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A penalty method for American options with jump diffusion processes. (English) Zbl 1126.91036
Summary: The fair price for an American option where the underlying asset follows a jump diffusion process can be formulated as a partial integral differential linear complementarity problem. We develop an implicit discretization method for pricing such American options. The jump diffusion correlation integral term is computed using an iterative method coupled with an FFT while the American constraint is imposed by using a penalty method. We derive sufficient conditions for global convergence of the discrete penalized equations at each timestep. Finally, we present numerical tests which illustrate such convergence.

91B28Finance etc. (MSC2000)
65M06Finite difference methods (IVP of PDE)
45K05Integro-partial differential equations
Full Text: DOI
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