Options Pricing Engine

A Python-based options pricing engine implementing multiple pricing models, Greeks, and quantitative analysis tools for European options.

---

Overview

This project builds a modular options pricing library from scratch, implementing:

• Analytical pricing (Black-Scholes)
• Numerical methods (Binomial Tree)
• Simulation methods (Monte Carlo)
• Greeks (risk sensitivities)
• Implied volatility solver
• Convergence and sensitivity analysis
• Visualisation and notebook-based exploration

The goal is to demonstrate both quantitative finance knowledge and software engineering skills relevant to quantitative developer roles.

---

Features

• Black-Scholes pricing model

• Binomial tree pricing model

• Monte Carlo simulation pricing

• Greeks calculation:

  • Delta
  • Gamma
  • Vega
  • Theta
  • Rho

• Implied volatility solver (numerical root finding)

• Model comparison and convergence analysis

• Sensitivity analysis and payoff visualisation

• Jupyter notebook for interactive analysis

• Full test suite using pytest

---

Project Structure

Options_Pricing_Engine/
│
├── src/
│   ├── models/           # Pricing models
│   ├── greeks/           # Greeks calculations
│   ├── utils/            # Helpers, validation, implied volatility
│   ├── visualisation/    # Plotting functions
│   └── main.py           # Example execution
│
├── tests/                # Unit tests
├── notebooks/            # Analysis notebook
├── outputs/figures/      # Generated figures
├── examples/             # Example scripts (e.g. export figures)
│
├── requirements.txt
└── README.md

---

Models Implemented

Black-Scholes

Closed-form analytical solution for pricing European options under log-normal assumptions.

Binomial Tree

Discrete-time model that approximates the continuous price process and converges to Black-Scholes as the number of steps increases.

Monte Carlo

Simulation-based approach using random sampling of price paths, useful for more complex derivatives.

---

Example Results

Model Comparison

Binomial Convergence

Monte Carlo Convergence

---

Sensitivity Analysis

Price vs Stock Price

Price vs Volatility

Delta vs Stock Price

Vega vs Volatility

---

Payoff Diagram

---

Example Usage

from models.black_scholes import black_scholes_price

price = black_scholes_price("call", 42, 40, 0.5, 0.05, 0.2)
print(price)

---

Running the Project

Install dependencies

pip install -r requirements.txt

Run example

python src/main.py

Export all figures

python examples/export_figures.py

---

Testing

Run all tests with:

pytest

---

Notebook Analysis

See:

notebooks/options_pricing_analysis.ipynb

Includes:

• Model comparisons
• Convergence analysis
• Sensitivity plots
• Greeks interpretation

---

Future Improvements

• Real market data integration (e.g. using yfinance)
• Volatility surface / volatility smile
• American options pricing
• Performance optimisation (NumPy / C++)
• Strategy development using model mispricing

---

Author

Olly Newport