 +\multicolumn{1}{|p{0.46in}}{TD } & +\multicolumn{1}{|p{2.81in}}{= Sgn(CNTRL) $\ast$ (1-\textbf{Pod}) $\ast$ PTD} & +\multicolumn{1}{|p{2.59in}}{\textbf{Led }= Tev} & + +\hhline{---} +%row no:5 +\multicolumn{1}{|p{0.46in}}{STD} & +\multicolumn{1}{|p{2.81in}}{= (1 - \textbf{Pod}) $\ast$ Sgn(CNTRL) $\ast$ (NT - RF($``$[CUR2]/[CUR]$"$ , MD) $\ast$ NT2) \par (Event Currency = CUR)} & +\multicolumn{1}{|p{2.59in}}{\textbf{Led }= Tev} & + +\hhline{---} +%row no:6 +\multicolumn{1}{|p{0.46in}}{STD\textsuperscript{1}} & +\multicolumn{1}{|p{2.81in}}{= (1 - \textbf{Pod}) $\ast$ Sgn(CNTRL) $\ast$ NT \par (Event Currency = CUR2)} & +\multicolumn{1}{|p{2.59in}}{\textbf{Led }= Tev} & + +\hhline{---} +%row no:7 +\multicolumn{1}{|p{0.46in}}{STD\textsuperscript{2}} & +\multicolumn{1}{|p{2.81in}}{= (1 - \textbf{Pod}) $\ast$ Sgn(CNTRL) $\ast$ (-1) $\ast$ NT2 \par (Event Currency = CUR2)} & +\multicolumn{1}{|p{2.59in}}{\textbf{Led }= Tev} & + +\hhline{---} +%row no:8 +\multicolumn{1}{|p{0.46in}}{CD} & +\multicolumn{1}{|p{2.81in}}{Same as PAM} & +\multicolumn{1}{|p{2.59in}}{\textbf{Pod }= RF(LEICP, Tev) \par \textbf{Led }= Tev} & + +\hhline{---} + +\end{tabular} + \end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 36 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsection{Swap (SWAPS)} +\subsubsection{Contract Events Generation} + + +%%%%%%%%%%%%%%%%%%%% Table No: 37 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \centering +\begin{tabular}{p{0.87in}p{3.21in}p{1.81in}} +\hline +%row no:1 +\multicolumn{1}{|p{0.87in}}{Event Type} & +\multicolumn{1}{|p{3.21in}}{Schedule} & +\multicolumn{1}{|p{1.81in}|}{Conditions} \\ +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.87in}}{AD} & +\multicolumn{1}{|p{3.21in}}{Same as PAM} & +\multicolumn{1}{|p{1.81in}|}{} \\ +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.87in}}{C1-events} & +\multicolumn{1}{|p{3.21in}}{all events of underlying 1 with CNTRL=RPA \par all events of underlying 1 with CNTRL=RPL \par } & +\multicolumn{1}{|p{1.81in}|}{if CNTRL=RFL \par if CNTRL=PFL \par } \\ +\hhline{---} +%row no:4 +\multicolumn{1}{|p{0.87in}}{C2-events} & +\multicolumn{1}{|p{3.21in}}{all events of underlying 2 with CNTRL=RPL \par all events of underlying 2 with CNTRL=RPA \par } & +\multicolumn{1}{|p{1.81in}|}{if CNTRL=RFL \par if CNTRL=PFL \par } \\ +\hhline{---} + +\end{tabular} + \end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 37 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsubsection{State Variables Initialization} + + +%%%%%%%%%%%%%%%%%%%% Table No: 38 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \centering +\begin{tabular}{p{0.5in}p{3.21in}p{2.19in}} +\hline +%row no:1 +\multicolumn{1}{|p{0.5in}}{State Variable} & +\multicolumn{1}{|p{3.21in}}{Contract Attribute} & +\multicolumn{1}{|p{2.19in}|}{Comments} \\ +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.5in}}{\textbf{Nvl}} & +\multicolumn{1}{|p{3.21in}}{= \textbf{Nvl }(of underlying 1) - \textbf{Nvl }(of underlying 2)} & +\multicolumn{1}{|p{2.19in}|}{} \\ +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.5in}}{\textbf{Nac}} & +\multicolumn{1}{|p{3.21in}}{= \textbf{Nac }(of underlying 1) - \textbf{Nac }(of underlying 2)} & +\multicolumn{1}{|p{2.19in}|}{} \\ +\hhline{---} +%row no:4 +\multicolumn{1}{|p{0.5in}}{\textbf{Nrt}} & +\multicolumn{1}{|p{3.21in}}{= \textbf{Nrt }(of underlying 1) - \textbf{Nrt }(of underlying 2)} & +\multicolumn{1}{|p{2.19in}|}{} \\ +\hhline{---} +%row no:5 +\multicolumn{1}{|p{0.5in}}{\textbf{Led}} & +\multicolumn{1}{|p{3.21in}}{Same as PAM} & +\multicolumn{1}{|p{2.19in}|}{} \\ +\hhline{---} +%row no:6 +\multicolumn{1}{|p{0.5in}}{\textbf{Pod}} & +\multicolumn{1}{|p{3.21in}}{Same as PAM} & +\multicolumn{1}{|p{2.19in}|}{} \\ +\hhline{---} + +\end{tabular} + \end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 38 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsubsection{Contract Events, State Transition Functions and Pay Off Functions} + + +%%%%%%%%%%%%%%%%%%%% Table No: 39 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \centering +\begin{tabular}{p{0.49in}p{1.82in}p{3.57in}p{0.04in}p{-0.02in}p{0.09in}p{-0.06in}p{-0.05in}} +\hline +%row no:1 +\multicolumn{1}{|p{0.49in}}{\textbf{Event Type}} & +\multicolumn{1}{|p{1.82in}}{\textbf{Pay Off