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Accurate evaluation of European and American options under the CGMY process. (English) Zbl 1151.91473
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 NlogN), rendering the method fast.
MSC:
91B28Finance etc. (MSC2000)
45K05Integro-partial differential equations
45D05Volterra integral equations
65R20Integral equations (numerical methods)