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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.

We study a stochastic control approach to managed futures portfolios. Building on the Schwartz (1997) stochastic convenience yield model for commodity prices, we formulate a utility maximization problem for dynamically trading a single-maturity futures or multiple futures contracts over a finite horizon. By analyzing the associated Hamilton-Jacobi-Bellman (HJB) equation, we solve the investor's utility maximization problem explicitly and derive the optimal dynamic trading strategies in closed form. We provide numerical examples and illustrate the optimal trading strategies using WTI crude oil futures data.

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