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 Kimâ€™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
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