📘 Project 2: Option Pricing Models

This repository explores classical option pricing models widely used in financial engineering.
Specifically, we implement and analyze two key methodologies: the Black-Scholes-Merton model and the Binomial Tree method. These tools are fundamental for valuing European options and understanding dynamic hedging strategies.

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📂 Notebook Overview

📄 Proj2_BlackScholesMerton.ipynb – Black-Scholes-Merton (BSM) Model

This notebook implements the closed-form Black-Scholes-Merton model for pricing European call and put options.
Key components include:

• Derivation of BSM formula using standard mathematical functions
• Application to real-world option parameters (e.g., volatility, interest rate, maturity)
• Calculation of option Greeks (Delta, Gamma, Vega, Theta, Rho)
• Sensitivity analysis of option prices to underlying parameters

This model assumes continuous trading, log-normal price distribution, and no arbitrage.

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📄 Proj2_BTREE.ipynb – Binomial Tree Option Pricing

This notebook implements a discrete-time binomial tree model for European and American options.
Key components include:

• Construction of an up/down binomial lattice
• Recursive backward valuation of call/put options
• Visualization of convergence to BSM price as steps increase
• Comparison between European and American style pricing

The binomial method is especially useful for American-style options that cannot be priced with BSM's closed-form solution.

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🔍 Concepts Covered

• 📈 European Option Valuation
• 🧮 Risk-Neutral Pricing and Arbitrage-Free Framework
• 🏗 Binomial Tree Lattice Construction
• 🎯 Sensitivity (Greeks) of Option Pricing Models
• 🔁 Convergence of Discrete Models to Continuous Models

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🛠 Libraries Used

• Python Standard Math Library
• NumPy
• Matplotlib (for plotting, optional)

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📁 Folder Structure

financial-engineering2/
└── project2_option_pricing/
├── Proj2_BlackScholesMerton.ipynb # Closed-form BSM pricing model
├── Proj2_BTREE.ipynb # Binomial tree implementation
└── README.md

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✅ Notes

These notebooks are developed for educational purposes as part of a university course on Financial Engineering.
They serve as a practical introduction to quantitative option pricing.