Optimal pairs trading strategy with stop-loss signal and path-dependent risk penalty

Abstract

The main purpose of this paper is to study the optimal strategy of pairs trading under a specific spread model. Based on the empirical evidence of mean reversion in the spread between pairs of stocks, we assume that the spread follows a inhomogeneous geometric Brownian motion (IGBM). Significantly different from the current related works, we propose the optimal entry strategy with stop-loss signal and incorporate a path-dependent risk penalty into the optimal stop strategy. We also obtain the analytic expression of the value functions via the first passage time of IGBM. Finally, through numerical illustrations, we give the value functions and optimal thresholds in the pairs trading across Mainland China and Hong Kong, reveal the performance of pairs trading strategy, and analyze the impact of model parameters on the optimal thresholds.