IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2212.10164.html
   My bibliography  Save this paper

Multi-asset market making under the quadratic rough Heston

Author

Listed:
  • Mathieu Rosenbaum
  • Jianfei Zhang

Abstract

Given the promising results on joint modeling of SPX/VIX smiles of the recently introduced quadratic rough Heston model, we consider a multi-asset market making problem on SPX and its derivatives, e.g. VIX futures, SPX and VIX options. The market maker tries to maximize its profit from spread capturing while controlling the portfolio's inventory risk, which can be fully explained by the value change of SPX under the particular setting of the quadratic rough Heston model. The high dimensionality of the resulting optimization problem is relaxed by several approximations. An asymptotic closed-form solution can be obtained. The accuracy and relevance of the approximations are illustrated through numerical experiments.

Suggested Citation

  • Mathieu Rosenbaum & Jianfei Zhang, 2022. "Multi-asset market making under the quadratic rough Heston," Papers 2212.10164, arXiv.org.
    • Handle: RePEc:arx:papers:2212.10164
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2212.10164
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. Aditi Dandapani & Paul Jusselin & Mathieu Rosenbaum, 2021. "From quadratic Hawkes processes to super-Heston rough volatility models with Zumbach effect," Quantitative Finance, Taylor & Francis Journals, vol. 21(8), pages 1235-1247, August.
    5. repec:hal:journl:hal-03885125 is not listed on IDEAS
    6. Jim Gatheral & Thibault Jaisson & Mathieu Rosenbaum, 2018. "Volatility is rough," Quantitative Finance, Taylor & Francis Journals, vol. 18(6), pages 933-949, June.
    7. Eduardo Abi Jaber & Omar El Euch, 2019. "Multi-factor approximation of rough volatility models," Post-Print hal-01697117, HAL.
    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. Philippe Bergault & David Evangelista & Olivier Guéant & Douglas Vieira, 2021. "Closed-form Approximations in Multi-asset Market Making," Applied Mathematical Finance, Taylor & Francis Journals, vol. 28(2), pages 101-142, March.
    10. 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.
    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. Bastien Baldacci & Philippe Bergault & Olivier Guéant, 2021. "Algorithmic market making for options," Quantitative Finance, Taylor & Francis Journals, vol. 21(1), pages 85-97, January.
    13. Marco Avellaneda & Sasha Stoikov, 2008. "High-frequency trading in a limit order book," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 217-224.
    14. Omar El Euch & Mathieu Rosenbaum, 2019. "The characteristic function of rough Heston models," Mathematical Finance, Wiley Blackwell, vol. 29(1), pages 3-38, January.
    15. Christian Bayer & Peter Friz & Jim Gatheral, 2016. "Pricing under rough volatility," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 887-904, June.
    16. Jim Gatheral & Paul Jusselin & Mathieu Rosenbaum, 2020. "The quadratic rough Heston model and the joint S&P 500/VIX smile calibration problem," Papers 2001.01789, arXiv.org.
    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. Justin Sirignano & Konstantinos Spiliopoulos, 2017. "DGM: A deep learning algorithm for solving partial differential equations," Papers 1708.07469, arXiv.org, revised Sep 2018.
    19. Philippe Bergault & David Evangelista & Olivier Guéant & Douglas Vieira, 2021. "Closed-form Approximations in Multi-asset Market Making," Post-Print hal-03885121, HAL.
    20. Aditi Dandapani & Paul Jusselin & Mathieu Rosenbaum, 2019. "From quadratic Hawkes processes to super-Heston rough volatility models with Zumbach effect," Papers 1907.06151, arXiv.org, revised Jan 2021.
    21. Mathieu Rosenbaum & Jianfei Zhang, 2022. "On the universality of the volatility formation process: when machine learning and rough volatility agree," Papers 2206.14114, arXiv.org.
    22. Mathieu Rosenbaum & Jianfei Zhang, 2021. "Deep calibration of the quadratic rough Heston model," Papers 2107.01611, arXiv.org, revised May 2022.
    23. Olivier Gu'eant, 2016. "Optimal market making," Papers 1605.01862, arXiv.org, revised May 2017.
    24. Pietro Fodra & Huy^en Pham, 2013. "High frequency trading and asymptotics for small risk aversion in a Markov renewal model," Papers 1310.1756, arXiv.org, revised Jan 2015.
    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. Philippe Bergault & Louis Bertucci & David Bouba & Olivier Gu'eant & Julien Guilbert, 2024. "Price-Aware Automated Market Makers: Models Beyond Brownian Prices and Static Liquidity," Papers 2405.03496, arXiv.org, revised May 2024.

