Quant Trading Lab 📈

A comprehensive collection of quantitative finance projects implemented in Python, covering stochastic simulations, derivatives pricing, volatility calibration, and algorithmic trading strategies.

📋 Overview

This repository serves as a research and development playground for quantitative trading algorithms and financial engineering models. Each project includes a core implementation, standardized data outputs, and a detailed LaTeX report.

📂 Project Directory

1. Option Pricing (PDE)

• Description: Numerical solution of the Black-Scholes PDE using Finite Difference Methods (Crank-Nicolson).
• Key Concepts: Heat equation mapping, stability analysis, Greeks calculation.

2. SDE Simulation

• Description: High-performance simulation of Stochastic Differential Equations.
• Key Concepts: Geometric Brownian Motion, Ornstein-Uhlenbeck processes, Euler-Maruyama scheme, convergence analysis.

3. Volatility Calibration

• Description: Calibration of local and stochastic volatility models to market data.
• Key Concepts: Dupire's formula, Heston model, Levenberg-Marquardt optimization, volatility surfaces.

4. Pairs Trading (Stat-Arb)

• Description: Statistical arbitrage strategy based on cointegration between equity pairs (e.g., XOM/CVX).
• Key Concepts: Engle-Granger test, Z-score signals, mean-reversion half-life, backtesting engine.

5. Portfolio Optimization

• Description: Mean-variance optimization and efficient frontier construction.
• Key Concepts: Markowitz optimization, Sharpe ratio maximization, risk parity, covariance matrix estimation.

6. Yield Curve Fitting

• Description: Modeling the term structure of interest rates.
• Key Concepts: Nelson-Siegel model, forward rate derivation, optimization of decay parameters.

🚀 Getting Started

Prerequisites

• Python 3.9+
• LaTeX distribution (e.g., TeX Live) for report generation.

Installation

1. Clone the repository.
2. Create and activate a virtual environment:

   python -m venv venv
   source venv/bin/activate  # On macOS/Linux

3. Install dependencies:

   pip install -r requirements.txt  # If available, otherwise install common libs: yfinance, pandas, numpy, scipy, statsmodels, matplotlib

📄 Documentation

A consolidated portfolio of all project reports is available in:

• master_report.pdf

Individual results and CSV exports are located within each project directory.

⚖️ License

MIT License