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Stochastic Differential Game in High Frequency Market

Author

Listed:
  • Taiga Saito

    (Faculty of Economics, The University of Tokyo)

  • Akihiko Takahashi

    (Faculty of Economics, The University of Tokyo)

Abstract

This paper presents an application of a linear quadratic stochastic differential game to a model in finance, which describes trading behaviors of different types of players in a high frequency stock market. Stability of the high frequency market is a central issue for financial markets. Building a model that expresses the trading behaviors of the different types of players and the price actions in turmoil is important to set regulations to maintain fair markets. Firstly, we represent trading behaviors of the three types of players, algorithmic traders, general traders, and market makers as well as the mid price process of a risky asset by a linear quadratic stochastic differential game. Secondly, we obtain a Nash equilibrium by solving a forward-backward stochastic differential equation (FBSDE) derived from the stochastic maximum principle. Finally, we present numerical examples of the Nash equilibrium and the corresponding price action of the risky asset, which agree with the empirical findings on trading behaviors of players in high frequency markets. This model can be used to investigate the impact of regulation changes on the market stability as well as trading strategies of the players.

Suggested Citation

  • Taiga Saito & Akihiko Takahashi, 2019. "Stochastic Differential Game in High Frequency Market," CIRJE F-Series CIRJE-F-1114, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2019cf1114
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    Cited by:

    1. Taiga Saito & Shivam Gupta, 2022. "Big Data Applications with Theoretical Models and Social Media in Financial Management," CIRJE F-Series CIRJE-F-1205, CIRJE, Faculty of Economics, University of Tokyo.
    2. Taiga Saito & Shivam Gupta, 2022. "Big data applications with theoretical models and social media in financial management," CARF F-Series CARF-F-550, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    3. Han, Jinhui & Li, Xiaolong & Ma, Guiyuan & Kennedy, Adrian Patrick, 2023. "Strategic trading with information acquisition and long-memory stochastic liquidity," European Journal of Operational Research, Elsevier, vol. 308(1), pages 480-495.
    4. Han, Jinhui & Ma, Guiyuan & Yam, Sheung Chi Phillip, 2022. "Relative performance evaluation for dynamic contracts in a large competitive market," European Journal of Operational Research, Elsevier, vol. 302(2), pages 768-780.
    5. Taiga Saito & Akihiko Takahashi, 2022. "Portfolio optimization with choice of a probability measure (forthcoming in proceedings of IEEE CIFEr 2022)," CARF F-Series CARF-F-534, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.

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