Ways to solve Heston model quickly???

OPTION88 · November 3rd, 2009, 8:50 am

hiDoes anyone know how to solve Heston model quickly??It is a good model but I can not calculate it AFAP.Does anyone try Fast Fourier or numerical method??

spursfan · November 3rd, 2009, 10:00 am

Lord and Kahl paper on Fourier Inversion at rogerlord.com - otherwise numerical integration with 128 Gauss-Legendre quadrature points is pretty quick

PierreG · November 3rd, 2009, 1:13 pm

What do you mean by solving Heston model ?For a fast and accurate pricing, Lord and Kahl paper is a good reference. Control variate technique (ie computing BS price using Fourier transform) can be used in addition to their remarks.For a very fast pricing, Benhamou, Gobet and Miri have derived a formula that involves BS price and greeks.For a fast calibration, I suggest that you read Gauthier and Rivaille work which is based on the previous paper.

AVt · November 3rd, 2009, 7:43 pm

Pierre,That is is nice, especially your condensed formula of Benhamou et al in Eq (14) [derivatives are meant, yes?].As soon as one has a fine initial guess (which you give) single smiles are fast to fit.Do you have similar for the 'Piterbarg' modification concerning averaging parameters over time [which I neverunderstood]?For precise computations one still can take Alan Lewis' method with numerical refinements(though its is not quite clear, whether the assumptions are satisfied for Heston's model).