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Trading Strategy with Stochastic Volatility in a Limit Order Book Market

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  • Wai-Ki Ching
  • Jia-Wen Gu
  • Tak-Kuen Siu
  • Qing-Qing Yang

Abstract

In this paper, we employ the Heston stochastic volatility model to describe the stock's volatility and apply the model to derive and analyze the optimal trading strategies for dealers in a security market. We also extend our study to option market making for options written on stocks in the presence of stochastic volatility. Mathematically, the problem is formulated as a stochastic optimal control problem and the controlled state process is the dealer's mark-to-market wealth. Dealers in the security market can optimally determine their ask and bid quotes on the underlying stocks or options continuously over time. Their objective is to maximize an expected profit from transactions with a penalty proportional to the variance of cumulative inventory cost.

Suggested Citation

  • Wai-Ki Ching & Jia-Wen Gu & Tak-Kuen Siu & Qing-Qing Yang, 2016. "Trading Strategy with Stochastic Volatility in a Limit Order Book Market," Papers 1602.00358, arXiv.org.
  • Handle: RePEc:arx:papers:1602.00358
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    References listed on IDEAS

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    More about this item

    JEL classification:

    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty
    • D9 - Microeconomics - - Micro-Based Behavioral Economics
    • G4 - Financial Economics - - Behavioral Finance

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