IDEAS home Printed from https://ideas.repec.org/a/taf/quantf/v21y2021i7p1083-1086.html
   My bibliography  Save this article

A note on the option price and ‘Mass at zero in the uncorrelated SABR model and implied volatility asymptotics’

Author

Listed:
  • Jaehyuk Choi
  • Lixin Wu

Abstract

Gulisashvili et al. [Quant. Finance, 2018, 18(10), 1753–1765] provide short term asymptotics for the mass at zero under the uncorrelated stochastic-alpha-beta-rho (SABR) model by approximating the integrated variance with a moment-matched lognormal distribution. We improve the accuracy of the numerical integration by using Gauss–Hermite quadrature. We further obtain the option price by similarly integrating the constant elasticity of variance (CEV) option prices without resorting to the small-strike volatility smile asymptotics of De Marco et al. [SIAM J. Financ. Math., 2017, 8(1), 709–737]. For the uncorrelated SABR model, the new option pricing method is accurate and arbitrage-free across all strike prices.

Suggested Citation

  • Jaehyuk Choi & Lixin Wu, 2021. "A note on the option price and ‘Mass at zero in the uncorrelated SABR model and implied volatility asymptotics’," Quantitative Finance, Taylor & Francis Journals, vol. 21(7), pages 1083-1086, July.
    • Handle: RePEc:taf:quantf:v:21:y:2021:i:7:p:1083-1086
    DOI: 10.1080/14697688.2021.1876908
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/14697688.2021.1876908
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/14697688.2021.1876908?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Jaehyuk Choi & Chenru Liu & Byoung Ki Seo, 2019. "Hyperbolic normal stochastic volatility model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(2), pages 186-204, February.
    2. Stefano De Marco & Caroline Hillairet & Antoine Jacquier, 2017. "Shapes of implied volatility with positive mass at zero," Working Papers 2017-77, Center for Research in Economics and Statistics.
    3. Archil Gulisashvili & Blanka Horvath & Antoine Jacquier, 2018. "Mass at zero in the uncorrelated SABR model and implied volatility asymptotics," Quantitative Finance, Taylor & Francis Journals, vol. 18(10), pages 1753-1765, October.
    4. Stefano De Marco & Caroline Hillairet & Antoine Jacquier, 2013. "Shapes of implied volatility with positive mass at zero," Papers 1310.1020, arXiv.org, revised May 2017.
    5. Choi, Jaehyuk & Wu, Lixin, 2021. "The equivalent constant-elasticity-of-variance (CEV) volatility of the stochastic-alpha-beta-rho (SABR) model," Journal of Economic Dynamics and Control, Elsevier, vol. 128(C).
    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. Jaehyuk Choi & Byoung Ki Seo, 2023. "Option pricing under the normal SABR model with Gaussian quadratures," Papers 2301.02797, arXiv.org.
    2. Choi, Jaehyuk & Wu, Lixin, 2021. "The equivalent constant-elasticity-of-variance (CEV) volatility of the stochastic-alpha-beta-rho (SABR) model," Journal of Economic Dynamics and Control, Elsevier, vol. 128(C).
    3. Jaehyuk Choi & Minsuk Kwak & Chyng Wen Tee & Yumeng Wang, 2021. "A Black-Scholes user's guide to the Bachelier model," Papers 2104.08686, arXiv.org, revised Feb 2022.
    4. Jaehyuk Choi & Lilian Hu & Yue Kuen Kwok, 2024. "Efficient simulation of the SABR model," Papers 2408.01898, arXiv.org.
    5. Jaehyuk Choi & Minsuk Kwak & Chyng Wen Tee & Yumeng Wang, 2022. "A Black–Scholes user's guide to the Bachelier model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(5), pages 959-980, May.

    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. Choi, Jaehyuk & Wu, Lixin, 2021. "The equivalent constant-elasticity-of-variance (CEV) volatility of the stochastic-alpha-beta-rho (SABR) model," Journal of Economic Dynamics and Control, Elsevier, vol. 128(C).
    2. Jaehyuk Choi & Minsuk Kwak & Chyng Wen Tee & Yumeng Wang, 2022. "A Black–Scholes user's guide to the Bachelier model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(5), pages 959-980, May.
    3. Jaehyuk Choi & Lilian Hu & Yue Kuen Kwok, 2024. "Efficient simulation of the SABR model," Papers 2408.01898, arXiv.org.
    4. Jaehyuk Choi & Byoung Ki Seo, 2023. "Option pricing under the normal SABR model with Gaussian quadratures," Papers 2301.02797, arXiv.org.
    5. Vimal Raval & Antoine Jacquier, 2021. "The Log Moment formula for implied volatility," Papers 2101.08145, arXiv.org.
    6. Cyril Grunspan & Joris van der Hoeven, 2020. "Effective asymptotic analysis for finance," Post-Print hal-01573621, HAL.
    7. Jaehyuk Choi & Jeonggyu Huh & Nan Su, 2023. "Tighter 'uniform bounds for Black-Scholes implied volatility' and the applications to root-finding," Papers 2302.08758, arXiv.org, revised Oct 2024.
    8. Claude Martini & Arianna Mingone, 2020. "No arbitrage SVI," Papers 2005.03340, arXiv.org, revised May 2021.
    9. Michael R. Tehranchi, 2020. "A Black–Scholes inequality: applications and generalisations," Finance and Stochastics, Springer, vol. 24(1), pages 1-38, January.
    10. Jaehyuk Choi & Minsuk Kwak & Chyng Wen Tee & Yumeng Wang, 2021. "A Black-Scholes user's guide to the Bachelier model," Papers 2104.08686, arXiv.org, revised Feb 2022.
    11. Cyril Grunspan & Joris Van Der Hoeven, 2020. "Effective Asymptotics Analysis For Finance," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(02), pages 1-23, March.
    12. Jaehyuk Choi, 2024. "Exact simulation scheme for the Ornstein-Uhlenbeck driven stochastic volatility model with the Karhunen-Lo\`eve expansions," Papers 2402.09243, arXiv.org.
    13. Choi, Jaehyuk & Kwok, Yue Kuen, 2024. "Simulation schemes for the Heston model with Poisson conditioning," European Journal of Operational Research, Elsevier, vol. 314(1), pages 363-376.
    14. Jaehyuk Choi & Yue Kuen Kwok, 2023. "Simulation schemes for the Heston model with Poisson conditioning," Papers 2301.02800, arXiv.org, revised Nov 2023.
    15. Blanka Horvath & Aitor Muguruza & Mehdi Tomas, 2019. "Deep Learning Volatility," Papers 1901.09647, arXiv.org, revised Aug 2019.

    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:taf:quantf:v:21:y:2021:i:7:p:1083-1086. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/RQUF20 .

    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.