Black-Scholes Option Pricing with Greeks Analysis

This Python program calculates the price of options using the Black-Scholes model and provides a detailed sensitivity analysis of Greeks, including Delta, Gamma, Vega, Theta, and Rho. It also allows users to update parameters interactively to observe changes in the Greeks and option prices.

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Features

• Option Pricing: Computes the price of European call and put options using the Black-Scholes formula.
• Greeks Analysis: Calculates the sensitivities (Delta, Gamma, Vega, Theta, Rho) for a given option.
• Interactive Mode: Allows users to update parameters (stock price, strike price, maturity, risk-free rate, volatility) to see real-time updates to Greeks and option prices.
• User-Friendly Input: Guides users through input steps for accurate calculations.

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How It Works

1. User Inputs:

   • Option type: Call or Put
   • Current stock price (S)
   • Strike price (K)
   • Maturity date (YYYY-MM-DD)
   • Risk-free interest rate (r) as a decimal (e.g., 0.05 for 5%)
   • Volatility (σ) as a decimal (e.g., 0.2 for 20%)

2. Black-Scholes Model:

   • Computes the option price using the following formula: [ d1 = \frac{\ln(\frac{S}{K}) + (r + \frac{\sigma^2}{2})T}{\sigma\sqrt{T}} ] [ d2 = d1 - \sigma\sqrt{T} ]
     • Call option price: ( S \cdot N(d1) - K \cdot e^{-rT} \cdot N(d2) )
     • Put option price: ( K \cdot e^{-rT} \cdot N(-d2) - S \cdot N(-d1) )

3. Sensitivity Analysis (Greeks):

   • Delta: Sensitivity to stock price changes.
   • Gamma: Sensitivity of Delta to stock price changes.
   • Vega: Sensitivity to volatility changes.
   • Theta: Sensitivity to time decay.
   • Rho: Sensitivity to changes in the risk-free rate.

4. Interactive Parameter Updates:

   • Modify parameters to see updated option prices and Greeks.

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Requirements

• Python 3.x
• Libraries:
  • numpy
  • scipy

Install required libraries using pip:

pip install numpy scipy

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Usage

1. Clone the Repository:

   git clone https://github.com/yourusername/black-scholes-option-pricing.git
   cd black-scholes-option-pricing

2. Run the Program:

   python black_scholes.py

3. Follow the Prompts:

   • Enter the required inputs when prompted (option type, stock price, strike price, etc.).
   • View the calculated option price and Greeks.

4. Update Parameters:

   • Choose to update parameters interactively and observe how the option price and Greeks change.

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Example Output

Initial Results:

Enter option type (call/put): call
Enter current stock price (S): 100
Enter strike price (K): 105
Enter maturity date (YYYY-MM-DD): 2025-01-01
Enter risk-free interest rate (r) as a decimal (e.g., 0.05 for 5%): 0.03
Enter volatility (sigma) as a decimal (e.g., 0.2 for 20%): 0.25

Option Price:
10.5724

Sensitivity Analysis of Greeks:
Delta: 0.5834
Gamma: 0.0158
Vega: 39.4745
Theta: -0.0452
Rho: 22.9174

Updated Results:

Do you want to update any parameters to see the new Greeks? (yes/no): yes

Which parameter would you like to update?
1. Stock price (S)
2. Strike price (K)
3. Maturity date
4. Risk-free interest rate (r)
5. Volatility (sigma)
Enter the number of your choice: 1
Enter new stock price (S): 110

Updated Option Price:
15.8924

Updated Sensitivity Analysis of Greeks:
Delta: 0.6835
Gamma: 0.0137
Vega: 37.2604
Theta: -0.0387
Rho: 31.2875