We study the problem of dynamically trading a futures contract and its underlying asset under a stochastic basis model. We describe the basis evolution by a scaled Brownian bridge, but also incorporate the possibility of non-convergence at maturity. The optimal trading strategies are determined from a utility maximization problem under hyperbolic absolute risk aversion (HARA) risk preferences. By analyzing the associated Hamilton-Jacobi-Bellman equation, we derive the exact conditions under which the equation admits a solution and solve the utility maximization explicitly. A series of numerical examples are provided to illustrate the optimal strategies and examine the effects of model parameters.
↧