Time-Changed Fast Mean-Reverting Stochastic Volatility Models
AbstractWe 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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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1010.5203.
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
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