Hot answers tagged numerical-methods
In SV model, it is well-known that the integrand for the call price can sometimes show high oscillation, can dampen very slowly along the integration axis, and can show discontinuities. Remedy The ‘‘Little Trap’’ formulation of Albrecher et al. Also , you can use Fourier transforms Bakshi and Madan (2000) Lewis,(2001). Gatheral (2006) Carr and ...
There has been a huge amount of work on this. Generally a Fourier transform approach is used. First, be careful to use the form of the characteristic function that does not wind about zero in order to avoid having to count the normal of windings. Second, using contour shifts can make the integral much better behaved. eg integrate along the line with $0.5$...
I'd use FFT or similar rather than direct integration. Here is an old paper with Heston example: Option pricing using fractional FFT
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