Optimal Strategy of the Dynamic Mean-Variance Problem for Pairs Trading under a Fast Mean-Reverting Stochastic Volatility Model

Yaoyuan Zhang and Dewen Xiong ()
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Yaoyuan Zhang: School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
Dewen Xiong: School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China

Mathematics, 2023, vol. 11, issue 9, 1-19

Abstract: We discuss the dynamic mean-variance (MV) problem for pairs trading with the assumptions that one of the security prices satisfies a stochastic volatility model (SVM) and the corresponding price spread follows an Ornstein–Uhlenbeck (OU) process. We provide a semi-closed-form of the optimal strategy based on the solution of a PDE, which is difficult to solve explicitly. Thus, we assume that one of the security prices satisfies the Scott model, a fast-mean-reverting volatility model, and give a closed-form approximation for the optimal strategy. Empirical studies, by using historical data from Chinese security markets, show that the Scott model produces a more stable strategy by better capturing mean-reverting volatility.

Keywords: stochastic volatility; Ornstein–Uhlenbeck process; asymptotic analysis; dynamic mean-variance problem; pairs trading (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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