Fourier Cosine Expansions and Put–Call Relations for Bermudan Options

In this chapter we describe the pricing of Bermudan options by means of Fourier cosine expansions. We propose a technique to price early-exercise call options with the help of the (European) put-call parity and put–call duality relations. Direct pricing of call options with cosine expansions may give rise to some sensitivity regarding the choice of the size of the domain in which the Fourier expansion is applied. By employing the put–call parity or put–call duality relations, this can be avoided so that call options governed by fat-tailed asset price distributions can be priced as robust and efficiently as put options. Bowen Zhang Delft Institute of Applied Mathematics, Delft University of Technology, the Netherlands, e-mail: [email protected] Cornelis W. Oosterlee CWI Center for Mathematics and Computer Science, Amsterdam, and Delft University of Technology, the Netherlands e-mail: [email protected]