IDEAS home Printed from https://ideas.repec.org/a/wly/jfutmk/v38y2018i9p1043-1061.html
   My bibliography  Save this article

An approximation formula for normal implied volatility under general local stochastic volatility models

Author

Listed:
  • Yasaman Karami
  • Kenichiro Shiraya

Abstract

We approximate normal implied volatilities by means of an asymptotic expansion method. The contribution of this paper is twofold: to our knowledge, this paper is the first to provide a unified approximation method for the normal implied volatility under general local stochastic volatility models. Second, we applied our framework to polynomial local stochastic volatility models with various degrees and could replicate the swaptions market data accurately. In addition we examined the accuracy of the results by comparison with the Monte‐Carlo simulations.

Suggested Citation

  • Yasaman Karami & Kenichiro Shiraya, 2018. "An approximation formula for normal implied volatility under general local stochastic volatility models," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(9), pages 1043-1061, September.
    • Handle: RePEc:wly:jfutmk:v:38:y:2018:i:9:p:1043-1061
    DOI: 10.1002/fut.21931
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/fut.21931
    Download Restriction: no
    File URL: https://libkey.io/10.1002/fut.21931?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
    ---><---

    References listed on IDEAS

    as
    1. Cristian Homescu, 2011. "Implied Volatility Surface: Construction Methodologies and Characteristics," Papers 1107.1834, arXiv.org.
    2. Jaehyuk Choi & Kwangmoon Kim & Minsuk Kwak, 2009. "Numerical Approximation of the Implied Volatility Under Arithmetic Brownian Motion," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(3), pages 261-268.
    3. Matthew Lorig & Stefano Pagliarani & Andrea Pascucci, 2017. "Explicit Implied Volatilities For Multifactor Local-Stochastic Volatility Models," Mathematical Finance, Wiley Blackwell, vol. 27(3), pages 926-960, July.
    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 & 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.
    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.

    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. Yasaman Karami & Kenichiro Shiraya, 2018. "An approximation formula for normal implied volatility under general local stochastic volatility models," CARF F-Series CARF-F-427, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    2. Aït-Sahalia, Yacine & Li, Chenxu & Li, Chen Xu, 2021. "Closed-form implied volatility surfaces for stochastic volatility models with jumps," Journal of Econometrics, Elsevier, vol. 222(1), pages 364-392.
    3. Matthew Lorig & Natchanon Suaysom, 2021. "Options on Bonds: Implied Volatilities from Affine Short-Rate Dynamics," Papers 2106.04518, arXiv.org.
    4. Filippo de Feo, 2020. "The Averaging Principle for Non-autonomous Slow-fast Stochastic Differential Equations and an Application to a Local Stochastic Volatility Model," Papers 2012.09082, arXiv.org, revised Jan 2021.
    5. Zheng Gong & Wojciech Frys & Renzo Tiranti & Carmine Ventre & John O'Hara & Yingbo Bai, 2022. "A new encoding of implied volatility surfaces for their synthetic generation," Papers 2211.12892, arXiv.org, revised Jun 2023.
    6. Akihiko Takahashi & Toshihiro Yamada, 2015. "On Error Estimates for Asymptotic Expansions with Malliavin Weights: Application to Stochastic Volatility Model," Mathematics of Operations Research, INFORMS, vol. 40(3), pages 513-541, March.
    7. Mnacho Echenim & Emmanuel Gobet & Anne-Claire Maurice, 2022. "Unbiasing and robustifying implied volatility calibration in a cryptocurrency market with large bid-ask spreads and missing quotes," Papers 2207.02989, arXiv.org.
    8. Ankush Agarwal & Matthew Lorig, 2019. "The implied Sharpe ratio," Papers 1908.04837, arXiv.org.
    9. Matthew Lorig, 2014. "Indifference prices and implied volatilities," Papers 1412.5520, arXiv.org, revised Sep 2015.
    10. David Berger & Ian Dew-Becker & Stefano Giglio, 2020. "Uncertainty Shocks as Second-Moment News Shocks," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 87(1), pages 40-76.
    11. repec:hal:wpaper:hal-03715921 is not listed on IDEAS
    12. Matthew Lorig & Stefano Pagliarani & Andrea Pascucci, 2013. "A Taylor series approach to pricing and implied vol for LSV models," Papers 1308.5019, arXiv.org.
    13. Matthew Lorig & Natchanon Suaysom, 2022. "Options on bonds: implied volatilities from affine short-rate dynamics," Annals of Finance, Springer, vol. 18(2), pages 183-216, June.
    14. Andrea Barletta & Elisa Nicolato & Stefano Pagliarani, 2019. "The short‐time behavior of VIX‐implied volatilities in a multifactor stochastic volatility framework," Mathematical Finance, Wiley Blackwell, vol. 29(3), pages 928-966, July.
    15. Wan, Xiangwei & Yang, Nian, 2021. "Hermite expansion of transition densities and European option prices for multivariate diffusions with jumps," Journal of Economic Dynamics and Control, Elsevier, vol. 125(C).
    16. Fernández, J.L. & Ferreiro, A.M. & García-Rodríguez, J.A. & Leitao, A. & López-Salas, J.G. & Vázquez, C., 2013. "Static and dynamic SABR stochastic volatility models: Calibration and option pricing using GPUs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 55-75.
    17. Martin Magris & Perttu Barholm & Juho Kanniainen, 2017. "Implied volatility smile dynamics in the presence of jumps," Papers 1711.02925, arXiv.org, revised May 2020.
    18. Ankush Agarwal & Ronnie Sircar, 2017. "Portfolio Benchmarking under Drawdown Constraint and Stochastic Sharpe Ratio," Working Papers hal-01388399, HAL.
    19. Kaustav Das & Nicolas Langren'e, 2018. "Closed-form approximations with respect to the mixing solution for option pricing under stochastic volatility," Papers 1812.07803, arXiv.org, revised Oct 2021.
    20. 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.
    21. Stefano Giglio & Ian Dew-Becker & David Berger, 2016. "Contractionary Volatility or Volatile Contractions?," 2016 Meeting Papers 673, Society for Economic Dynamics.

    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:wly:jfutmk:v:38:y:2018:i:9:p:1043-1061. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.interscience.wiley.com/jpages/0270-7314/ .

    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.