Time-Changed Fast Mean-Reverting Stochastic Volatility Models
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.
|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|
|Contact details of provider:|| Web page: http://arxiv.org/|
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- 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.
- 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.
- Josep Perello & Jaume Masoliver & Jean-Philippe Bouchaud, 2003. "Multiple time scales in volatility and leverage correlations: An stochastic volatility model," Papers cond-mat/0302095, arXiv.org.
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- Mikhail Chernov & A. Ronald Gallant & Eric Ghysels & George Tauchen, 2002. "Alternative Models for Stock Price Dynamics," CIRANO Working Papers 2002s-58, CIRANO.
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- Eric Hillebrand, 2003. "Overlaying Time Scales and Persistence Estimation in GARCH(1,1) Models," Econometrics 0301003, EconWPA. Full references (including those not matched with items on IDEAS)
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