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.

Optimal Dynamic Futures Portfolios Under a Multiscale Central Tendency Ornstein-Uhlenbeck Model

“…Remark 1: If the stochastic mean of log price X (1) is only modeled by X (2) or X (3) , instead of their sum, it will reduce to the CTOU model, which is used in [13] for pricing VIX futures. Under this model, the futures portfolio optimization problem has been studied in [5].…”

“…To that end, our model falls within the multi-factor Gassian model for futures pricing, as used for oil futures in [2]. The utility maximization approach is used to derive dynamic futures trading strategies under two-factor models in [5] and [6]. A general regime-switching framework for dynamic futures trading can be found in [7].…”

Optimal trading of a basket of futures contracts

“…Among the authors' recent related studies, Leung and Yan (2018) and Leung and Yan (2019) applied utility maximization approach to derive dynamic pairs trading strategies for futures under two-factor spot models. Most recently and relevantly, Angoshtari and Leung (2019) analyzed the problem of dynamically trading a futures contract and its underlying asset.…”

A stochastic control approach to managed futures portfolios

“…They motivate us to consider a stochastic spot model that can generate no-arbitrage futures prices and effectively capture their joint price evolutions. In our companion paper Leung and Yan (2018), we focus on dynamic pairs trading of VIX futures under a Central Tendency Ornstein-Uhlenbeck no-arbitrage pricing model. All these studies propose a stochastic control approach to futures trading.…”