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Time-Changed Fast Mean-Reverting Stochastic Volatility Models

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  • Matthew Lorig

Abstract

We introduce a class of randomly time-changed fast mean-reverting stochastic volatility models and, using spectral theory and singular perturbation techniques, we derive an approximation for the prices of European options in this setting. Three examples of random time-changes are provided and the implied volatility surfaces induced by these time-changes are examined as a function of the model parameters. Three key features of our framework are that we are able to incorporate jumps into the price process of the underlying asset, allow for the leverage effect, and accommodate multiple factors of volatility, which operate on different time-scales.

Suggested Citation

  • Matthew Lorig, 2010. "Time-Changed Fast Mean-Reverting Stochastic Volatility Models," Papers 1010.5203, arXiv.org, revised Apr 2012.
  • Handle: RePEc:arx:papers:1010.5203
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    References listed on IDEAS

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    1. Josep Perello & Jaume Masoliver & Jean-Philippe Bouchaud, 2004. "Multiple time scales in volatility and leverage correlations: a stochastic volatility model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 11(1), pages 27-50.
    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, 2005. "Overlaying Time Scales in Financial Volatility Data," Econometrics 0501015, EconWPA.
    4. Chernov, Mikhail & Ronald Gallant, A. & Ghysels, Eric & Tauchen, George, 2003. "Alternative models for stock price dynamics," Journal of Econometrics, Elsevier, pages 225-257.
    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.
    6. Eric Hillebrand, 2003. "Overlaying Time Scales and Persistence Estimation in GARCH(1,1) Models," Econometrics 0301003, EconWPA.
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