IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1810.03399.html
   My bibliography  Save this paper

Deep calibration of rough stochastic volatility models

Author

Listed:
  • Christian Bayer
  • Benjamin Stemper

Abstract

Sparked by Al\`os, Le\'on, and Vives (2007); Fukasawa (2011, 2017); Gatheral, Jaisson, and Rosenbaum (2018), so-called rough stochastic volatility models such as the rough Bergomi model by Bayer, Friz, and Gatheral (2016) constitute the latest evolution in option price modeling. Unlike standard bivariate diffusion models such as Heston (1993), these non-Markovian models with fractional volatility drivers allow to parsimoniously recover key stylized facts of market implied volatility surfaces such as the exploding power-law behaviour of the at-the-money volatility skew as time to maturity goes to zero. Standard model calibration routines rely on the repetitive evaluation of the map from model parameters to Black-Scholes implied volatility, rendering calibration of many (rough) stochastic volatility models prohibitively expensive since there the map can often only be approximated by costly Monte Carlo (MC) simulations (Bennedsen, Lunde, & Pakkanen, 2017; McCrickerd & Pakkanen, 2018; Bayer et al., 2016; Horvath, Jacquier, & Muguruza, 2017). As a remedy, we propose to combine a standard Levenberg-Marquardt calibration routine with neural network regression, replacing expensive MC simulations with cheap forward runs of a neural network trained to approximate the implied volatility map. Numerical experiments confirm the high accuracy and speed of our approach.

