Heston Model for European Option Pricing

This Python program calculates the price of European options using the Heston Model, a widely used stochastic volatility model in quantitative finance. The program allows users to input key parameters, computes the option price through numerical integration, and offers a modular design for further extensions.

Features

• Option Pricing: Calculates European option prices based on the Heston stochastic volatility model.
• User-Friendly Interface: Prompts users to input the required model parameters interactively.
• Numerical Integration: Utilizes the characteristic function of the Heston model for accurate pricing through integration.
• Extensibility: The implementation allows for easy customization and extension of the model.

How It Works

1. Model Parameters:

   • ( S_0 ): Initial price of the underlying asset.
   • ( K ): Strike price.
   • ( T ): Time to maturity (in years).
   • ( r ): Risk-free interest rate.
   • ( v_0 ): Initial variance (square of the initial volatility).
   • ( \theta ): Long-term average variance.
   • ( \kappa ): Speed of mean reversion of variance to its long-term average.
   • ( \sigma ): Volatility of volatility (vol of var).
   • ( \rho ): Correlation between asset price and volatility.

2. Characteristic Function:

   • Computes the characteristic function of the log of the asset price under the risk-neutral measure.

3. Numerical Integration:

   • Integrates the real part of the characteristic function to calculate the option price.

4. User Interaction:

   • Prompts users to enter model parameters interactively.

Requirements

• Python 3.x
• Libraries:
  • numpy
  • scipy
  • matplotlib (optional, for visualization if extended)

Install required libraries using pip:

pip install numpy scipy matplotlib

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Usage

1. Clone the Repository:

   git clone https://github.com/yourusername/heston-model-option-pricing.git
   cd heston-model-option-pricing

2. Run the Program:

   python heston_model.py

3. Follow the Prompts:

   • Enter the required inputs when prompted (initial price, strike price, maturity, etc.).
   • View the calculated European option price.

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Example

Input:

Please enter the parameters for the Heston model:
Initial price of the underlying asset (e.g., 100): 100
Strike price (e.g., 100): 100
Time to maturity (in years) (e.g., 1): 1
Risk-free rate (e.g., 0.05): 0.05
Initial volatility (variance) (e.g., 0.04): 0.04
Long-term variance (e.g., 0.04): 0.04
Rate of mean reversion (e.g., 2.0): 2.0
Volatility of volatility (e.g., 0.5): 0.5
Correlation between asset price and volatility (e.g., -0.7): -0.7

Output:

The European option price using the Heston model is: 12.3456

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File Structure

heston-model-option-pricing/
│
├── heston_model.py      # Main Python script for option pricing
├── README.md            # Documentation file

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Key Functions

• HestonModel.characteristic_function(u):
  • Computes the characteristic function of the Heston model.
• HestonModel.heston_price(num_points=1000, max_iter=10):
  • Calculates the European option price using numerical integration.
• get_input(prompt, type_cast=float):
  • Helper function for interactive user input with type validation.

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Limitations

• Assumes constant risk-free rate and no dividends.
• Pricing is specific to European options and may not apply to American or exotic options without modifications.