Simulating Trades Under a Levy-Driven Mean-Reverting Framework

Monte Carlo simulation for pairs trading with jumps — theory & implementation

Photo by Hans-Jürgen Weinhardt 2019

We present a Monte Carlo framework for pairs trading on mean-reverting spreads modeled by Levy-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.

For the spread process X (black line), a trade is entered when the price passes ±d, whichever happens first (red lines), and exited when it passes ±c = 0 (blue line). The value of the spread at the entry (red point) and exit (blue point) times are shown. Here, X ∼ OU-VG(1, 5, 0, 0.015, 0) (i.e. OU process driven by a Variance Gamma Levy process). Source: Leung and Lu (2023).

You can find more details on the theory and implementation in the full paper.

Reference:

Tim Leung and Kevin Lu (2023). Monte Carlo Simulation for Trading Under a Levy-Driven Mean-Reverting Framework. arXiv preprint:2309.05512.