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Algorithmic market making for options

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  • Bastien Baldacci
  • Philippe Bergault
  • Olivier Guéant

Abstract

In this article, we tackle the problem of a market maker in charge of a book of options on a single liquid underlying asset. By using an approximation of the portfolio in terms of its vega, we show that the seemingly high-dimensional stochastic optimal control problem of an option market maker is in fact tractable. More precisely, when volatility is modeled using a classical stochastic volatility model—e.g. the Heston model—the problem faced by an option market maker is characterized by a low-dimensional functional equation that can be solved numerically using a Euler scheme along with interpolation techniques, even for large portfolios. In order to illustrate our findings, numerical examples are provided.

Suggested Citation

  • Bastien Baldacci & Philippe Bergault & Olivier Guéant, 2021. "Algorithmic market making for options," Quantitative Finance, Taylor & Francis Journals, vol. 21(1), pages 85-97, January.
    • Handle: RePEc:taf:quantf:v:21:y:2021:i:1:p:85-97
    DOI: 10.1080/14697688.2020.1766099
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    Cited by:

    1. Burcu Aydoğan & Ömür Uğur & Ümit Aksoy, 2023. "Optimal Limit Order Book Trading Strategies with Stochastic Volatility in the Underlying Asset," Computational Economics, Springer;Society for Computational Economics, vol. 62(1), pages 289-324, June.
    2. Bastien Baldacci & Philippe Bergault & Dylan Possamai, 2022. "A mean-field game of market-making against strategic traders," Papers 2203.13053, arXiv.org.
    3. Philippe Bergault & Louis Bertucci & David Bouba & Olivier Gu'eant, 2022. "Automated Market Makers: Mean-Variance Analysis of LPs Payoffs and Design of Pricing Functions," Papers 2212.00336, arXiv.org, revised Nov 2023.
    4. Mathieu Rosenbaum & Jianfei Zhang, 2022. "Multi-asset market making under the quadratic rough Heston," Papers 2212.10164, arXiv.org.
    5. Zhou Fang & Haiqing Xu, 2023. "Market Making of Options via Reinforcement Learning," Papers 2307.01814, arXiv.org.
    6. Joseph Jerome & Leandro Sanchez-Betancourt & Rahul Savani & Martin Herdegen, 2022. "Model-based gym environments for limit order book trading," Papers 2209.07823, arXiv.org.

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