Option Pricing Models

Introduction

This repository contains tools for calculating European option prices using three different methods:

1. Black-Scholes model
2. Monte Carlo simulation
3. Binomial model

It consists of two main parts:

1. Python Library (option_pricing/): A flexible and efficient Python package for option pricing, designed to be easily plugged into backtesting systems.
2. Web Simulation (docs/): A browser-based simulation for visualizing option pricing (hosted on GitHub Pages).

Option Pricing Methods

1. Black-Scholes Model

A mathematical model used to calculate the theoretical price of European-style options.

2. Monte Carlo Simulation

A probabilistic method that uses random sampling to estimate option prices. The Python implementation is vectorized for high performance.

3. Binomial Model

A discrete-time model (Binomial Tree) for calculating option prices.

Project Structure

• option_pricing/: Python package containing model implementations.
  • black_scholes.py: Black-Scholes model (class and function).
  • monte_carlo.py: Monte Carlo simulation (class and vectorized function).
  • binomial.py: Binomial Tree model (class and function).
• docs/: Web-based simulation (HTML/JS/CSS) for GitHub Pages.
• verify_real_data.py: Script to verify models using real-world data from Yahoo Finance.
• requirements.txt: Python dependencies.

Usage

Python Library

Install dependencies:

pip install -r requirements.txt

Example usage:

from option_pricing import black_scholes_price, monte_carlo_price

S = 100  # Spot Price
K = 100  # Strike Price
T = 1.0  # Time to Maturity (Years)
r = 0.05 # Risk-free Rate
sigma = 0.2 # Volatility

price_bs = black_scholes_price(S, K, T, r, sigma, 'call')
print(f"Black-Scholes Price: {price_bs}")

price_mc = monte_carlo_price(S, K, T, r, sigma, 'call')
print(f"Monte Carlo Price: {price_mc}")

Verification with Real Data

You can verify the models against real market data (fetched via yfinance) by running:

python verify_real_data.py

Bid-Ask Spread Prediction

To estimate the fair Bid and Ask prices for an option based on its Last Price, Strike, and Underlying Price, use estimate_fair_value.py. This uses a polynomial model trained on market data to predict the spread.

python estimate_fair_value.py <LAST_PRICE> <STRIKE> <UNDERLYING> <Calendar_DAYS_TO_EXPIRE> [optional: --type call/put]

Note on Days to Expiration: For option pricing models (Black-Scholes), it is standard to use Calendar Days (365 days/year) because interest accumulates daily. While trading days (252) are often used for volatility, using calendar days for time-to-decay is the convention. Please input the number of calendar days until expiration (e.g., 30 for one month).

Example:

python estimate_fair_value.py 10.50 200 205 30 --type call

Web Simulation

The web-based simulation is automatically deployed to GitHub Pages. You can access it here: Option Pricing Simulation

(Note: Replace hallop with your GitHub username if different.)

To run locally, simply open docs/index.html in your web browser.