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Asymptotic analysis for stochastic volatility: martingale expansion


  • Masaaki Fukasawa



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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

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    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. 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.
    5. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, June.
    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.
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    Cited by:

    1. Omar El Euch & Mathieu Rosenbaum, 2016. "The characteristic function of rough Heston models," Papers 1609.02108,
    2. repec:wsi:ijfexx:v:04:y:2017:i:01:n:s2424786317500141 is not listed on IDEAS
    3. 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.
    4. 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.
    5. Martin Forde & Hongzhong Zhang, 2016. "Asymptotics for rough stochastic volatility models," Papers 1610.08878,
    6. repec:kap:annfin:v:13:y:2017:i:1:d:10.1007_s10436-016-0289-1 is not listed on IDEAS
    7. Josselin Garnier & Knut Solna, 2015. "Correction to Black-Scholes formula due to fractional stochastic volatility," Papers 1509.01175,, revised Mar 2017.
    8. 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,, revised Mar 2018.
    9. Antoine Jacquier & Mikko S. Pakkanen & Henry Stone, 2017. "Pathwise large deviations for the Rough Bergomi model," Papers 1706.05291,, revised Jan 2018.
    10. Masaaki Fukasawa, 2015. "Short-time at-the-money skew and rough fractional volatility," Papers 1501.06980,
    11. Jim Gatheral & Thibault Jaisson & Mathieu Rosenbaum, 2014. "Volatility is rough," Papers 1410.3394,
    12. Huy N. Chau & Miklos Rasonyi, 2016. "On optimal investment with processes of long or negative memory," Papers 1608.00768,, revised Mar 2017.
    13. 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.
    14. Eduardo Abi Jaber & Omar El Euch, 2018. "Multi-factor approximation of rough volatility models," Working Papers hal-01697117, HAL.
    15. Hamza Guennoun & Antoine Jacquier & Patrick Roome & Fangwei Shi, 2014. "Asymptotic behaviour of the fractional Heston model," Papers 1411.7653,, revised Aug 2017.
    16. Omar El Euch & Mathieu Rosenbaum, 2017. "Perfect hedging in rough Heston models," Papers 1703.05049,
    17. 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.
    18. Eduardo Abi Jaber & Omar El Euch, 2018. "Multi-factor approximation of rough volatility models," Papers 1801.10359,, revised Apr 2018.
    19. Christian Bayer & Peter K. Friz & Paul Gassiat & Joerg Martin & Benjamin Stemper, 2017. "A regularity structure for rough volatility," Papers 1710.07481,
    20. Archil Gulisashvili & Frederi Viens & Xin Zhang, 2015. "Small-time asymptotics for Gaussian self-similar stochastic volatility models," Papers 1505.05256,, revised Mar 2016.
    21. 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.
    22. 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.
    23. 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


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