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A Fast Mean-Reverting Correction to Heston's Stochastic Volatility Model

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  • Jean-Pierre Fouque
  • Matthew Lorig
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    Abstract

    We propose a multi-scale stochastic volatility model in which a fast mean-reverting factor of volatility is built on top of the Heston stochastic volatility model. A singular pertubative expansion is then used to obtain an approximation for European option prices. The resulting pricing formulas are semi-analytic, in the sense that they can be expressed as integrals. Difficulties associated with the numerical evaluation of these integrals are discussed, and techniques for avoiding these difficulties are provided. Overall, it is shown that computational complexity for our model is comparable to the case of a pure Heston model, but our correction brings significant flexibility in terms of fitting to the implied volatility surface. This is illustrated numerically and with option data.

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    File URL: http://arxiv.org/pdf/1007.4366
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1007.4366.

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    Date of creation: Jul 2010
    Date of revision: Apr 2012
    Publication status: Published in SIAM J. Finan. Math. 2, 221-254 (2011)
    Handle: RePEc:arx:papers:1007.4366

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    Web page: http://arxiv.org/

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    1. Mikhail Chernov & A. Ronald Gallant & Eric Ghysels & George Tauchen, 2002. "Alternative Models for Stock Price Dynamics," CIRANO Working Papers 2002s-58, CIRANO.
    2. Fiorentini, Gabriele & Leon, Angel & Rubio, Gonzalo, 2002. "Estimation and empirical performance of Heston's stochastic volatility model: the case of a thinly traded market," Journal of Empirical Finance, Elsevier, vol. 9(2), pages 225-255, March.
    3. Eric Hillebrand, 2003. "Overlaying Time Scales and Persistence Estimation in GARCH(1,1) Models," Econometrics 0301003, EconWPA.
    4. Roger Lord & Christian Kahl, 2006. "Why the Rotation Count Algorithm works," Tinbergen Institute Discussion Papers 06-065/2, Tinbergen Institute.
    5. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265.
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