June 15th, 2014, 7:39 am

Hi all,

I am currently writing a paper on the Heston SV Model and in this context comparing different representations. I implemented the approaches of Heston, Carr Madan (with and without FFT) and the Cosine Method.

With all 3 methods I get results very similar to those posted by Alan. Compared to the results in Rouah (2013) on page 140, however, I tend to have some bias.

Model set up:

dS/S = (r-q)*dt + sqrt(V)*dW1

dV = k(theta-V)*dt + sigma*sqrt(V)*dW2

dW1dW2 = rho*dt

Parameters: S0 = 50, K = [41.4102, 44.0956, 46.9551, 50, 53.2424, 56.695, 60.3716],

k = 0.2, theta = V0 = 0.05, sigma = 0.3, rho = -0.7

Remarks:

-for Heston and Carr Madan I used a 32 point gauss laguerre quadrature for integration (Rouah used the same technique)

-for The Carr Madan approach I used alpha = 1.5

-for the COS approach I used [a,b] = [-300,300] and N = 2^15 to get accurate results for OTM options

Results for European Call Option:

Rouah: _________[8.6378, 6.4765, 4.4453, 2.6778, 1.3269, 0.502, 0.1421]

My COSINE:_____[8.63813, 6.47604, 4.44533, 2.67824, 1.32661, 0.50194, 0.14228]

My CM (w/o FFT):_[8.63800, 6.47604, 4.44549, 2.67805, 1.32670, 0.50189, 0.14233]

My Heston:______[8.63811, 6.47604, 4.44538, 2.67815, 1.32671, 0.50179, 0.14241]

I would be very grateful if anyone could confirm either my or Rouah's results (I could also post additional digits to my results, if needed). Many thanks in advance!

Last edited by

JustusQuant on June 14th, 2014, 10:00 pm