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

Abstract

We study the problem of dynamically trading multiple futures whose underlying asset price follows a multiscale central tendency Ornstein-Uhlenbeck (MCTOU) model. Under this model, we derive the closed-form no-arbitrage prices for the futures contracts. Applying a utility maximization approach, we solve for the optimal trading strategies under different portfolio configurations by examining the associated system of Hamilton-Jacobi-Bellman (HJB) equations. The optimal strategies depend on not only the parameters of the underlying asset price process, but also the risk premia embedded in the futures prices. Numerical examples are provided to illustrate the investor's optimal positions and optimal wealth over time.