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Zbl 1126.91036
d'Halluin, Y.; Forsyth, P.A.; Labahn, G.
A penalty method for American options with jump diffusion processes. (English)
[J] Numer. Math. 97, No. 2, 321-352 (2004). ISSN 0029-599X; ISSN 0945-3245/e

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.

MSC 2000:: *91B28 Finance etc.
65M06 Finite difference methods (IVP of PDE)
45K05 Integro-partial differential equations

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Zentralblatt MATH Berlin [Germany]