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

ArXiv ID: 2309.05512 “View on arXiv”

Authors: Unknown

Abstract

We present a Monte Carlo approach to pairs trading on mean-reverting spreads modeled by Lévy-driven Ornstein-Uhlenbeck processes. Specifically, we focus on using a variance gamma driving process, an infinite activity pure jump process to allow for more flexible models of the price spread than is available in the classical model. However, this generalization comes at the cost of not having analytic formulas, so we apply Monte Carlo methods to determine optimal trading levels and develop a variance reduction technique using control variates. Within this framework, we numerically examine how the optimal trading strategies are affected by the parameters of the model. In addition, we extend our method to bivariate spreads modeled using a weak variance alpha-gamma driving process, and explore the effect of correlation on these trades.

Keywords: pairs trading, Ornstein-Uhlenbeck process, variance gamma process, Monte Carlo methods, statistical arbitrage

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper is mathematically dense, employing advanced concepts like Lévy processes, infinite activity, and multivariate extensions, evidenced by heavy formulas and LaTeX notation. It demonstrates high empirical rigor by extending a modeling framework to a real trading problem (pairs trading), implementing Monte Carlo simulations with specific variance reduction techniques (control variates), and numerically exploring the impact of parameters and correlation on optimal strategies, making it backtest-ready despite the absence of raw code snippets.

  flowchart TD
    A["Research Goal: <br/>Model & Optimize Pairs Trading<br/>under Lévy-Driven Mean-Reversion"] --> B["Methodology: <br/>Monte Carlo Simulation & Variance Reduction"]
    B --> C["Data/Inputs: <br/>Model Parameters & Market Data"]
    C --> D{"Computational Process"}
    D --> D1["Generate Paths: <br/>VG / VWAP Driven OU Processes"]
    D --> D2["Apply Control Variates<br/>for Variance Reduction"]
    D1 & D2 --> E["Simulation Outcomes"]
    E --> F1["Optimal Trading Levels<br/>& Thresholds"]
    E --> F2["Parameter Sensitivity Analysis"]
    E --> F3["Effect of Correlation<br/>on Bivariate Spreads"]