Download This PaperThe Smile in Stochastic Volatility Models
15 Pages Posted: 3 Dec 2011 Last revised: 6 May 2012
Date Written: December 2, 2011
Abstract
We consider general stochastic volatility models with no local volatility component and derive the general expression of the volatility smile at order two in volatility-of-volatility. We show how, at this order, the smile only depends on three dimensionless numbers whose precise expressions as functionals of the model's spot/variance and variance/variance covariance functions we provide.
Finally we assess the accuracy of our order two expansion using realistic levels of volatility-of-volatility.
JEL Classification: G13
Suggested Citation: Suggested Citation
Bergomi, Lorenzo and Guyon, Julien, The Smile in Stochastic Volatility Models (December 2, 2011). Available at SSRN: https://ssrn.com/abstract=1967470 or http://dx.doi.org/10.2139/ssrn.1967470
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