SKEWED LEVY MODELS AND IMPLIED VOLATILITY SKEW

We introduce skewed Levy models, characterized by a symmetric jump measure multiplied by a damping exponential factor. These models exhibit a clear implied volatility pattern, where the damping parameter controls the implied volatility curve's skew, resulting in a measure of the model's skewness. We show that the variation of this parameter produces the typical smirk observed in implied volatility curves. Some theoretical facts supporting these findings are proved.