Numerical Valuation of American Options Under the CGMY Process
نویسنده
چکیده
American put options written on an underlying stock following a Carr-Madan-Geman-Yor (CGMY) process are considered. It is known that American option prices satisfy a Partial Integro-Differential Equation (PIDE) on a moving domain. These equations are reformulated as a Linear Complementarity Problem, and solved iteratively by an implicit-explicit type of iteration based on a convenient splitting of the Integro-Differential operator. The solution to the discrete complementarity problems is found by the Brennan-Schwartz algorithm and computations are accelerated by the Fast Fourier Transform. The method is illustrated throughout a series of numerical experiments.
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