This repository presents a comparative study of two foundational models used in European option pricing: the Binomial Tree model and the Black-Scholes closed-form formula.
This project aims to:
- Implement pricing algorithms for European call and put options using:
- β Binomial Tree method (with adjustable steps)
- β Black-Scholes formula (including Option Greeks)
- Compare mathematical assumptions (discrete vs. continuous time, volatility, etc.)
- Study convergence of Binomial prices to Black-Scholes values
- Analyze sensitivity to:
- Volatility (Ο)
- Time to maturity (T)
- Risk-free interest rate (r)
- Strike price (K)
- Validate with real market data (e.g., SPY, AAPL) and assess model performance
- Binomial model offers flexibility but increases in complexity with time steps
- Black-Scholes is efficient and elegant, but depends on strict assumptions
- Real-world data introduces imperfections that influence model accuracy
- Python
- NumPy, Pandas
- Matplotlib
- yFinance
- β Binomial Tree option pricer with custom steps
- β Black-Scholes pricer with Greeks (Delta, Gamma, Theta, Vega, Rho)
- β Price convergence analysis
- β Sensitivity analysis for key parameters
- β Real market comparison
- β
Performance report covering:
- Pricing accuracy
- Computational efficiency
- Error convergence over steps
π¦ Option Pricing Project
βββ European_Option_Pricing_Comparison.ipynb # Main project notebook
βββ README.md # This file
- Black-Scholes assumes constant volatility & risk-free rates
- Binomial Tree becomes slower with large number of steps
- Market prices may reflect American-style options or implied volatility
- Options, Futures and Other Derivatives β John C. Hull (Chapters 10β13, 15)
- yFinance documentation
- Quantitative finance resources