Function}} & +\multicolumn{1}{|p{3.57in}}{\textbf{State Transition Function}} & + +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.49in}}{AD} & +\multicolumn{1}{|p{1.82in}}{= 0.0} & +\multicolumn{1}{|p{3.57in}}{\textbf{Nvl }= \textbf{Nvl }(of underlying 1) - \textbf{Nvl }(of underlying 2) \par \textbf{Nac }= \textbf{Nac }(of underlying 1) - \textbf{Nac }(of underlying 2) \par \textbf{Nrt }= \textbf{Nrt }(of underlying 1) - \textbf{Nrt }(of underlying 2) \par \textbf{Led }= Tev} & + +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.49in}}{C1- events} & +\multicolumn{1}{|p{1.82in}}{Respective payoff functions of underlying} & +\multicolumn{1}{|p{3.57in}}{Respective state transition functions of underlying} & + +\hhline{---} +%row no:4 +\multicolumn{1}{|p{0.49in}}{C2- events} & +\multicolumn{1}{|p{1.82in}}{Respective payoff functions of underlying} & +\multicolumn{1}{|p{3.57in}}{Respective state transition functions of underlying} & + +\hhline{---} + +\end{tabular} + \end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 39 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsubsection{Settlement vs. Delivery} +If DS = ‘D’ then: Delivery case + +\tab Return the events of the underlyings, i.e. C1 and C2 events + +Else (DS = ‘S’): Settlement case + +\tab For all events ev(i) \( \in C1 \cup C2 \) \par + +Define for event ev(i):\par + +\begin{adjustwidth}{0.5in}{0.0in} +Tev(i) = event date + +\end{adjustwidth} + +\begin{adjustwidth}{0.5in}{0.0in} +Tpe(i) = event type + +\end{adjustwidth} + +\begin{adjustwidth}{0.5in}{0.0in} +Vle(i) = event value + +\end{adjustwidth} + +\begin{adjustwidth}{0.5in}{0.0in} +Nvl(i) = Nominal value state variable + +\end{adjustwidth} + +\begin{adjustwidth}{0.5in}{0.0in} +Nac(i) = Nominal accrued state variable + +\end{adjustwidth} + +\begin{adjustwidth}{0.5in}{0.0in} +Nrt(i) = Nominal rate state variable + +\end{adjustwidth} + +\begin{adjustwidth}{0.5in}{0.0in} +Led(i) = Last event date state variable + +\end{adjustwidth} + +If for two events ev(i) and ev(j) with \( i \neq j \) Tev(i) = Tev(j) And Tpe(i) = Tpe(j) Then + +\tab Remove ev(j) and set + +\tab Tev(i) = Tev(i)\par + +\begin{adjustwidth}{0.5in}{0.0in} +Tpe(i) = Tpe(i)\par + +\end{adjustwidth} + +\begin{adjustwidth}{0.5in}{0.0in} +Vle(i) = Vle(i) - Vle(j)\par + +\end{adjustwidth} + +\begin{adjustwidth}{0.5in}{0.0in} +Nvl(i) = Nvl(i) - Nvl(j)\par + +\end{adjustwidth} + +\begin{adjustwidth}{0.5in}{0.0in} +Nac(i) = Nac(i) - Nac(j)\par + +\end{adjustwidth} + +\begin{adjustwidth}{0.5in}{0.0in} +Nrt(i) = Nrt(i) - Nrt(j)\par + +\end{adjustwidth} + +\begin{adjustwidth}{0.5in}{0.0in} +Led(i) = Led(i)\par + +\end{adjustwidth} + +End + +\subsection{Plain Vanilla Interest Rate Swap (SWPPV)} +\subsubsection{Contract Events Generation} + + +%%%%%%%%%%%%%%%%%%%% Table No: 40 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \centering +\begin{tabular}{p{0.34in}p{3.05in}p{2.49in}} +\hline +%row no:1 +\multicolumn{1}{|p{0.34in}}{Event Type} & +\multicolumn{1}{|p{3.05in}}{Schedule} & +\multicolumn{1}{|p{2.49in}|}{Conditions} \\ +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.34in}}{AD} & +\multicolumn{1}{|p{3.05in}}{Same as PAM} & +\multicolumn{1}{|p{2.49in}|}{} \\ +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.34in}}{PRD} & +\multicolumn{1}{|p{3.05in}}{Same as PAM} & +\multicolumn{1}{|p{2.49in}|}{Same as PAM} \\ +\hhline{---} +%row no:4 +\multicolumn{1}{|p{0.34in}}{TD} & +\multicolumn{1}{|p{3.05in}}{Same as PAM} & +\multicolumn{1}{|p{2.49in}|}{Same as PAM} \\ +\hhline{---} +%row no:5 +\multicolumn{1}{|p{0.34in}}{IED} & +\multicolumn{1}{|p{3.05in}}{Same as PAM} & +\multicolumn{1}{|p{2.49in}|}{Same as PAM} \\ +\hhline{---} +%row no:6 +\multicolumn{1}{|p{0.34in}}{PR} & +\multicolumn{1}{|p{3.05in}}{Same as PAM} & +\multicolumn{1}{|p{2.49in}|}{Same as PAM} \\ +\hhline{---} +%row no:7 +\multicolumn{1}{|p{0.34in}}{\multirowcell{8}{}{\begin{tabular}{p{0.34in}}IP\\IP\\IP\textsuperscript{1}, IP\textsuperscript{2}\\IP\textsuperscript{1}, IP\textsuperscript{2}\\\end{tabular}}} & +\multicolumn{1}{|p{3.05in}}{\multirowcell{13}{}{\begin{tabular}{p{3.05in}}single event at MD\\single schedule Sdl(Tstrt, IPCL, MD, EOMC, BDC) >= SD\\two events at MD\\two schedules Sdl(Tstrt, IPCL, MD, EOMC, BDC) >= SD\\where \\Tstrt: \\=IPANX, if IPANX != NULL,\\=IED+IPCL, else\\\end{tabular}}} & +\multicolumn{1}{|p{2.49in}|}{\multirowcell{9}{}{\begin{tabular}{p{2.49in}}if IPCL == NULL and DS == ‘S’\\else if DS == ‘S’\\else if IPCL == NULL and DS == ‘D’\\else if DS == ‘D’\\\end{tabular}}} \\ + +\hhline{~~~} +%row no:8 +\multicolumn{1}{|p{0.34in}}{\multirow{1}{*}{\begin{tabular}{p{0.34in}}\end{tabular}}} & +\multicolumn{1}{|p{3.05in}}{\multirow{1}{*}{\begin{tabular}{p{3.05in}}\end{tabular}}} & +\multicolumn{1}{|p{2.49in}|}{\multirow{1}{*}{\begin{tabular}{p{2.49in}}\end{tabular}}} \\ + +\hhline{~~~} +%row no:9 +\multicolumn{1}{|p{0.34in}}{\multirow{1}{*}{\begin{tabular}{p{0.34in}}\end{tabular}}} & +\multicolumn{1}{|p{3.05in}}{\multirow{1}{*}{\begin{tabular}{p{3.05in}}\end{tabular}}} & +\multicolumn{1}{|p{2.49in}|}{\multirow{1}{*}{\begin{tabular}{p{2.49in}}\end{tabular}}} \\ + +\hhline{~~~} +%row no:10 +\multicolumn{1}{|p{0.34in}}{RR} & +\multicolumn{1}{|p{3.05in}}{single date at MD \par single schedule Sdl(Tstrt, RRCL, MD, EOMC, BDC) >= SD \par where \par Tstrt: \par =RRANX, if RRANX != NULL, \par =IED+RRCL, else \par } & +\multicolumn{1}{|p{2.49in}|}{if RRCL == NULL \par else \par } \\ +\hhline{---} +%row no:11 +\multicolumn{1}{|p{0.34in}}{CD} & +\multicolumn{1}{|p{3.05in}}{no event \par dates of RF(LEICP) \par } & +\multicolumn{1}{|p{2.49in}|}{if RF(LEICP) == $ \{ $ $ \} $ $\ast$ \par if RF(LEICP) != $ \{ $ $ \} $ $\ast$ \par $\ast$ credit default risk factor for LEICP is an empty (==$ \{ $ $ \} $ ) or non-empty (!=$ \{ $ $ \} $ ), respectively, set of Date/Value pairs \par } \\ +\hhline{---} + +\end{tabular} + \end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 40 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsubsection{State Variables Initialization} + + +%%%%%%%%%%%%%%%%%%%% Table No: 41 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \centering +\begin{tabular}{p{0.48in}p{2.79in}p{2.63in}} +\hline +%row no:1 +\multicolumn{1}{|p{0.48in}}{State Variable} & +\multicolumn{1}{|p{2.79in}}{Contract Attribute} & +\multicolumn{1}{|p{2.63in}|}{Comments} \\ +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.48in}}{\textbf{Nvl}} & +\multicolumn{1}{|p{2.79in}}{Same as PAM} & +\multicolumn{1}{|p{2.63in}|}{CNTRL==’R’: receive fix why NT>0 \par CNTRL==’P’: pay fix why NT<0} \\ +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.48in}}{\textbf{Nrt}} & +\multicolumn{1}{|p{2.79in}}{If SD < IED Then 0.0 \par Else IPNR2} & +\multicolumn{1}{|p{2.63in}|}{Nominal interest rate of variable leg is IPNR2} \\ +\hhline{---} +%row no:4 +\multicolumn{1}{|p{0.48in}}{\textbf{Nac}} & +\multicolumn{1}{|p{2.79in}}{If IPAC != DOUBLE\_NULL Then IPAC \par Else Yfr(IP(t-1), SD) $\ast$ \textbf{Nvl }$\ast$ (IPNR\textbf{ - Nrt})} & +\multicolumn{1}{|p{2.63in}|}{Same as PAM} \\ +\hhline{---} +%row no:5 +\multicolumn{1}{|p{0.48in}}{\textbf{Nac1}} & +\multicolumn{1}{|p{2.79in}}{Yfr(IP(t-1), SD) $\ast$ \textbf{Nvl }$\ast$ IPNR} & +\multicolumn{1}{|p{2.63in}|}{} \\ +\hhline{---} +%row no:6 +\multicolumn{1}{|p{0.48in}}{\textbf{Nac2}} & +\multicolumn{1}{|p{2.79in}}{Yfr(IP(t-1), SD) $\ast$ (-1) $\ast$ \textbf{Nvl }$\ast$ \textbf{Nrt}} & +\multicolumn{1}{|p{2.63in}|}{} \\ +\hhline{---} +%row no:7 +\multicolumn{1}{|p{0.48in}}{\textbf{Led}} & +\multicolumn{1}{|p{2.79in}}{SD} & +\multicolumn{1}{|p{2.63in}|}{} \\ +\hhline{---} +%row no:8 +\multicolumn{1}{|p{0.48in}}{\textbf{Pod}} & +\multicolumn{1}{|p{2.79in}}{Same as PAM} & +\multicolumn{1}{|p{2.63in}|}{Same as PAM} \\ +\hhline{---} + +\end{tabular} + \end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 41 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsubsection{Contract Events, State Transition Functions and Pay Off Functions} + + +%%%%%%%%%%%%%%%%%%%% Table No: 42 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \centering +\begin{tabular}{p{0.49in}p{2.81in}p{2.62in}p{0.15in}p{0.05in}p{0.23in}p{0.01in}p{0.02in}} +\hline +%row no:1 +\multicolumn{1}{|p{0.49in}}{\textbf{Event Type}} & +\multicolumn{1}{|p{2.81in}}{\textbf{Pay Off Function}} & +\multicolumn{1}{|p{2.62in}}{\textbf{State Transition Function}} & + +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.49in}}{AD} & +\multicolumn{1}{|p{2.81in}}{Same as PAM} & +\multicolumn{1}{|p{2.62in}}{\textbf{Nvl} = 0.0 \par \textbf{Nac }= \textbf{Nac }+ Yfr(\textbf{Led},Tev) $\ast$ (\textbf{IPNR }- \textbf{Nrt})\textbf{ }$\ast$ \textbf{Nvl} \par \textbf{Nac1 }= \textbf{Nac1 }+ Yfr(\textbf{Led},Tev) $\ast$ IPNR\textbf{ }$\ast$ \textbf{Nvl} \par \textbf{Nac2 }= \textbf{Nac2 }+ Yfr(\textbf{Led},Tev) $\ast$ \textbf{Nrt }$\ast$ (-1)\textbf{ }$\ast$ \textbf{Nvl} \par \textbf{Led }= Tev} & + +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.49in}}{IED} & +\multicolumn{1}{|p{2.81in}}{= 0} & +\multicolumn{1}{|p{2.62in}}{\textbf{Nvl }= Sgn(CNTRL) $\ast$ NT \par \textbf{Nac }= 0.0 \par \textbf{Nac1 }= 0.0 \par \textbf{Nac2 }= 0.0 \par \textbf{Nrt }= IPNR2 \par \textbf{Led }= Tev} & + +\hhline{---} +%row no:4 +\multicolumn{1}{|p{0.49in}}{PR} & +\multicolumn{1}{|p{2.81in}}{= 0} & +\multicolumn{1}{|p{2.62in}}{\textbf{Nvl }= 0.0 \par \textbf{Nac }= 0.0 \par \textbf{Nac1 }= 0.0 \par \textbf{Nac2 }= 0.0 \par \textbf{Nrt }= 0.0 \par \textbf{Led }= Tev} & + +\hhline{---} +%row no:5 +\multicolumn{1}{|p{0.49in}}{PRD} & +\multicolumn{1}{|p{2.81in}}{Same as FXOUT} & +\multicolumn{1}{|p{2.62in}}{\textbf{Nac }= \textbf{Nac }+ Yfr(\textbf{Led},Tev) $\ast$ (\textbf{IPNR }- \textbf{Nrt})\textbf{ }$\ast$ \textbf{Nvl} \par \textbf{Nac1 }= \textbf{Nac1 }+ Yfr(\textbf{Led},Tev) $\ast$ IPNR\textbf{ }$\ast$ \textbf{Nvl} \par \textbf{Nac2 }= \textbf{Nac2 }+ Yfr(\textbf{Led},Tev) $\ast$ \textbf{Nrt }$\ast$ (-1)\textbf{ }$\ast$ \textbf{Nvl} \par \textbf{Led }= Tev} & + +\hhline{---} +%row no:6 +\multicolumn{1}{|p{0.49in}}{TD } & +\multicolumn{1}{|p{2.81in}}{Same as FXOUT} & +\multicolumn{1}{|p{2.62in}}{\textbf{Nvl }= 0.0 \par \textbf{Nac }= 0.0 \par \textbf{Nac1 }= 0.0 \par \textbf{Nac2 }= 0.0 \par \textbf{Nrt }= 0.0 \par \textbf{Led }= Tev} & + +\hhline{---} +%row no:7 +\multicolumn{1}{|p{0.49in}}{IP} & +\multicolumn{1}{|p{2.81in}}{= (1 - \textbf{Pod}) $\ast$ (\textbf{Nac + }Yfr(\textbf{Led},Tev) $\ast$ (IPNR\textbf{ }- \textbf{Nrt}) $\ast$ \textbf{Nvl})} & +\multicolumn{1}{|p{2.62in}}{\textbf{Nac }= 0.0 \par \textbf{Led }= Tev} & + +\hhline{---} +%row no:8 +\multicolumn{1}{|p{0.49in}}{IP\textsuperscript{1}} & +\multicolumn{1}{|p{2.81in}}{= (1 - \textbf{Pod}) $\ast$ (\textbf{Nac1 + }Yfr(\textbf{Led},Tev) $\ast$ IPNR $\ast$ \textbf{Nvl})} & +\multicolumn{1}{|p{2.62in}}{\textbf{Nac }= 0.0 \par \textbf{Nac1 }= 0.0 \par \textbf{Led }= Tev} & + +\hhline{---} +%row no:9 +\multicolumn{1}{|p{0.49in}}{IP\textsuperscript{2}} & +\multicolumn{1}{|p{2.81in}}{= (1 - \textbf{Pod}) $\ast$ (\textbf{Nac2 + }(-1) $\ast$ Yfr(\textbf{Led},Tev) $\ast$ \textbf{Nrt }$\ast$ \textbf{Nvl})} & +\multicolumn{1}{|p{2.62in}}{\textbf{Nac }= 0.0 \par \textbf{Nac2 }= 0.0 \par \textbf{Led }= Tev} & + +\hhline{---} +%row no:10 +\multicolumn{1}{|p{0.49in}}{RR} & +\multicolumn{1}{|p{2.81in}}{Same as PAM} & +\multicolumn{1}{|p{2.62in}}{\textbf{Nac }= \textbf{Nac }+ Yfr(\textbf{Led},Tev) $\ast$ (\textbf{IPNR }- \textbf{Nrt})\textbf{ }$\ast$ \textbf{Nvl} \par \textbf{Nac1 }= \textbf{Nac1 }+ Yfr(\textbf{Led},Tev) $\ast$ IPNR\textbf{ }$\ast$ \textbf{Nvl} \par \textbf{Nac2 }= \textbf{Nac2 }+ Yfr(\textbf{Led},Tev) $\ast$ \textbf{Nrt }$\ast$ (-1)\textbf{ }$\ast$ \textbf{Nvl} \par \textbf{Nrt }= RF(RRMO, Tev, Yfr(Tev, Tev+RRCL)) \par \textbf{Led }= Tev} & + +\hhline{---} +%row no:11 +\multicolumn{1}{|p{0.49in}}{CD} & +\multicolumn{1}{|p{2.81in}}{Same as PAM} & +\multicolumn{1}{|p{2.62in}}{\textbf{Pod }= RF(LEICP, Tev) \par \textbf{Nac }= \textbf{Nac }+ Yfr(\textbf{Led},Tev) $\ast$ (\textbf{IPNR }- \textbf{Nrt})\textbf{ }$\ast$ \textbf{Nvl} \par \textbf{Nac1 }= \textbf{Nac1 }+ Yfr(\textbf{Led},Tev) $\ast$ IPNR\textbf{ }$\ast$ \textbf{Nvl} \par \textbf{Nac2 }= \textbf{Nac2 }+ Yfr(\textbf{Led},Tev) $\ast$ \textbf{Nrt }$\ast$ (-1)\textbf{ }$\ast$ \textbf{Nvl} \par \textbf{Led }= Tev} & + +\hhline{---} + +\end{tabular} + \end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 42 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} + +\vspace{\baselineskip} + +\vspace{\baselineskip} +\subsection{Margining Contract (MRGNG)} +A generic margining contract + +\subsection{Future (FUTUR)} +Shortcut to Forward + Margining + +\subsection{Option (OPTNS)} +\subsubsection{Contract Events Generation} + + +%%%%%%%%%%%%%%%%%%%% Table No: 43 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \centering +\begin{tabular}{p{0.34in}p{3.05in}p{2.49in}} +\hline +%row no:1 +\multicolumn{1}{|p{0.34in}}{Event