Vanilla options calculator

Black-Scholes model in pure Python

Without SciPy, NumPy or other external dependencies

PyOption Pricing & Greeks

This project provides a set of tools in Python for calculating the theoretical price of options using the Black-Scholes-Merton (BSM) model, as well as the main Greeks (Delta, Vega, Theta, and Gamma). Additionally, it offers functionalities to visualize the P&L (Profit and Loss) and the Greeks of an option portfolio under different price scenarios and expiration dates.

Key Features

• Option Pricing: Implementation of the Black-Scholes-Merton model to calculate the theoretical price of call and put options.
• Greeks Calculation: Provides functions to calculate option sensitivities:
  • Delta ($\mathrm{\Delta }$): Measures the sensitivity of the option price to a change in the underlying asset price.
  • Vega ($\nu$): Measures the sensitivity of the option price to a change in the implied volatility of the underlying asset.
  • Theta ($\mathrm{\Theta }$): Measures the sensitivity of the option price to the passage of time (time decay).
  • Gamma ($\mathrm{\Gamma }$): Measures the rate of change of Delta with respect to a change in the underlying asset price.
• Portfolio Analysis: Allows for the analysis of a portfolio composed of multiple options and the underlying asset, calculating the total Greeks and P&L of the portfolio.
• Graphical Visualization: Utilizes the matplotlib library to generate graphs of:
  • Portfolio P&L as a function of the underlying asset price for different expiration dates.
  • The Greeks (Delta, Theta, Vega, Gamma) of the portfolio as a function of the underlying asset price for different expiration dates.
• (In Development) Delta Neutral Search: The searching.py module appears to contain in-development functionalities for finding prices where a specific individual option neutralizes the portfolio's Delta.

How to Use

Prerequisites

• Python 3.x
• matplotlib library

Installation

1. Ensure you have Python 3 installed on your system.
2. Install the matplotlib library using pip if you haven't already:

   pip install matplotlib

Usage Examples

1. Calculating Greeks for an Option: Run the exemple_greeks.py script:

   python exemple_greeks.py

   This script demonstrates how to instantiate the BSM class and calculate the theoretical price, Delta, Theta, Vega, and Gamma for a Bitcoin option with example parameters.

2. Visualizing Portfolio P&L and Greeks: Run the exemple_plot.py script:

   python exemple_plot.py

   This script uses the Plot class to generate graphs showing the P&L, Delta, Theta, Vega, and Gamma of an option portfolio defined within the script, across different expiration dates. The legends on the graphs indicate the number of days until expiration.

3. (In Development) Delta Neutral Search: The searching.py script contains a Search class with a searchDelta method. To use it (remember it's under development), you can execute the script and observe the output:

   python searching.py

   The output displays a table with the underlying asset price, option type, strike price, quantity, individual option Delta, total portfolio Delta, and the theoretical option price, searching for points where the individual option's Delta offsets the total portfolio Delta.

Project Structure

• bsm.py: Contains the implementation of the BSM class with methods to calculate the theoretical price (theo), the Greeks (delta, vega, theta, gamma), and the standard normal distribution functions (pdf and cdf).
• pricing.py: Extends the BSM class and implements methods to calculate the total Greeks (deltaFull, vegaFull, thetaFull, gammaFull) and the P&L (p_l) of a portfolio of assets and options.
• plot.py: Utilizes the Pricing class and the matplotlib library to generate graphs of the portfolio's P&L and Greeks as a function of the underlying asset price for different expiration dates.
• exemple_greeks.py: An example script demonstrating how to use the BSM class to calculate the Greeks of a single option.
• exemple_plot.py: An example script that uses the Plot class to generate graphical visualizations of an option portfolio.
• searching.py: A script containing a Search class with functionalities under development to assist in finding delta-neutral positions, comparing the delta of an individual option with the total portfolio delta.

Contributing

Contributions are welcome! Feel free to open issues to report bugs or suggest improvements, and submit pull requests with your implementations.