This project implements a vectorized Binomial Option Pricing Model in Python to evaluate European and American options. The model is validated against the Black-Scholes analytical benchmark and calibrated to real-world Amazon (AMZN) market data.
- Vectorized Implementation: High-performance Numpy implementation of the CRR Binomial Tree.
- American Options: Handles early exercise boundary conditions.
- Market Calibration: Numerical root-finding (SLSQP) to extract Implied Volatility from market prices.
-
Convergence Analysis: Visualizes the asymptotic convergence to Black-Scholes as
$N \to \infty$ .
- Python: NumPy, SciPy (Optimization/Stats), Matplotlib
- LaTeX: For the mathematical documentation and final report.
- Amazon (AMZN) Analysis: found a significant volatility risk premium, with implied volatility (~41%) exceeding historical volatility.
- Early Exercise: Confirmed that American Put premiums are driven by the optimal stopping boundary in deep ITM conditions.
code/: Contains the Jupyter Notebook (.ipynb) with the pricing engine.report/: Contains the LaTeX source code and the final PDF report.