    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 & 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.
    2. Philippe Bergault & Louis Bertucci & David Bouba & Olivier Gu'eant & Julien Guilbert, 2024. "Automated Market Making: the case of Pegged Assets," Papers 2411.08145, arXiv.org.
    3. 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.
    4. Philippe Bergault & Louis Bertucci & David Bouba & Olivier Gu'eant & Julien Guilbert, 2024. "Price-Aware Automated Market Makers: Models Beyond Brownian Prices and Static Liquidity," Papers 2405.03496, arXiv.org, revised May 2024.
    5. Marcello Monga, 2024. "Automated Market Making and Decentralized Finance," Papers 2407.16885, arXiv.org.
    6. Bastien Baldacci & Philippe Bergault & Dylan Possamai, 2022. "A mean-field game of market-making against strategic traders," Papers 2203.13053, arXiv.org.
    7. 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.
    8. 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.
    9. Bastien Baldacci & Philippe Bergault & Olivier Gu'eant, 2019. "Algorithmic market making for options," Papers 1907.12433, arXiv.org, revised Jul 2020.
    10. 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.
    11. Mathieu Rosenbaum & Jianfei Zhang, 2021. "Deep calibration of the quadratic rough Heston model," Papers 2107.01611, arXiv.org, revised May 2022.
    12. Jonathan Ch'avez-Casillas & Jos'e E. Figueroa-L'opez & Chuyi Yu & Yi Zhang, 2024. "Adaptive Optimal Market Making Strategies with Inventory Liquidation Cos," Papers 2405.11444, arXiv.org.
    13. Philippe Bergault & Olivier Gu'eant, 2023. "Liquidity Dynamics in RFQ Markets and Impact on Pricing," Papers 2309.04216, arXiv.org, revised Jun 2024.
    14. Mathieu Rosenbaum & Jianfei Zhang, 2022. "On the universality of the volatility formation process: when machine learning and rough volatility agree," Papers 2206.14114, arXiv.org.
    15. Bastien Baldacci & Joffrey Derchu & Iuliia Manziuk, 2020. "An approximate solution for options market-making in high dimension," Papers 2009.00907, arXiv.org.
    16. Bastien Baldacci & Jerome Benveniste & Gordon Ritter, 2020. "Optimal trading without optimal control," Papers 2012.12945, arXiv.org.
    17. Giulia Di Nunno & Kk{e}stutis Kubilius & Yuliya Mishura & Anton Yurchenko-Tytarenko, 2023. "From constant to rough: A survey of continuous volatility modeling," Papers 2309.01033, arXiv.org, revised Sep 2023.
    18. Olivier Guéant, 2022. "Computational methods for market making algorithms," Post-Print hal-04590381, HAL.
    19. Jingtang Ma & Wensheng Yang & Zhenyu Cui, 2021. "Semimartingale and continuous-time Markov chain approximation for rough stochastic local volatility models," Papers 2110.08320, arXiv.org, revised Oct 2021.
    20. Alexander Barzykin & Philippe Bergault & Olivier Gu'eant, 2021. "Market making by an FX dealer: tiers, pricing ladders and hedging rates for optimal risk control," Papers 2112.02269, arXiv.org, revised Jun 2023.

    More about this item

    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:2212.10164. 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.