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A Stochastic Volatility Model for Optimal Market-Making

In: Mathematical and Statistical Methods for Actuarial Sciences and Finance

Author

Listed:
  • Zubier Arfan

    (The University of Manchester)

  • Paul Johnson

    (The University of Manchester)

Abstract

The electronification of financial markets and the rise of algorithmic trading has sparked interest from the mathematical community, for the market-making problem in particular. The research presented in this paper solves the classic stochastic control problem for the optimal trading strategy of a market-maker, which is then applied to real limit order book trading data. Often models in the literature assume constant volatility for the asset price, and therefore may not be best suited to intra-day data. The stochastic volatility model is introduced to describe the intra-day price and variance process of the asset. The market-maker’s objective function is optimized to find the optimal two-way limit-order quotes. The results show that the stochastic volatility market-making model is more suited to a market-maker pursuing a strategy that returns stable profits.

Suggested Citation

  • Zubier Arfan & Paul Johnson, 2021. "A Stochastic Volatility Model for Optimal Market-Making," Springer Books, in: Marco Corazza & Manfred Gilli & Cira Perna & Claudio Pizzi & Marilena Sibillo (ed.), Mathematical and Statistical Methods for Actuarial Sciences and Finance, pages 33-38, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-78965-7_6
    DOI: 10.1007/978-3-030-78965-7_6
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