Optimal Dynamic Pairs Trading of Futures Under a Two-Factor Mean-Reverting Model

Abstract

We study the problem of dynamically trading a pair of futures contracts. We consider a two-factor mean-reverting model, where the spot price tends to evolve around its stochastic equilibrium that is also mean-reverting. We derive the futures price dynamics and determine the optimal futures trading strategy by solving a utility maximization problem. By analyzing the associated Hamilton-Jacobi-Bellman equation, we solve the utility maximization explicitly and provide the optimal trading strategies in closed form. Our strategies are applied to volatility (VIX) futures trading, and illustrated in a series of numerical examples.

Keywords: dynamic trading, futures portfolio, mean-reverting model, utility maximization

JEL Classification: C61, D53, G11, G13