Hi,I am trying to use the FFT to calculate call prices in the Heston model according to Carr & Madan, but my code gives negative call prices for some strikes.I'm using the stable characteristic function suggested by e.g. Albrecher et al, but still get problems.However, it seems like the code works if I change the Simpson weighting to 1/3*(3 + ( -i )^j - delta) rather than the suggested 1/3*(3 + ( -1 )^j - delta).Would appreciate if anyone has any idea why this solves the problem or, maybe even better, why I get the problem in the first place.The code is provided below for reference.Thanks,Niklas function [c k] = HestonFFT(x,r)N = 4096; eta = 0.15; b = pi/eta;alpha = 0.75;u = (0:N-1) * eta;k = -b + (0:N-1) * 2*b/N;cf = HestonCF(alpha, u, x)% Simpson weightsS = 1/3 * (3 + (-1).^(1:N) - eye(1,N));f_FFT = exp(i*b*u) .* exp(-r*t) * cf .* S ./ (alpha^2 + alpha - u.^2 + i*(2*alpha+1)*u);FFT = fft(f_FFT);c = real(FFT .* exp(-alpha*k) / pi);end

Anyone...?

Indeed, even you use the unchanged weired Simpson's rule, you still get negative prices somewhere in the middle.

Try to use the logarithm of the characteristic function as much as you can and transform back at the end of your calculation.I have implemented the Carr Madan (first and refined) method. Indeed there are some traps (alpha - dampening, ...) but in principle it works.If you want to use a very stable method go for Fang/Osterlee Cosine method. That works fine and you can do Bermudans with that...Best, Lapsi

Code looks a little off to me.Similar but working code in python (using the lovely numpy/scipy libraries) - tested against some results by wim schoetens. have provided VG and BS characteristic functions but as it is modular and therefore is easy to add heston, heston with jumps etc.enjoy