IDEAS home Printed from
   My bibliography  Save this article

Asymptotic analysis for stochastic volatility: martingale expansion


  • Masaaki Fukasawa



No abstract is available for this item.

Suggested Citation

  • Masaaki Fukasawa, 2011. "Asymptotic analysis for stochastic volatility: martingale expansion," Finance and Stochastics, Springer, vol. 15(4), pages 635-654, December.
  • Handle: RePEc:spr:finsto:v:15:y:2011:i:4:p:635-654 DOI: 10.1007/s00780-010-0136-6

    Download full text from publisher

    File URL:
    Download Restriction: Access to full text is restricted to subscribers.

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

    References listed on IDEAS

    1. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
    2. Jean-Pierre Fouque & George Papanicolaou & Ronnie Sircar & Knut Solna, 2004. "Maturity cycles in implied volatility," Finance and Stochastics, Springer, vol. 8(4), pages 451-477, November.
    3. Jean-Pierre Fouque & Ronnie Sircar & Knut Sølna, 2006. "Stochastic Volatility Effects on Defaultable Bonds," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(3), pages 215-244.
    4. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv.
    5. 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.
    6. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Omar El Euch & Mathieu Rosenbaum, 2016. "The characteristic function of rough Heston models," Papers 1609.02108,
    2. Antoine Jacquier & Mikko S. Pakkanen & Henry Stone, 2017. "Pathwise large deviations for the Rough Bergomi model," Papers 1706.05291,, revised Jan 2018.
    3. Jean-Pierre Fouque & Matthew Lorig & Ronnie Sircar, 2016. "Second order multiscale stochastic volatility asymptotics: stochastic terminal layer analysis and calibration," Finance and Stochastics, Springer, vol. 20(3), pages 543-588, July.
    4. Eduardo Abi Jaber & Omar El Euch, 2018. "Multi-factor approximation of rough volatility models," Papers 1801.10359,
    5. Christian Bayer & Peter K. Friz & Paul Gassiat & Joerg Martin & Benjamin Stemper, 2017. "A regularity structure for rough volatility," Papers 1710.07481,
    6. Martin Forde & Hongzhong Zhang, 2016. "Asymptotics for rough stochastic volatility models," Papers 1610.08878,
    7. repec:kap:annfin:v:13:y:2017:i:1:d:10.1007_s10436-016-0289-1 is not listed on IDEAS
    8. Masaaki Fukasawa, 2015. "Short-time at-the-money skew and rough fractional volatility," Papers 1501.06980,
    9. Jim Gatheral & Thibault Jaisson & Mathieu Rosenbaum, 2014. "Volatility is rough," Papers 1410.3394,
    10. Huy N. Chau & Miklos Rasonyi, 2016. "On optimal investment with processes of long or negative memory," Papers 1608.00768,, revised Mar 2017.
    11. Park, Sang-Hyeon & Kim, Jeong-Hoon, 2013. "A semi-analytic pricing formula for lookback options under a general stochastic volatility model," Statistics & Probability Letters, Elsevier, vol. 83(11), pages 2537-2543.
    12. Alev{s} v{C}ern'y & Stephan Denkl & Jan Kallsen, 2013. "Hedging in L\'evy Models and the Time Step Equivalent of Jumps," Papers 1309.7833,, revised Jul 2017.
    13. Elisa Alòs & Kenichiro Shiraya, 2017. "Estimating the Hurst parameter from short term volatility swaps," CARF F-Series CARF-F-407, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    14. Hamza Guennoun & Antoine Jacquier & Patrick Roome & Fangwei Shi, 2014. "Asymptotic behaviour of the fractional Heston model," Papers 1411.7653,, revised Aug 2017.
    15. Archil Gulisashvili & Frederi Viens & Xin Zhang, 2015. "Small-time asymptotics for Gaussian self-similar stochastic volatility models," Papers 1505.05256,, revised Mar 2016.
    16. repec:wsi:ijfexx:v:04:y:2017:i:01:n:s2424786317500141 is not listed on IDEAS
    17. Jean-Pierre Fouque & Matthew Lorig & Ronnie Sircar, 2012. "Second Order Multiscale Stochastic Volatility Asymptotics: Stochastic Terminal Layer Analysis & Calibration," Papers 1208.5802,, revised Sep 2015.
    18. Josselin Garnier & Knut Solna, 2015. "Correction to Black-Scholes formula due to fractional stochastic volatility," Papers 1509.01175,, revised Mar 2017.
    19. Christian Bayer & Peter K. Friz & Archil Gulisashvili & Blanka Horvath & Benjamin Stemper, 2017. "Short-time near-the-money skew in rough fractional volatility models," Papers 1703.05132,
    20. Omar El Euch & Mathieu Rosenbaum, 2017. "Perfect hedging in rough Heston models," Papers 1703.05049,
    21. Omar El Euch & Masaaki Fukasawa & Jim Gatheral & Mathieu Rosenbaum, 2018. "Short-term at-the-money asymptotics under stochastic volatility models," Papers 1801.08675,, revised Jan 2018.
    22. Kazuki Nagashima & Tsz-Kin Chung & Keiichi Tanaka, 2014. "Asymptotic Expansion Formula of Option Price Under Multifactor Heston Model," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 21(4), pages 351-396, November.

    More about this item


    Asymptotic expansion; Fast mean reversion; Fractional Brownian motion; Jump-diffusion; Partial Malliavin calculus; Yoshida’s formula; 60F05; 91B70; C13; G13;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing


    Access and download statistics


    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:spr:finsto:v:15:y:2011:i:4:p:635-654. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla) or (Rebekah McClure). General contact details of provider: .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.