IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1907.12433.html
   My bibliography  Save this paper

Algorithmic market making for options

Author

Listed:
  • Bastien Baldacci
  • Philippe Bergault
  • Olivier Gu'eant

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 Gu'eant, 2019. "Algorithmic market making for options," Papers 1907.12433, arXiv.org, revised Jul 2020.
    • Handle: RePEc:arx:papers:1907.12433
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1907.12433
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Olivier Guéant & Charles-Albert Lehalle, 2015. "General Intensity Shapes In Optimal Liquidation," Mathematical Finance, Wiley Blackwell, vol. 25(3), pages 457-495, July.
    2. Olivier Guéant & Iuliia Manziuk, 2019. "Deep Reinforcement Learning for Market Making in Corporate Bonds: Beating the Curse of Dimensionality," Post-Print hal-03252505, HAL.
    3. Sanford J. Grossman & Merton H. Miller, 1988. "Liquidity and Market Structure," NBER Working Papers 2641, National Bureau of Economic Research, Inc.
    4. Olivier Gu'eant & Charles-Albert Lehalle & Joaquin Fernandez Tapia, 2011. "Dealing with the Inventory Risk. A solution to the market making problem," Papers 1105.3115, arXiv.org, revised Aug 2012.
    5. Sasha Stoikov & Mehmet Sağlam, 2009. "Option market making under inventory risk," Review of Derivatives Research, Springer, vol. 12(1), pages 55-79, April.
    6. Olivier Guéant, 2017. "Optimal market making," Post-Print hal-02862554, HAL.
    7. Grossman, Sanford J & Miller, Merton H, 1988. " Liquidity and Market Structure," Journal of Finance, American Finance Association, vol. 43(3), pages 617-637, July.
    8. Olivier Gu'eant & Iuliia Manziuk, 2019. "Deep reinforcement learning for market making in corporate bonds: beating the curse of dimensionality," Papers 1910.13205, arXiv.org.
    9. Fabien Guilbaud & Huyên Pham, 2013. "Optimal high-frequency trading with limit and market orders," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 79-94, January.
    10. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    11. Ho, Thomas & Stoll, Hans R., 1981. "Optimal dealer pricing under transactions and return uncertainty," Journal of Financial Economics, Elsevier, vol. 9(1), pages 47-73, March.
    12. Olivier Guéant, 2017. "Optimal market making," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-02862554, HAL.
    13. Olivier Guéant & Iuliia Manziuk, 2019. "Deep Reinforcement Learning for Market Making in Corporate Bonds: Beating the Curse of Dimensionality," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-03252505, HAL.
    14. Marco Avellaneda & Sasha Stoikov, 2008. "High-frequency trading in a limit order book," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 217-224.
    15. Olivier Guéant & Iuliia Manziuk, 2019. "Deep Reinforcement Learning for Market Making in Corporate Bonds: Beating the Curse of Dimensionality," Applied Mathematical Finance, Taylor & Francis Journals, vol. 26(5), pages 387-452, September.
    16. Philippe Bergault & Olivier Gu'eant, 2019. "Size matters for OTC market makers: general results and dimensionality reduction techniques," Papers 1907.01225, arXiv.org, revised Sep 2022.
    17. Fabien Guilbaud & Huyên Pham, 2015. "Optimal High-Frequency Trading In A Pro Rata Microstructure With Predictive Information," Mathematical Finance, Wiley Blackwell, vol. 25(3), pages 545-575, July.
    18. Olivier Gu'eant, 2016. "Optimal market making," Papers 1605.01862, arXiv.org, revised May 2017.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Joaquin Fernandez-Tapia & Olivier Gu'eant, 2020. "Recipes for hedging exotics with illiquid vanillas," Papers 2005.10064, arXiv.org, revised May 2020.
    2. Philippe Bergault & Olivier Gu'eant, 2019. "Size matters for OTC market makers: general results and dimensionality reduction techniques," Papers 1907.01225, arXiv.org, revised Sep 2022.
    3. Philippe Bergault & Olivier Guéant, 2021. "Size matters for OTC market makers: General results and dimensionality reduction techniques," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 279-322, January.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Philippe Bergault & Olivier Gu'eant, 2019. "Size matters for OTC market makers: general results and dimensionality reduction techniques," Papers 1907.01225, arXiv.org, revised Sep 2022.
    2. Philippe Bergault & Olivier Guéant, 2020. "Size matters for OTC market makers: general results and dimensionality reduction techniques," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-02987894, HAL.
    3. Philippe Bergault & Olivier Guéant, 2020. "Size matters for OTC market makers: general results and dimensionality reduction techniques," Working Papers hal-02987894, HAL.
    4. Philippe Bergault & Olivier Guéant, 2021. "Size matters for OTC market makers: General results and dimensionality reduction techniques," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 279-322, January.
    5. Alexander Barzykin & Philippe Bergault & Olivier Gu'eant, 2021. "Algorithmic market making in dealer markets with hedging and market impact," Papers 2106.06974, arXiv.org, revised Dec 2022.
    6. Bastien Baldacci & Joffrey Derchu & Iuliia Manziuk, 2020. "An approximate solution for options market-making in high dimension," Papers 2009.00907, arXiv.org.
    7. Alexander Barzykin & Philippe Bergault & Olivier Guéant, 2023. "Algorithmic market making in dealer markets with hedging and market impact," Mathematical Finance, Wiley Blackwell, vol. 33(1), pages 41-79, January.
    8. 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.
    9. Mathieu Rosenbaum & Jianfei Zhang, 2022. "Multi-asset market making under the quadratic rough Heston," Papers 2212.10164, arXiv.org.
    10. Bastien Baldacci & Philippe Bergault & Dylan Possamai, 2022. "A mean-field game of market-making against strategic traders," Papers 2203.13053, arXiv.org.
    11. Thomas Spooner & Rahul Savani, 2020. "Robust Market Making via Adversarial Reinforcement Learning," Papers 2003.01820, arXiv.org, revised Jul 2020.
    12. Philippe Bergault & David Evangelista & Olivier Gu'eant & Douglas Vieira, 2018. "Closed-form approximations in multi-asset market making," Papers 1810.04383, arXiv.org, revised Sep 2022.
    13. Olivier Guéant, 2016. "The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making," Post-Print hal-01393136, HAL.
    14. 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.
    15. Bastien Baldacci & Jerome Benveniste & Gordon Ritter, 2020. "Optimal trading without optimal control," Papers 2012.12945, arXiv.org.
    16. Bastien Baldacci & Iuliia Manziuk, 2020. "Adaptive trading strategies across liquidity pools," Papers 2008.07807, arXiv.org.
    17. Bruno Gašperov & Stjepan Begušić & Petra Posedel Šimović & Zvonko Kostanjčar, 2021. "Reinforcement Learning Approaches to Optimal Market Making," Mathematics, MDPI, vol. 9(21), pages 1-22, October.
    18. Ben Hambly & Renyuan Xu & Huining Yang, 2021. "Recent Advances in Reinforcement Learning in Finance," Papers 2112.04553, arXiv.org, revised Feb 2023.
    19. Olivier Gu'eant & Jiang Pu, 2018. "Mid-price estimation for European corporate bonds: a particle filtering approach," Papers 1810.05884, arXiv.org, revised Mar 2019.
    20. Pankaj Kumar, 2021. "Deep Hawkes Process for High-Frequency Market Making," Papers 2109.15110, arXiv.org.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1907.12433. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.