The optimal strategy of the dynamic mean−variance problem for pairs trading with a common stochastic factor

Abstract

This paper studies the optimal pairs trading strategy of the mean−variance (MV) objective function under a continuous-time cointegration model with a common stochastic factor. Although this common stochastic factor is not directly tradable, it significantly impacts asset prices. We first provide a semiclosed-form solution under a general model. We then specify the common factor model to be a mean-reverting process with time-varying parameters and provide closed-form optimal strategies for pairs trading with fixed and flexible ratios, respectively. Empirical analysis based on historical data from Chinese securities markets shows the effectiveness of both optimal strategies. The optimal flexible-ratio strategy outperforms the optimal fixed-ratio strategy in terms of both profit and risk.

Keywords

Continuous-time cointegration model / Dynamic mean-variance problem / Pairs trading / Mean-reverting process

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