Monte Carlo Simulation for Trading Under a Lévy-Driven Mean-Reverting Framework

Overview

This project explores the application of Monte Carlo simulations in a Lévy-driven mean-reverting framework for pairs trading. We use synthetic data to demonstrate the methodology and backtest a trading strategy.

Data

The synthetic data is generated to represent two assets with a mean-reverting spread. The spread is modeled using the Ornstein-Uhlenbeck process.

Methodology

Data Generation

• Synthetic data is generated using the data_generation.py script.
• The spread between the two assets is modeled using an Ornstein-Uhlenbeck process.

Model Calibration

• The Ornstein-Uhlenbeck process is calibrated to the synthetic spread data using the model_calibration.py script.

Monte Carlo Simulation

• Potential future paths for the spread are simulated using the calibrated Ornstein-Uhlenbeck process.
• Simulations are performed using the monte_carlo_simulation.py script.

Backtesting

• A pairs trading strategy is backtested on the synthetic data using thresholds determined from the Monte Carlo simulations.
• Backtesting is performed using the backtesting.py script.

Results

The project demonstrates how to use Monte Carlo simulations in a mean-reverting framework for pairs trading. The strategy shows positive returns on the synthetic data, but it's essential to consider real-world factors and risks when applying to actual trading scenarios.

How to Run

1. Generate synthetic data using data_generation.py.
2. Calibrate the model using model_calibration.py.
3. Run Monte Carlo simulations using monte_carlo_simulation.py.
4. Backtest the strategy using backtesting.py.

Contact

For questions, feedback, or contributions, please open an issue or submit a pull request.