Optimal Pairs Trading: Static and Dynamic Models

Pairs trading has been a popular statistical arbitrage strategy among hedge funds. One important research field in pairs trading is to maximize the return under differential constraints and assumptions. In this thesis, we develop two models to optimize the performance of pairs trading. In the static model, we find the analytic solution of optimal thresholds for pairs trading to maximize the long run profit per unit time. Comparison is made between the optimal rules we developed and the common practice. To overcome limitations of the static model, we extend our research to dynamic pairs trading, where a continuous time Markov chain is used to model the change of parameters. Our objective is to maximize the expected return in the finite horizon under the Constant Relative Risk Aversion (CRRA) utility. Numerical examples are presented to illustrate the impact of price limits, risk aversion rate and regime switching on consumers' investment decision.MAS