Monte Carlo Pairs Trading with Lévy-Driven Mean-Reverting Spreads

Summary

This study develops a Monte Carlo method for pairs trading when the spread follows a mean-reverting Ornstein–Uhlenbeck process driven by jumps. It uses a variance gamma process, which allows infinite activity and more flexible spread dynamics than the classical model. Because the generalized model lacks analytic formulas, simulations are used to find optimal trading levels.

The method also introduces control variates to reduce Monte Carlo variance. The authors numerically investigate how model parameters affect the resulting trading strategies, then extend the framework to bivariate spreads driven by a weak variance alpha-gamma process and examine the role of correlation. The document describes a modeling and numerical approach rather than evidence of live or historical trading profitability. Its conclusions depend on the selected processes and parameter assumptions, and no specific performance figures are provided in the text.

Key ideas

• The spread is modeled as a mean-reverting Ornstein–Uhlenbeck process with Lévy jumps.\nA variance gamma driver allows more flexible spread dynamics than the classical model.\nMonte Carlo simulation estimates optimal trading levels where analytic formulas are unavailable.\nControl variates are used to reduce simulation variance.\nThe bivariate extension explores how correlation affects trades under a weak variance alpha-gamma driver.

Tags

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


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









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.

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