Mathematics for various disciplines The numerical treatment of pricing early exercise options under L'evy processes

2007-04-11 10:30 - 2007-04-11 11:30
Graduate School of Mathematical Sciences the University of Tokyo, Room #056
C. W. Oosterlee (Delft University of Technology)
In this presentation we will discuss the pricing of American and Bermudan options under L'evy process dynamics. Two different approaches will be discussed: First of all, modelling with differential operators gives rise to the numerical solution of a partial-integro differential equation for obtaining Europeanoption prices. For American prices a linear complementarity problem with thepartial integro-differential operator needs to be solved. We outline thedifficulties and possible solutions in this context. At the same time we would also like to present a different pricing approachbased on numerical integration and the fast Fourier Transform. Both approachesare compared in terms of accuracy and efficiency.