ON FOURIER AND LAPLACE TRANSFORM METHODS FOR SIMPLE, MULTI-ASSET, AND PATH-DEPENDENT OPTIONS -ACCURACY AND EFFICIENCY

This talk consists of two parts: In the first part we consider various integral representations
for payoffs of simple, multi-asset, path-dependent derivatives and their relation. Those results emerged as a by-product on our work on variance-optimal hedging but are useful for all pricing and hedging problems, where transform-based methods, characteristic function techniques, etc. can be applied. In the second part we discuss various general issues concerning the accuracy and efficiency of the above, and give some numerical illustrations.