Type} & +\multicolumn{1}{|p{3.05in}}{Schedule} & +\multicolumn{1}{|p{2.49in}|}{Conditions} \\ +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.34in}}{AD} & +\multicolumn{1}{|p{3.05in}}{Same as PAM} & +\multicolumn{1}{|p{2.49in}|}{} \\ +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.34in}}{PRD} & +\multicolumn{1}{|p{3.05in}}{single event at PRD} & +\multicolumn{1}{|p{2.49in}|}{if PRD >= SD} \\ +\hhline{---} +%row no:4 +\multicolumn{1}{|p{0.34in}}{TD} & +\multicolumn{1}{|p{3.05in}}{single event at TD} & +\multicolumn{1}{|p{2.49in}|}{if TD >= SD} \\ +\hhline{---} +%row no:5 +\multicolumn{1}{|p{0.34in}}{MD} & +\multicolumn{1}{|p{3.05in}}{single event at MD} & +\multicolumn{1}{|p{2.49in}|}{if TD == NULL} \\ +\hhline{---} +%row no:6 +\multicolumn{1}{|p{0.34in}}{STD} & +\multicolumn{1}{|p{3.05in}}{single event at STD \par single event at MD \par } & +\multicolumn{1}{|p{2.49in}|}{if STD != NULL \par Else \par } \\ +\hhline{---} +%row no:7 +\multicolumn{1}{|p{0.34in}}{CD} & +\multicolumn{1}{|p{3.05in}}{no event \par dates of RF(LEICP) \par } & +\multicolumn{1}{|p{2.49in}|}{if RF(LEICP) == $ \{ $ $ \} $ $\ast$ \par if RF(LEICP) != $ \{ $ $ \} $ $\ast$ \par $\ast$ credit default risk factor for LEICP is an empty (==$ \{ $ $ \} $ ) or non-empty (!=$ \{ $ $ \} $ ), respectively, set of Date/Value pairs \par } \\ +\hhline{---} + +\end{tabular} + \end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 43 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsubsection{State Variables Initialization} + + +%%%%%%%%%%%%%%%%%%%% Table No: 44 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \centering +\begin{tabular}{p{0.48in}p{2.79in}p{2.63in}} +\hline +%row no:1 +\multicolumn{1}{|p{0.48in}}{State Variable} & +\multicolumn{1}{|p{2.79in}}{Contract Attribute} & +\multicolumn{1}{|p{2.63in}|}{Comments} \\ +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.48in}}{\textbf{Led}} & +\multicolumn{1}{|p{2.79in}}{SD} & +\multicolumn{1}{|p{2.63in}|}{} \\ +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.48in}}{\textbf{Pos}} & +\multicolumn{1}{|p{2.79in}}{0} & +\multicolumn{1}{|p{2.63in}|}{} \\ +\hhline{---} +%row no:4 +\multicolumn{1}{|p{0.48in}}{\textbf{Pod}} & +\multicolumn{1}{|p{2.79in}}{Same as PAM} & +\multicolumn{1}{|p{2.63in}|}{Same as PAM} \\ +\hhline{---} + +\end{tabular} + \end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 44 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsubsection{Contract Events, State Transition Functions and Pay Off Functions} + + +%%%%%%%%%%%%%%%%%%%% Table No: 45 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \centering +\begin{tabular}{p{0.4in}p{-1.56in}p{-1.56in}p{0.26in}p{0.12in}p{0.37in}p{0.06in}p{0.09in}} +\hline +%row no:1 +\multicolumn{1}{|p{0.4in}}{\textbf{Event Type}} & +\multicolumn{1}{|p{-1.56in}}{\textbf{Pay Off Function}} & +\multicolumn{1}{|p{-1.56in}}{\textbf{State Transition Function}} & + +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.4in}}{AD} & +\multicolumn{1}{|p{-1.56in}}{Same as PAM} & +\multicolumn{1}{|p{-1.56in}}{\textbf{Led }= Tev} & + +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.4in}}{PRD} & +\multicolumn{1}{|p{-1.56in}}{=\ (-1) $\ast$ (1-\textbf{Pod}) $\ast$ QT $\ast$ PPRD} & +\multicolumn{1}{|p{-1.56in}}{\textbf{Led} = Tev} & + +\hhline{---} +%row no:4 +\multicolumn{1}{|p{0.4in}}{TD } & +\multicolumn{1}{|p{-1.56in}}{= (1-\textbf{Pod}) $\ast$ QT $\ast$ PTD} & +\multicolumn{1}{|p{-1.56in}}{\textbf{Led }= Tev} & + +\hhline{---} +%row no:5 +\multicolumn{1}{|p{0.4in}}{MD} & +\multicolumn{1}{|p{-1.56in}}{= 0.0 \par if OPTP == C \par else if OPTP == P \par else if OPTP == CP \par } & +\multicolumn{1}{|p{-1.56in}}{\textbf{Led }= Tev \par \textbf{Pos }= max[0, VL(Tev, underlying, RF) - OPS1] \par \textbf{Pos }= max[0, OPS1 - VL(Tev, underlying, RF)] \par \textbf{Pos }= max[0, VL(Tev, underlying, RF) - OPS1] + max[0, OPS2 - VL(Tev, underlying, RF)]} & + +\hhline{---} +%row no:6 +\multicolumn{1}{|p{0.4in}}{STD} & +\multicolumn{1}{|p{-1.56in}}{= Sgn(CNTRL) $\ast$ (1-\textbf{Pod}) $\ast$ \textbf{Pos}} & +\multicolumn{1}{|p{-1.56in}}{\textbf{Led }= Tev \par \textbf{Pos }= 0.0} & + +\hhline{---} +%row no:7 +\multicolumn{1}{|p{0.4in}}{CD} & +\multicolumn{1}{|p{-1.56in}}{= 0.0} & +\multicolumn{1}{|p{-1.56in}}{\textbf{Pod }= RF(LEICP, Tev) \par \textbf{Led }= Tev} & + +\hhline{---} + +\end{tabular} + \end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 45 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsection{Credit Enhancement Guarantee (CEG)} +\subsubsection{Contract Events Generation} + + +%%%%%%%%%%%%%%%%%%%% Table No: 46 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \centering +\begin{tabular}{p{0.34in}p{3.05in}p{2.49in}} +\hline +%row no:1 +\multicolumn{1}{|p{0.34in}}{Event Type} & +\multicolumn{1}{|p{3.05in}}{Schedule} & +\multicolumn{1}{|p{2.49in}|}{Conditions} \\ +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.34in}}{AD} & +\multicolumn{1}{|p{3.05in}}{Same as PAM} & +\multicolumn{1}{|p{2.49in}|}{} \\ +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.34in}}{PRD} & +\multicolumn{1}{|p{3.05in}}{no event \par single event at PRD \par } & +\multicolumn{1}{|p{2.49in}|}{if PRD == NULL \par else \par } \\ +\hhline{---} +%row no:4 +\multicolumn{1}{|p{0.34in}}{MD} & +\multicolumn{1}{|p{3.05in}}{single event at MD \par single event at max(Tev among all underlyings) \par } & +\multicolumn{1}{|p{2.49in}|}{if MD != NULL \par else \par } \\ +\hhline{---} +%row no:5 +\multicolumn{1}{|p{0.34in}}{CD} & +\multicolumn{1}{|p{3.05in}}{no event \par dates of RF(LEICP) <= Tev(MD) \par } & +\multicolumn{1}{|p{2.49in}|}{if RF(LEICP) == $ \{ $ $ \} $ $\ast$ \par if RF(LEICP) != $ \{ $ $ \} $ $\ast$ \par $\ast$ credit default risk factor for LEICP is an empty (==$ \{ $ $ \} $ ) or non-empty (!=$ \{ $ $ \} $ ), respectively, set of Date/Value pairs \par } \\ +\hhline{---} +%row no:6 +\multicolumn{1}{|p{0.34in}}{STD} & +\multicolumn{1}{|p{3.05in}}{no event \par shift(dates of RF(LEICP) <= Tev(MD) ) + CEMD, CLDR, BDC, EOMC) \par } & +\multicolumn{1}{|p{2.49in}|}{if RF(LEICP) == $ \{ $ $ \} $ $\ast$ \par Else \par $\ast$ or if no CD event occurence \par } \\ +\hhline{---} +%row no:7 +\multicolumn{1}{|p{0.34in}}{FP} & +\multicolumn{1}{|p{3.05in}}{no event \par Sdl(Tstrt, FECL, Tmd, EOMC, BDC) >= SD \par where \par Tstrt: \par =FEANX, if FEANX != NULL, \par =CDD+FECL, else \par } & +\multicolumn{1}{|p{2.49in}|}{if FECL == NULL \par Else \par } \\ +\hhline{---} + +\end{tabular} + \end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 46 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsubsection{State Variables Initialization} + + +%%%%%%%%%%%%%%%%%%%% Table No: 47 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \centering +\begin{tabular}{p{0.48in}p{2.79in}p{2.63in}} +\hline +%row no:1 +\multicolumn{1}{|p{0.48in}}{State Variable} & +\multicolumn{1}{|p{2.79in}}{Contract Attribute} & +\multicolumn{1}{|p{2.63in}|}{Comments} \\ +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.48in}}{\textbf{Led}} & +\multicolumn{1}{|p{2.79in}}{SD} & +\multicolumn{1}{|p{2.63in}|}{} \\ +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.48in}}{\textbf{Pod}} & +\multicolumn{1}{|p{2.79in}}{same as PAM} & +\multicolumn{1}{|p{2.63in}|}{same as PAM} \\ +\hhline{---} +%row no:4 +\multicolumn{1}{|p{0.48in}}{\textbf{Pos}} & +\multicolumn{1}{|p{2.79in}}{0} & +\multicolumn{1}{|p{2.63in}|}{} \\ +\hhline{---} +%row no:5 +\multicolumn{1}{|p{0.48in}}{\textbf{Nvl}} & +\multicolumn{1}{|p{2.79in}}{0 \par NT \par sum(Nvl per SD over all $``$Covered Contracts$"$ ) \par } & +\multicolumn{1}{|p{2.63in}|}{if FECL == NULL or FB == ‘A’ \par else if NT != NULL \par else \par } \\ +\hhline{---} +%row no:6 +\multicolumn{1}{|p{0.48in}}{\textbf{Nrt}} & +\multicolumn{1}{|p{2.79in}}{0 \par FR \par } & +\multicolumn{1}{|p{2.63in}|}{if FECL == NULL \par else \par } \\ +\hhline{---} +%row no:7 +\multicolumn{1}{|p{0.48in}}{\textbf{Nac}} & +\multicolumn{1}{|p{2.79in}}{=0 \par =FEAC \par Yfr(FP(t-1), SD) $\ast$ \textbf{Nvl }$\ast$ \textbf{Nrt} \par Yfr(FP(t-1),SD)/Yfr(FP(t-1)+FECL) $\ast$ \textbf{Nrt} \par with FP(t-1) refers to the time of the previous Fee Payment Event according to the Fee Payment schedule \par } & +\multicolumn{1}{|p{2.63in}|}{if FECL == NULL \par else if FEAC != NULL \par else if FB == ‘N’ \par else \par } \\ +\hhline{---} + +\end{tabular} + \end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 47 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsubsection{Contract Events, State Transition Functions and Pay Off Functions} + + +%%%%%%%%%%%%%%%%%%%% Table