Option pricing under generalized Lévy processes with state dependent parameters and the volatility surface

This paper presents a very general option pricing formula incorporating both thenLévy process methodology and the level dependent volatility approach. An approximate solution to the pricing problem is obtained throughout the construction of a parametrix by means of the pseudo differential calculus. Some examples are provided to illustrate the comprehensiveness of the framework. Finally, the implications in terms of the volatility smile are discussed.