Implied volatility smirk in Lévy markets

Abstract

We introduce skewed L evy models, characterized by a symmetric jump measure multiplied by dumping exponential factor. This models exhibit a clear implied volatility pattern, where the dumping parameter controls the skew of the implied volatility curve, resulting in a measure of the skewness of the model. We show that the variation of this parameter produces the typical smirk observed in implied volatility curves. Some theoretical facts supporting this ndings are proved, and some open questions are posed.