The purpose of this paper is to propose several approximating methods to obtain the American option prices under jump-diffusion processes. The first method is to extend an approximating method to the optimal exercise boundary by a multipiece exponential function suggested by Ju . The second approach is to modify the analytical methods of MacMillan  and Zhang  in a discrete time space. The third approach is to apply the simulation technique of Ibanez and Zapareto  to the problem of American option pricing when the jumps are allowed. Finally, we compare the numerical performance of each suggesting method with those of the previous numerical approaches.
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