IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1004.2106.html

Asymptotic analysis for stochastic volatility: Edgeworth expansion

Author

Listed:
  • Masaaki Fukasawa

Abstract

The validity of an approximation formula for European option prices under a general stochastic volatility model is proved in the light of the Edgeworth expansion for ergodic diffusions. The asymptotic expansion is around the Black-Scholes price and is uniform in bounded payoff func- tions. The result provides a validation of an existing singular perturbation expansion formula for the fast mean reverting stochastic volatility model.

Suggested Citation

  • Masaaki Fukasawa, 2010. "Asymptotic analysis for stochastic volatility: Edgeworth expansion," Papers 1004.2106, arXiv.org.
    • Handle: RePEc:arx:papers:1004.2106
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1004.2106
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
    2. Fitzsimmons, P. J. & Pitman, Jim, 1999. "Kac's moment formula and the Feynman-Kac formula for additive functionals of a Markov process," Stochastic Processes and their Applications, Elsevier, vol. 79(1), pages 117-134, January.
    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. Christian Bayer & Peter Friz & Jim Gatheral, 2016. "Pricing under rough volatility," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 887-904, June.
    2. Blanka Horvath & Josef Teichmann & Zan Zuric, 2021. "Deep Hedging under Rough Volatility," Papers 2102.01962, arXiv.org.
    3. Antoine Jacquier & Claude Martini & Aitor Muguruza, 2018. "On VIX futures in the rough Bergomi model," Quantitative Finance, Taylor & Francis Journals, vol. 18(1), pages 45-61, January.

    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. Buckle, Mike & Chen, Jing & Guo, Qian & Li, Xiaoxi, 2023. "Does smile help detect the UK's price leadership change after MiFID?," International Review of Economics & Finance, Elsevier, vol. 84(C), pages 756-769.
    2. Audrino, Francesco & Fengler, Matthias R., 2015. "Are classical option pricing models consistent with observed option second-order moments? Evidence from high-frequency data," Journal of Banking & Finance, Elsevier, vol. 61(C), pages 46-63.
    3. Nielsen, Morten Ørregaard & Frederiksen, Per, 2008. "Finite sample accuracy and choice of sampling frequency in integrated volatility estimation," Journal of Empirical Finance, Elsevier, vol. 15(2), pages 265-286, March.
    4. Becker, Ralf & Clements, Adam E., 2008. "Are combination forecasts of S&P 500 volatility statistically superior?," International Journal of Forecasting, Elsevier, vol. 24(1), pages 122-133.
    5. Mattiussi, V. & Iori, G., 2006. "Currency futures volatility during the 1997 East Asian crisis: an application of Fourier analysis," Working Papers 06/09, Department of Economics, City St George's, University of London.
    6. Degiannakis, Stavros & Floros, Christos, 2016. "Intra-day realized volatility for European and USA stock indices," Global Finance Journal, Elsevier, vol. 29(C), pages 24-41.
    7. Christophe Chorro & Florian Ielpo & Benoît Sévi, 2017. "The contribution of jumps to forecasting the density of returns," Post-Print halshs-01442618, HAL.
    8. N. Antonakakis & J. Darby, 2013. "Forecasting volatility in developing countries' nominal exchange returns," Applied Financial Economics, Taylor & Francis Journals, vol. 23(21), pages 1675-1691, November.
    9. Beyer, Deborah B. & Fan, Zaifeng S., 2023. "The calming effects of conflict: The impact of partisan conflict on market volatility," International Review of Financial Analysis, Elsevier, vol. 85(C).
    10. Woerner Jeannette H. C., 2003. "Variational sums and power variation: a unifying approach to model selection and estimation in semimartingale models," Statistics & Risk Modeling, De Gruyter, vol. 21(1), pages 47-68, January.
    11. Ferland, Rene & Lalancette, Simon, 2006. "Dynamics of realized volatilities and correlations: An empirical study," Journal of Banking & Finance, Elsevier, vol. 30(7), pages 2109-2130, July.
    12. Jinliang Li & Chihwa Kao & Wei David Zhang, 2010. "Bounded influence estimator for GARCH models: evidence from foreign exchange rates," Applied Economics, Taylor & Francis Journals, vol. 42(11), pages 1437-1445.
    13. Raggi, Davide & Bordignon, Silvano, 2012. "Long memory and nonlinearities in realized volatility: A Markov switching approach," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3730-3742.
    14. Kaeck, Andreas & Rodrigues, Paulo & Seeger, Norman J., 2017. "Equity index variance: Evidence from flexible parametric jump–diffusion models," Journal of Banking & Finance, Elsevier, vol. 83(C), pages 85-103.
    15. Hooper, Vincent J. & Ng, Kevin & Reeves, Jonathan J., 2008. "Quarterly beta forecasting: An evaluation," International Journal of Forecasting, Elsevier, vol. 24(3), pages 480-489.
    16. Dell'Era Mario, M.D., 2008. "Pricing of Double Barrier Options by Spectral Theory," MPRA Paper 17502, University Library of Munich, Germany.
    17. Christophe Chorro & Florian Ielpo & Benoît Sévi, 2020. "The contribution of intraday jumps to forecasting the density of returns," Post-Print halshs-02505861, HAL.
    18. Toshiaki Ogawa & Masato Ubukata & Toshiaki Watanabe, 2020. "Stock Return Predictability and Variance Risk Premia around the ZLB," IMES Discussion Paper Series 20-E-09, Institute for Monetary and Economic Studies, Bank of Japan.
    19. Athanasia Gavala & Nikolay Gospodinov & Deming Jiang, 2006. "Forecasting volatility," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(6), pages 381-400.
    20. Huiling Yuan & Kexin Lu & Guodong Li & Junhui Wang, 2024. "High‐Frequency‐Based Volatility Model with Network Structure," Journal of Time Series Analysis, Wiley Blackwell, vol. 45(4), pages 533-557, July.

    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:1004.2106. 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.