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Martingale expansion for stochastic volatility

Author

Listed:
  • Masaaki Fukasawa

Abstract

The martingale expansion provides a refined approximation to the marginal distributions of martingales beyond the normal approximation implied by the martingale central limit theorem. We develop a martingale expansion framework specifically suited to continuous stochastic volatility models. Our approach accommodates both small volatility-of-volatility and fast mean-reversion models, yielding first-order perturbation expansions under essentially minimal conditions.

Suggested Citation

  • Masaaki Fukasawa, 2026. "Martingale expansion for stochastic volatility," Papers 2601.09324, arXiv.org, revised Feb 2026.
    • Handle: RePEc:arx:papers:2601.09324
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    File URL: http://arxiv.org/pdf/2601.09324
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    References listed on IDEAS

    as
    1. Masaaki Fukasawa, 2021. "Volatility has to be rough," Quantitative Finance, Taylor & Francis Journals, vol. 21(1), pages 1-8, January.
    2. Christian Bayer & Peter Friz & Jim Gatheral, 2016. "Pricing under rough volatility," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 887-904, June.
    3. Josselin Garnier & Knut Sølna, 2019. "Option pricing under fast‐varying long‐memory stochastic volatility," Mathematical Finance, Wiley Blackwell, vol. 29(1), pages 39-83, January.
    4. Masaaki Fukasawa, 2011. "Asymptotic analysis for stochastic volatility: martingale expansion," Finance and Stochastics, Springer, vol. 15(4), pages 635-654, December.
    5. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv.
    6. Omar El Euch & Masaaki Fukasawa & Jim Gatheral & Mathieu Rosenbaum, 2018. "Short-term at-the-money asymptotics under stochastic volatility models," Papers 1801.08675, arXiv.org, revised Mar 2019.
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    Cited by:

    1. Masaaki Fukasawa, 2026. "On the Skew Stickiness Ratio," Papers 2602.05241, arXiv.org.

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