Optimal Signaling Mechanism for Statistical Arbitrage Strategy

Nowadays, statistical arbitrage ([1-9]) strategy is becoming more and more popular and useful in securities trading, especially in high-frequency trading. As the most basic and important type of statistical arbitrage strategy, pairs trading ([9]) has been studied by many researchers ([9-20]). Signaling mechanism is an integral part of pairs trading. Focusing on studying signaling mechanism of pairs trading, this paper provides two representative signaling mechanisms and derives analytical formulae of the optimal signal points. The ultimate goal is to obtain the solution of optimal signaling mechanism for pairs trading. Under the help of co-integration ([20-23]) approach, we construct an asset portfolio whose price process follows mean-reverting Ornstein-Uhlenbeck process ([23-28]). Through using some known results to make some suitable simplifications and transformations, we derive two mathematical models of expected revenue optimization problems corresponding to the two signaling mechanisms. Then approximate analytical solutions of two problems are respectively worked out. A comparison between the two models of optimization problems is made to draw a significant conclusion about the best choice of signaling mechanism in pairs trading.