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Black Scholes Merton Model - Python Implementation

Nov 27, 2022

Summary
The Python code implements the Black-Scholes-Merton (BSM) option pricing model, allowing for flexible pricing and analysis of option contracts with customizable parameters. It calculates option prices and Greek measures, supports both long and short positions, and employs the Newton-Raphson method for volatility approximation. Advantages include flexibility, comprehensiveness, readability, and ease of use. However, it lacks support for American options and may require further optimization for numerical stability. Integration with real-world data sources would enhance its practical applicability.
Github Repo.

Project Overview

The implementation facilitates flexible pricing and analysis of option contracts. Users can customize parameters to suit various financial scenarios, making the tool adaptable to different market conditions. The code's ability to compute both option prices and Greek measures adds to its analytical depth.

Technical Details

The core of the system employs the Newton-Raphson method, known for its efficiency in approximating volatility, which is crucial for accurate option pricing. This numerical approach enhances the model’s capability to deliver reliable results promptly.

Advantages and Limitations

The main advantages of this implementation include its flexibility, comprehensiveness, readability, and user-friendliness. These qualities make it accessible to a wide range of users, from financial analysts to academic researchers. However, the current version does not support American options, representing a limitation that could be addressed in future updates. Additionally, the numerical methods employed may require optimization to improve numerical stability.

Future Directions

To enhance its practical applicability, future development could integrate real-world data sources, enabling real-time financial analysis. Expanding the model to support American options and optimizing the numerical algorithms for greater stability are also potential areas for improvement.

Usage

#option = BsmOption(isLong, Type, Spot, Strike, DTE, Risk-Free Rate, Volatility, marketValue, Dividend Yield %)

#Option init using market value
option = BsmOption(True, 'C', 8.86, 10, 18, 0.06, value=2.70)
print("Price = " + str(option.price()))
print("Sigma = " + str(option.sigma()))
print("Delta = " + str(option.delta()))
print("Gamma = " + str(option.gamma()))
print("Vega  = " + str(option.vega()))
print("Theta = " + str(option.theta()))
print("Rho   = " + str(option.rho()))


#Option init using vol
option = BsmOption(True, 'C', 8.86, 10, 18, 0.06, sigma=.7)
print("Price = " + str(option.price()))
print("Sigma = " + str(option.sigma()))
print("Delta = " + str(option.delta()))
print("Gamma = " + str(option.gamma()))
print("Vega  = " + str(option.vega()))
print("Theta = " + str(option.theta()))
print("Rho   = " + str(option.rho()))


#Position init (Short Straddle)
position = OptionPosition()
call = BsmOption(False, 'C', 15.00, 15, 53, 0.05, value=1.75)
put = BsmOption(False, 'P', 15.00, 15, 53, 0.05, value=1.68)
position.addLegs([call, put])
print("Price = " + str(position.price()))
print("Sigma = " + str(position.sigma()))
print("Delta = " + str(position.delta()))
print("Gamma = " + str(position.gamma()))
print("Vega  = " + str(position.vega()))
print("Theta = " + str(position.theta()))
print("Rho   = " + str(position.rho()))