Suggested Citation

  • Christian Bayer & Benjamin Stemper, 2018. "Deep calibration of rough stochastic volatility models," Papers 1810.03399, arXiv.org.
    • Handle: RePEc:arx:papers:1810.03399
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1810.03399
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jim Gatheral & Thibault Jaisson & Mathieu Rosenbaum, 2018. "Volatility is rough," Quantitative Finance, Taylor & Francis Journals, vol. 18(6), pages 933-949, June.
    2. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    3. Ryan McCrickerd & Mikko S. Pakkanen, 2018. "Turbocharging Monte Carlo pricing for the rough Bergomi model," Quantitative Finance, Taylor & Francis Journals, vol. 18(11), pages 1877-1886, November.
    4. Elisa Alòs & Jorge León & Josep Vives, 2007. "On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility," Finance and Stochastics, Springer, vol. 11(4), pages 571-589, October.
    5. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    6. 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.
    7. Christian Bayer & Peter Friz & Jim Gatheral, 2016. "Pricing under rough volatility," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 887-904, June.
    8. Masaaki Fukasawa, 2017. "Short-time at-the-money skew and rough fractional volatility," Quantitative Finance, Taylor & Francis Journals, vol. 17(2), pages 189-198, February.
    9. Masaaki Fukasawa, 2011. "Asymptotic analysis for stochastic volatility: martingale expansion," Finance and Stochastics, Springer, vol. 15(4), pages 635-654, December.
    10. Blanka Horvath & Antoine Jacquier & Aitor Muguruza & Andreas Sojmark, 2017. "Functional central limit theorems for rough volatility," Papers 1711.03078, arXiv.org, revised Nov 2023.
    11. Mikkel Bennedsen & Asger Lunde & Mikko S. Pakkanen, 2015. "Hybrid scheme for Brownian semistationary processes," Papers 1507.03004, arXiv.org, revised May 2017.
    12. Mikkel Bennedsen & Asger Lunde & Mikko S. Pakkanen, 2017. "Hybrid scheme for Brownian semistationary processes," Finance and Stochastics, Springer, vol. 21(4), pages 931-965, October.
    13. David Silver & Julian Schrittwieser & Karen Simonyan & Ioannis Antonoglou & Aja Huang & Arthur Guez & Thomas Hubert & Lucas Baker & Matthew Lai & Adrian Bolton & Yutian Chen & Timothy Lillicrap & Fan , 2017. "Mastering the game of Go without human knowledge," Nature, Nature, vol. 550(7676), pages 354-359, October.
    14. Ryan McCrickerd & Mikko S. Pakkanen, 2017. "Turbocharging Monte Carlo pricing for the rough Bergomi model," Papers 1708.02563, arXiv.org, revised Mar 2018.
    15. Christian Bayer & Peter K. Friz & Paul Gassiat & Joerg Martin & Benjamin Stemper, 2017. "A regularity structure for rough volatility," Papers 1710.07481, arXiv.org.
    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. Antoine Jacquier & Emma R. Malone & Mugad Oumgari, 2019. "Stacked Monte Carlo for option pricing," Papers 1903.10795, arXiv.org.
    2. Marc Sabate-Vidales & David v{S}iv{s}ka & Lukasz Szpruch, 2020. "Solving path dependent PDEs with LSTM networks and path signatures," Papers 2011.10630, arXiv.org.
    3. Guido Gazzani & Julien Guyon, 2024. "Pricing and calibration in the 4-factor path-dependent volatility model," Papers 2406.02319, arXiv.org.
    4. Giorgia Callegaro & Martino Grasselli & Gilles Paèes, 2021. "Fast Hybrid Schemes for Fractional Riccati Equations (Rough Is Not So Tough)," Mathematics of Operations Research, INFORMS, vol. 46(1), pages 221-254, February.
    5. Patrick Büchel & Michael Kratochwil & Maximilian Nagl & Daniel Rösch, 2022. "Deep calibration of financial models: turning theory into practice," Review of Derivatives Research, Springer, vol. 25(2), pages 109-136, July.
    6. Patryk Gierjatowicz & Marc Sabate-Vidales & David v{S}iv{s}ka & Lukasz Szpruch & v{Z}an v{Z}uriv{c}, 2020. "Robust pricing and hedging via neural SDEs," Papers 2007.04154, arXiv.org.
    7. Damiano Brigo & Xiaoshan Huang & Andrea Pallavicini & Haitz Saez de Ocariz Borde, 2021. "Interpretability in deep learning for finance: a case study for the Heston model," Papers 2104.09476, arXiv.org.
    8. Mariano Zeron & Ignacio Ruiz, 2020. "Tensoring volatility calibration," Papers 2012.07440, arXiv.org, revised Dec 2020.
    9. Luca Di Persio & Emanuele Lavagnoli & Marco Patacca, 2022. "Calibrating FBSDEs Driven Models in Finance via NNs," Risks, MDPI, vol. 10(12), pages 1-19, November.
    10. Fred Espen Benth & Nils Detering & Luca Galimberti, 2022. "Pricing options on flow forwards by neural networks in Hilbert space," Papers 2202.11606, arXiv.org.
    11. Johannes Ruf & Weiguan Wang, 2019. "Neural networks for option pricing and hedging: a literature review," Papers 1911.05620, arXiv.org, revised May 2020.
    12. Fabio Baschetti & Giacomo Bormetti & Pietro Rossi, 2023. "Deep calibration with random grids," Papers 2306.11061, arXiv.org, revised Jan 2024.
    13. Christa Cuchiero & Eva Flonner & Kevin Kurt, 2024. "Robust financial calibration: a Bayesian approach for neural SDEs," Papers 2409.06551, arXiv.org, revised Sep 2024.
    14. Fred Espen Benth & Nils Detering & Silvia Lavagnini, 2020. "Accuracy of Deep Learning in Calibrating HJM Forward Curves," Papers 2006.01911, arXiv.org, revised May 2021.
    15. Fred Espen Benth & Nils Detering & Silvia Lavagnini, 2021. "Accuracy of deep learning in calibrating HJM forward curves," Digital Finance, Springer, vol. 3(3), pages 209-248, December.
    16. Henry Stone, 2018. "Calibrating rough volatility models: a convolutional neural network approach," Papers 1812.05315, arXiv.org, revised Jul 2019.

