IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2309.07023.html
   My bibliography  Save this paper

Weak Markovian Approximations of Rough Heston

Author

Listed:
  • Christian Bayer
  • Simon Breneis

Abstract

The rough Heston model is a very popular recent model in mathematical finance; however, the lack of Markov and semimartingale properties poses significant challenges in both theory and practice. A way to resolve this problem is to use Markovian approximations of the model. Several previous works have shown that these approximations can be very accurate even when the number of additional factors is very low. Existing error analysis is largely based on the strong error, corresponding to the $L^2$ distance between the kernels. Extending earlier results by [Abi Jaber and El Euch, SIAM Journal on Financial Mathematics 10(2):309--349, 2019], we show that the weak error of the Markovian approximations can be bounded using the $L^1$-error in the kernel approximation for general classes of payoff functions for European style options. Moreover, we give specific Markovian approximations which converge super-polynomially in the number of dimensions, and illustrate their numerical superiority in option pricing compared to previously existing approximations. The new approximations also work for the hyper-rough case $H > -1/2$.

Suggested Citation

  • Christian Bayer & Simon Breneis, 2023. "Weak Markovian Approximations of Rough Heston," Papers 2309.07023, arXiv.org.
    • Handle: RePEc:arx:papers:2309.07023
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2309.07023
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ernst Eberlein & Kathrin Glau & Antonis Papapantoleon, 2010. "Analysis of Fourier Transform Valuation Formulas and Applications," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(3), pages 211-240.
    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. Antonis Papapantoleon & Jasper Rou, 2024. "A time-stepping deep gradient flow method for option pricing in (rough) diffusion models," Papers 2403.00746, arXiv.org.
    2. Aur'elien Alfonsi & Edoardo Lombardo, 2024. "High order approximations of the log-Heston process semigroup," Papers 2407.17151, arXiv.org.
    3. Ulrich Horst & Wei Xu & Rouyi Zhang, 2023. "Convergence of Heavy-Tailed Hawkes Processes and the Microstructure of Rough Volatility," Papers 2312.08784, arXiv.org, revised Nov 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. Asai, Manabu & McAleer, Michael, 2015. "Leverage and feedback effects on multifactor Wishart stochastic volatility for option pricing," Journal of Econometrics, Elsevier, vol. 187(2), pages 436-446.
    2. Martijn Pistorius & Johannes Stolte, 2012. "Fast computation of vanilla prices in time-changed models and implied volatilities using rational approximations," Papers 1203.6899, arXiv.org.
    3. Michael Schmutz & Thomas Zürcher, 2014. "Static Hedging with Traffic Light Options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(7), pages 690-702, July.
    4. Stefan Waldenberger, 2015. "The affine inflation market models," Papers 1503.04979, arXiv.org.
    5. Alessandro Ramponi, 2012. "Fourier Transform Methods For Regime-Switching Jump-Diffusions And The Pricing Of Forward Starting Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(05), pages 1-26.
    6. Fontana, Claudio & Gnoatto, Alessandro & Szulda, Guillaume, 2023. "CBI-time-changed Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 163(C), pages 323-349.
    7. Fred Espen Benth & Giulia Di Nunno & Asma Khedher & Maren Diane Schmeck, 2015. "Pricing of Spread Options on a Bivariate Jump Market and Stability to Model Risk," Applied Mathematical Finance, Taylor & Francis Journals, vol. 22(1), pages 28-62, March.
    8. Christian Bayer & John Schoenmakers, 2015. "Option pricing in affine generalized Merton models," Papers 1512.03677, arXiv.org.
    9. Alfeus, Mesias & Grasselli, Martino & Schlögl, Erik, 2020. "A consistent stochastic model of the term structure of interest rates for multiple tenors," Journal of Economic Dynamics and Control, Elsevier, vol. 114(C).
    10. Ernst Eberlein & Christoph Gerhart & Zorana Grbac, 2019. "Multiple curve Lévy forward price model allowing for negative interest rates," Post-Print hal-03898912, HAL.
    11. repec:uts:finphd:41 is not listed on IDEAS
    12. Flavio Angelini & Katia Colaneri & Stefano Herzel & Marco Nicolosi, 2021. "Implicit incentives for fund managers with partial information," Computational Management Science, Springer, vol. 18(4), pages 539-561, October.
    13. Christian Bayer & Chiheb Ben Hammouda & Antonis Papapantoleon & Michael Samet & Ra'ul Tempone, 2024. "Quasi-Monte Carlo for Efficient Fourier Pricing of Multi-Asset Options," Papers 2403.02832, arXiv.org.
    14. Holger Fink & Stefan Mittnik, 2021. "Quanto Pricing beyond Black–Scholes," JRFM, MDPI, vol. 14(3), pages 1-27, March.
    15. Michael Schmutz & Thomas Zurcher, 2010. "Static replications with traffic light options," Papers 1011.4795, arXiv.org.
    16. Mesias Alfeus & Erik Schlögl, 2018. "On Numerical Methods for Spread Options," Research Paper Series 388, Quantitative Finance Research Centre, University of Technology, Sydney.
    17. St'ephane Goutte & Nadia Oudjane & Francesco Russo, 2013. "Variance optimal hedging for continuous time additive processes and applications," Papers 1302.1965, arXiv.org.
    18. Samuel Drapeau & Michael Kupper & Antonis Papapantoleon, 2012. "A Fourier Approach to the Computation of CV@R and Optimized Certainty Equivalents," Papers 1212.6732, arXiv.org, revised Dec 2013.
    19. Fajardo, José, 2015. "Barrier style contracts under Lévy processes: An alternative approach," Journal of Banking & Finance, Elsevier, vol. 53(C), pages 179-187.
    20. Yannis G. Yatracos, 2013. "Option pricing, Bayes risks and Applications," Papers 1304.5156, arXiv.org.
    21. Rihito Sakurai & Haruto Takahashi & Koichi Miyamoto, 2024. "Learning parameter dependence for Fourier-based option pricing with tensor trains," Papers 2405.00701, arXiv.org, revised Oct 2024.

    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:2309.07023. 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.