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Time-Changed Fast Mean-Reverting Stochastic Volatility Models

  • Matthew Lorig
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    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.

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    File URL: http://arxiv.org/pdf/1010.5203
    File Function: Latest version
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    Paper provided by arXiv.org in its series Papers with number 1010.5203.

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    Date of creation: Oct 2010
    Date of revision: Apr 2012
    Publication status: Published in International Journal of Theoretical and Applied Finance Vol. 14, No. 8 (2011) 1355-1383
    Handle: RePEc:arx:papers:1010.5203
    Contact details of provider: 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. Eric Hillebrand, 2005. "Overlaying Time Scales in Financial Volatility Data," Econometrics 0501015, EconWPA.
    3. 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.
    4. Josep Perello & Jaume Masoliver & Jean-Philippe Bouchaud, 2003. "Multiple time scales in volatility and leverage correlation: A stochastic volatility model," Science & Finance (CFM) working paper archive 50001, Science & Finance, Capital Fund Management.
    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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