    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. Christian Bayer & Blanka Horvath & Aitor Muguruza & Benjamin Stemper & Mehdi Tomas, 2019. "On deep calibration of (rough) stochastic volatility models," Papers 1908.08806, arXiv.org.
    2. Siow Woon Jeng & Adem Kilicman, 2020. "Series Expansion and Fourth-Order Global Padé Approximation for a Rough Heston Solution," Mathematics, MDPI, vol. 8(11), pages 1-26, November.
    3. Peter K. Friz & Paul Gassiat & Paolo Pigato, 2022. "Short-dated smile under rough volatility: asymptotics and numerics," Quantitative Finance, Taylor & Francis Journals, vol. 22(3), pages 463-480, March.
    4. Florian Bourgey & Stefano De Marco & Peter K. Friz & Paolo Pigato, 2023. "Local volatility under rough volatility," Mathematical Finance, Wiley Blackwell, vol. 33(4), pages 1119-1145, October.
    5. Qinwen Zhu & Gregoire Loeper & Wen Chen & Nicolas Langrené, 2021. "Markovian approximation of the rough Bergomi model for Monte Carlo option pricing," Post-Print hal-02910724, HAL.
    6. Christian Bayer & Chiheb Ben Hammouda & Raul Tempone, 2018. "Hierarchical adaptive sparse grids and quasi Monte Carlo for option pricing under the rough Bergomi model," Papers 1812.08533, arXiv.org, revised Jan 2020.
    7. Qinwen Zhu & Grégoire Loeper & Wen Chen & Nicolas Langrené, 2021. "Markovian Approximation of the Rough Bergomi Model for Monte Carlo Option Pricing," Mathematics, MDPI, vol. 9(5), pages 1-21, March.
    8. Siow Woon Jeng & Adem Kiliçman, 2021. "On Multilevel and Control Variate Monte Carlo Methods for Option Pricing under the Rough Heston Model," Mathematics, MDPI, vol. 9(22), pages 1-32, November.
    9. Antoine Jacquier & Alexandre Pannier, 2020. "Large and moderate deviations for stochastic Volterra systems," Papers 2004.10571, arXiv.org, revised Apr 2022.
    10. Jacquier, Antoine & Pannier, Alexandre, 2022. "Large and moderate deviations for stochastic Volterra systems," Stochastic Processes and their Applications, Elsevier, vol. 149(C), pages 142-187.
    11. Raul Merino & Jan Posp'iv{s}il & Tom'av{s} Sobotka & Tommi Sottinen & Josep Vives, 2019. "Decomposition formula for rough Volterra stochastic volatility models," Papers 1906.07101, arXiv.org, revised Aug 2019.
    12. Qinwen Zhu & Gr'egoire Loeper & Wen Chen & Nicolas Langren'e, 2020. "Markovian approximation of the rough Bergomi model for Monte Carlo option pricing," Papers 2007.02113, arXiv.org.
    13. Blanka Horvath & Antoine Jacquier & Peter Tankov, 2018. "Volatility options in rough volatility models," Papers 1802.01641, arXiv.org, revised Jan 2019.
    14. Florian Bourgey & Stefano De Marco & Emmanuel Gobet, 2022. "Weak approximations and VIX option price expansions in forward variance curve models," Papers 2202.10413, arXiv.org, revised May 2022.
    15. Etienne Chevalier & Sergio Pulido & Elizabeth Zúñiga, 2022. "American options in the Volterra Heston model," Post-Print hal-03178306, HAL.
    16. Qinwen Zhu & Gregoire Loeper & Wen Chen & Nicolas Langrené, 2021. "Markovian approximation of the rough Bergomi model for Monte Carlo option pricing," Working Papers hal-02910724, HAL.
    17. Jan Matas & Jan Posp'iv{s}il, 2021. "On simulation of rough Volterra stochastic volatility models," Papers 2108.01999, arXiv.org, revised Aug 2022.
    18. Blanka Horvath & Aitor Muguruza & Mehdi Tomas, 2019. "Deep Learning Volatility," Papers 1901.09647, arXiv.org, revised Aug 2019.
    19. Eduardo Abi Jaber, 2022. "The characteristic function of Gaussian stochastic volatility models: an analytic expression," Working Papers hal-02946146, HAL.
    20. Eduardo Abi Jaber, 2022. "The characteristic function of Gaussian stochastic volatility models: an analytic expression," Finance and Stochastics, Springer, vol. 26(4), pages 733-769, October.

    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:1810.03399. 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.