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Large-time asymptotics for an uncorrelated stochastic volatility model

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  • Forde, Martin

Abstract

We derive a large-time large deviation principle for the log stock price under an uncorrelated stochastic volatility model. For this we use a Donsker-Varadhan-type large deviation principle for the occupation measure of the Ornstein-Uhlenbeck process, combined with a simple application of the contraction principle and exponential tightness.

Suggested Citation

  • Forde, Martin, 2011. "Large-time asymptotics for an uncorrelated stochastic volatility model," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1230-1232, August.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:8:p:1230-1232
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    Citations

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    Cited by:

    1. Forde, Martin, 2014. "The large-maturity smile for the Stein–Stein model," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 145-152.
    2. Zhi Jun Guo & Eckhard Platen, 2012. "The Small And Large Time Implied Volatilities In The Minimal Market Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(08), pages 1-23.
    3. Dan Pirjol & Lingjiong Zhu, 2020. "Asymptotics of the time-discretized log-normal SABR model: The implied volatility surface," Papers 2001.09850, arXiv.org, revised Mar 2020.
    4. Martin Forde & Stefan Gerhold & Benjamin Smith, 2019. "Small-time, large-time and $H\to 0$ asymptotics for the Rough Heston model," Papers 1906.09034, arXiv.org, revised Oct 2020.
    5. Martin Forde & Stefan Gerhold & Benjamin Smith, 2021. "Small‐time, large‐time, and H→0 asymptotics for the Rough Heston model," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 203-241, January.

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