Dynamic Spread Trading

This paper is concerned with a dynamic trading strategy, which involves multiple synthetic spreads each of which involves long positions in a basket of underlying securities and short positions in another basket. We assume that the spreads can be modeled as mean-reverting Ornstein-Uhlenbeck (OU) processes. The dynamic trading strategy is implemented as the solution to a stochastic optimal control problem that dynamically allocates capital over the spreads and a risk-free asset over a finite horizon to maximize a general constant relative risk aversion (CRRA) or constant absolute risk aversion (CARA) utility function of the terminal wealth. We show that this stochastic control problem is computationally tractable. Specifically, we show that the coefficient functions defining the optimal feedback law are the solutions of a system of ordinary differential equations (ODEs) that are the essence of the tractability of the stochastic optimal control problem. We illustrate the dynamic trading strategy with four pairs that consist of seven S&P 500 index stocks, which shows that the performance achieved by the dynamic spread trading strategy is significant and robust to realistic transaction costs.