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

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Listed:
  • 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)

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.

Suggested Citation

  • Yaoyuan Zhang & Dewen Xiong, 2023. "Optimal Strategy of the Dynamic Mean-Variance Problem for Pairs Trading under a Fast Mean-Reverting Stochastic Volatility Model," Mathematics, MDPI, vol. 11(9), pages 1-19, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2191-:d:1140591
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    References listed on IDEAS

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