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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 $O\left({N}_{t}NlogN\right)$, rendering the method fast.
##### MSC:
 91B28 Finance etc. (MSC2000) 45K05 Integro-partial differential equations 45D05 Volterra integral equations 65R20 Integral equations (numerical methods)