The Valuation of Multiple Asset American Options under Jump Diffusion Processes

We consider American versions of multiple asset options when the underlying assets follow jump-diffusion processes, for example exchange options and max-options. We consider various representations of the option value and in particular apply Fourier transform techniques to the integro-partial differential equations determining the option value to obtain the jump-diffusion extension of Kim’s integral equation. We also discuss the corresponding perpetual option and the shape of the early exercise region. We particularly focus on numerical implementations when the jump times are governed by a Poisson process and the jump sizes are lognormally distributed. We compare the efficacy of the method of lines, the Crank-Nicholson scheme and solution of the integral equations in generating numerical values of the option