Pricing and hedging in exponential Lévy models: Review of recent results

Abstract

These lecture notes cover a major part of the crash course on financial modeling with jump processes given by the author in Bologna on May 21-22, 2009. After a brief introduction, we discuss three aspects of exponential Lévy models: absence of arbitrage, including more recent results on the absence of arbitrage in multidimensional models, properties of implied volatility, and modern approaches to hedging in these models.