19 Pages Posted: 1 Jan 2015
Date Written: December 30, 2014
We introduce skewed Lévy models, that have a symmetric jump measure multiplied by dumping exponential factor, in order to study the implied volatility smirk in Lévy markets. The dumping factor depends on a parameter beta, this results in a measure of the skewness of the model. We show that variation of this parameter produces the typical smirk observed in implied volatility curves. Our main result shows a particular monotonicity behavior of the implied volatility of skewed models around the symmetry point beta = -1/2. These results, which apply to many models in the literature, hold independent of any finite maturity.
Keywords: Skewness, Lévy Processes, Implied Volatility Smirk.
JEL Classification: G10, G12
Suggested Citation: Suggested Citation
De Olivera, Federico and Fajardo, José and Mordecki, Ernesto, Implied Volatility Smirk in Lévy Markets (December 30, 2014). Available at SSRN: https://ssrn.com/abstract=2544108 or http://dx.doi.org/10.2139/ssrn.2544108