No: 48 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \centering +\begin{tabular}{p{0.33in}p{-1.82in}p{-1.82in}p{0.08in}p{0.01in}p{0.15in}p{-0.03in}p{-0.02in}} +\hline +%row no:1 +\multicolumn{1}{|p{0.33in}}{\textbf{Event Type}} & +\multicolumn{1}{|p{-1.82in}}{\textbf{Pay Off Function}} & +\multicolumn{1}{|p{-1.82in}}{\textbf{State Transition Function}} & + +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.33in}}{AD} & +\multicolumn{1}{|p{-1.82in}}{Same as PAM} & +\multicolumn{1}{|p{-1.82in}}{if (FB == ‘N’ ) then \par \textbf{Nac }= Yfr(\textbf{Led},Tev) $\ast$ \textbf{Nrt }$\ast$ \textbf{Nvl} \par else \par \textbf{Nac }= Yfr(\textbf{Led},Tev)/Yfr(Tev-FECL, Tev) $\ast$ \textbf{Nrt} \par end \par \textbf{Led }= Tev} & + +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.33in}}{PRD} & +\multicolumn{1}{|p{-1.82in}}{= Sgn(CNTRL) $\ast$ (-1) $\ast$ (1-\textbf{Pod}) $\ast$ PPRD} & +\multicolumn{1}{|p{-1.82in}}{if (FB == ‘N’ ) then \par \textbf{Nac }= Yfr(\textbf{Led},Tev) $\ast$ \textbf{Nrt }$\ast$ \textbf{Nvl} \par else \par \textbf{Nac }= Yfr(\textbf{Led},Tev)/Yfr(Tev-FECL, Tev) $\ast$ \textbf{Nrt} \par end \par \textbf{Led }= Tev} & + +\hhline{---} +%row no:4 +\multicolumn{1}{|p{0.33in}}{FP} & +\multicolumn{1}{|p{-1.82in}}{= (1-\textbf{Pod}) $\ast$ ( \textbf{Nac + } fac) \par with \par if (FEB == ‘N’ ) then \par fac = Yfr(\textbf{Led},Tev) $\ast$ \textbf{Nrt }$\ast$ \textbf{Nvl} \par else \par fac = Yfr(\textbf{Led},Tev)/Yfr(Tev-FECL, Tev) $\ast$ \textbf{Nrt} \par \textbf{ }end} & +\multicolumn{1}{|p{-1.82in}}{\textbf{Nac }= 0.0 \par \textbf{Led }= Tev} & + +\hhline{---} +%row no:5 +\multicolumn{1}{|p{0.33in}}{MD} & +\multicolumn{1}{|p{-1.82in}}{= 0.0} & +\multicolumn{1}{|p{-1.82in}}{\textbf{Led }= Tev \par \textbf{Nvl }= 0 \par \textbf{Nrt }= 0 \par \textbf{Nac }= 0\textbf{\ \ }} & + +\hhline{---} +%row no:6 +\multicolumn{1}{|p{0.33in}}{CD} & +\multicolumn{1}{|p{-1.82in}}{= 0.0} & +\multicolumn{1}{|p{-1.82in}}{if NT != NULL then \par \ \ \ \ \ \textbf{Pos }= NT \par else if CEGE == ‘N’ then \par \textbf{\ \ \ \ \ Pos }= sum(Nvl at Tev over all $``$Covered Contracts$"$ ) \par else if CEGE == ‘I’ then \par \textbf{\ \ \ \ \ Pos }= sum(Nvl+Nac at Tev over all $``$Covered Contracts$"$ ) \par else (if CEGE == $``$M$"$ ) \par \ \ \ \ \ \textbf{Pos }= sum(VL(Tev, ct, RF) over all ct in $``$Covered Contracts$"$ ) \par end \par \textbf{Pos }= CECV $\ast$ \textbf{Pos }+ \textbf{Nac }+ fac \par \textbf{Pod }= RF(LEICP, Tev) \par \textbf{Led }= Tev \par \textbf{Nac }= 0 \par with \par if (FB == ‘N’ ) then \par fac = Yfr(\textbf{Led},Tev) $\ast$ \textbf{Nrt }$\ast$ \textbf{Nvl} \par else \par fac = Yfr(\textbf{Led},Tev)/Yfr(Tev-FECL, Tev) $\ast$ \textbf{Nrt} \par end} & + +\hhline{---} +%row no:7 +\multicolumn{1}{|p{0.33in}}{STD} & +\multicolumn{1}{|p{-1.82in}}{= (1-\textbf{Pod}) $\ast$ \textbf{Pos}} & +\multicolumn{1}{|p{-1.82in}}{\textbf{Led }= Tev \par \textbf{Pos }= 0.0} & + +\hhline{---} + +\end{tabular} + \end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 48 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsection{Credit Enhancement Collateral (CEC)} +\subsubsection{Contract Events Generation} + + +%%%%%%%%%%%%%%%%%%%% Table No: 49 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \centering +\begin{tabular}{p{0.34in}p{3.05in}p{2.49in}} +\hline +%row no:1 +\multicolumn{1}{|p{0.34in}}{Event Type} & +\multicolumn{1}{|p{3.05in}}{Schedule} & +\multicolumn{1}{|p{2.49in}|}{Conditions} \\ +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.34in}}{AD} & +\multicolumn{1}{|p{3.05in}}{Same as PAM} & +\multicolumn{1}{|p{2.49in}|}{} \\ +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.34in}}{MD} & +\multicolumn{1}{|p{3.05in}}{single event at max(Tev among all underlyings)} & +\multicolumn{1}{|p{2.49in}|}{} \\ +\hhline{---} +%row no:4 +\multicolumn{1}{|p{0.34in}}{CD} & +\multicolumn{1}{|p{3.05in}}{no event \par dates of RF(LEICP) <= Tev(MD) \par } & +\multicolumn{1}{|p{2.49in}|}{if RF(LEICP) == $ \{ $ $ \} $ $\ast$ \par if RF(LEICP) != $ \{ $ $ \} $ $\ast$ \par $\ast$ credit default risk factor for LEICP is an empty (==$ \{ $ $ \} $ ) or non-empty (!