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Zbl 1151.91473
Almendral, Ariel; Oosterlee, Cornelis W.
Accurate evaluation of European and American options under the CGMY process. (English)
[J] SIAM J. Sci. Comput. 29, No. 1, 93-117 (2007). ISSN 1064-8275; ISSN 1095-7197/e

Summary: A finite-difference method for integro-differential equations arising from Lévy driven asset processes in finance is discussed. The equations are discretized in space by the collocation method and in time by an explicit backward differentiation formula. The discretization is shown to be second-order accurate for a relevant parameter range determining the degree of the singularity in the Lévy measure. The singularity is dealt with by means of an integration by parts technique. An application of the fast Fourier transform gives the overall amount of work $O(N_t N\log N)$, rendering the method fast.

MSC 2000:: *91B28 Finance etc.
45K05 Integro-partial differential equations
45D05 Volterra integral equations
65R20 Integral equations (numerical methods)

Keywords: partial integro-differential equations; collocation method; option pricing

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Zentralblatt MATH Berlin [Germany]