American Call Options Under Jump-Diffusion Processes — A Fourier Transform Approach

摘要

We consider the American option pricing problem in the case where the underlyingasset follows a jump-diffusion process. We apply the method of Jamshidian to transform theproblem of solving a homogeneous integro-partial differential equation (IPDE) on a regionrestricted by the early exercise (free) boundary to that of solving an inhomogeneous IPDE on anunrestricted region. We apply the Fourier transform technique to this inhomogeneous IPDE inthe case of a call option on a dividend paying underlying to obtain the solution in the form of apair of linked integral equations for the free boundary and the option price. We also derive newresults concerning the limit for the free boundary at expiry. Finally, we present a numericalalgorithm for the solution of the linked integral equation system for the American call price, itsdelta and the early exercise boundary. We use the numerical results to quantify the impact ofjumps on American call prices and the early exercise boundary.