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Numerical valuation of European and american options under Kou’s jump-diffusion model. (English) Zbl 1178.35225
In this paper a numerical valuation of European and American options under Kou’s jump-diffusion is developed. After a detailed theoretical development a number of experiments are developed and illustrated the theory in practice. Numerical experiments confirm that the developed methods are very efficient as fairly accurate option prices can be computed in a few milliseconds on a PC.

MSC:
35K85 Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35Q91 PDEs in connection with game theory, economics, social and behavioral sciences
91G80 Financial applications of other theories
91B25 Asset pricing models (MSC2010)
35A35 Theoretical approximation in context of PDEs
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