=$ \{ $ $ \} $ ), respectively, set of Date/Value pairs \par } \\ +\hhline{---} +%row no:5 +\multicolumn{1}{|p{0.34in}}{STD} & +\multicolumn{1}{|p{3.05in}}{no event \par shift(dates of RF(LEICP) <= Tev(MD) ) + CEMD, CLDR, BDC, EOMC) \par } & +\multicolumn{1}{|p{2.49in}|}{if RF(LEICP) == $ \{ $ $ \} $ $\ast$ \par Else \par $\ast$ or if no CD event occurence \par } \\ +\hhline{---} + +\end{tabular} + \end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 49 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsubsection{State Variables Initialization} + + +%%%%%%%%%%%%%%%%%%%% Table No: 50 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \centering +\begin{tabular}{p{0.48in}p{2.79in}p{2.63in}} +\hline +%row no:1 +\multicolumn{1}{|p{0.48in}}{State Variable} & +\multicolumn{1}{|p{2.79in}}{Contract Attribute} & +\multicolumn{1}{|p{2.63in}|}{Comments} \\ +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.48in}}{\textbf{Led}} & +\multicolumn{1}{|p{2.79in}}{SD} & +\multicolumn{1}{|p{2.63in}|}{} \\ +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.48in}}{\textbf{Pod}} & +\multicolumn{1}{|p{2.79in}}{0} & +\multicolumn{1}{|p{2.63in}|}{} \\ +\hhline{---} +%row no:4 +\multicolumn{1}{|p{0.48in}}{\textbf{Pos}} & +\multicolumn{1}{|p{2.79in}}{0} & +\multicolumn{1}{|p{2.63in}|}{} \\ +\hhline{---} + +\end{tabular} + \end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 50 ends here %%%%%%%%%%%%%%%%%%%% + + +\vspace{\baselineskip} +\subsubsection{Contract Events, State Transition Functions and Pay Off Functions} + + +%%%%%%%%%%%%%%%%%%%% Table No: 51 starts here %%%%%%%%%%%%%%%%%%%% + + +\begin{table}[H] + \centering +\begin{tabular}{p{0.45in}p{1.77in}p{3.77in}p{0.15in}p{0.05in}p{0.23in}p{0.01in}p{0.02in}} +\hline +%row no:1 +\multicolumn{1}{|p{0.45in}}{\textbf{Event Type}} & +\multicolumn{1}{|p{1.77in}}{\textbf{Pay Off Function}} & +\multicolumn{1}{|p{3.77in}}{\textbf{State Transition Function}} & + +\hhline{---} +%row no:2 +\multicolumn{1}{|p{0.45in}}{AD} & +\multicolumn{1}{|p{1.77in}}{Same as PAM} & +\multicolumn{1}{|p{3.77in}}{\textbf{Led} = Tev} & + +\hhline{---} +%row no:3 +\multicolumn{1}{|p{0.45in}}{MD} & +\multicolumn{1}{|p{1.77in}}{= 0.0} & +\multicolumn{1}{|p{3.77in}}{\textbf{Led }= Tev} & + +\hhline{---} +%row no:4 +\multicolumn{1}{|p{0.45in}}{CD} & +\multicolumn{1}{|p{1.77in}}{= 0.0} & +\multicolumn{1}{|p{3.77in}}{if CEGE == ‘N’ then \par \textbf{\ \ \ \ \ Pos }= max(0, \par sum(Nvl at Tev over all $``$Covered Contracts$"$ ) - sum(VL(Tev, ct, RF) over all ct in $``$Covering Contracts$"$ ) \par ) \par else if CEGE == ‘I’ then \par \textbf{\ \ \ \ \ Pos }= max(0, \par sum(Nvl+Nac at Tev over all $``$Covered Contracts$"$ ) - sum(VL(Tev, ct, RF) over all ct in "Covering Contracts" ) \par ) \par else (if CEGE == $M$ ) \par \ \ \ \ \ \textbf{Pos }= max(0, \par sum(VL(Tev, ct, RF) over all ct in "Covered Contracts" ) - sum(VL(Tev, ct, RF) over all ct in "Covering Contracts" ) \par ) \par end \par \textbf{Pod }= RF(LEICP, Tev) \par \textbf{Led }= Tev} & + +\hhline{---} +%row no:5 +\multicolumn{1}{|p{0.45in}}{STD} & +\multicolumn{1}{|p{1.77in}}{= (1-\textbf{Pod}) $\ast$ \textbf{Pos}} & +\multicolumn{1}{|p{3.77in}}{\textbf{Led }= Tev \par \textbf{Pos }= 0.0} & + +\hhline{---} + +\end{tabular} + \end{table} + + +%%%%%%%%%%%%%%%%%%%% Table No: 51 ends here %%%%%%%%%%%%%%%%%%%% + + +\fi + + +\bibliography{bibliography} + +\end{document} diff --git a/bibliography.bib b/bibliography.bib new file mode 100644 index 0000000..5b44fb3 --- /dev/null +++ b/bibliography.bib @@ -0,0 +1 @@ +% repository of tex-bib references diff --git a/build.sh b/build.sh new file mode 100644 index 0000000..37c632a --- /dev/null +++ b/build.sh @@ -0,0 +1,37 @@ +#!/usr/bin/env bash + +## +## Usage: build.sh +## +## Note: no arguments to the build script currently in use +## + + +set -e + +rm -rf build_options.tex + +if [ -d ".git" ]; then + +TAG=`git describe` || true +SHA=`git rev-parse --short --verify HEAD` +DATE=`git show -s --format="%cd" --date=short HEAD` +REV="$TAG-$SHA-$DATE" +echo "\def\VersionNumber{$REV}" >> build_options.tex + +fi + + +if grep '=========' actus-techspecs.tex +then + echo "merge conflict?" + exit 1 +fi + +mkdir -p build +pdflatex -output-directory=build -interaction=errorstopmode -halt-on-error actus-techspecs.tex && \ +bibtex build/actus-techspecs && \ +pdflatex -output-directory=build 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