Matching volatility in Heston and BS

Tropp · January 24th, 2003, 1:22 pm

Hi,I want to compare Hestons density (Heston-1993 model with stochastic volatility) with the Black-Scholes density in order to show that Hestons model can create skewness. But I have problem: Which volatility (variance) should I use in the BS density? I'm interested in the skewness effects and not in different variances, and for that reason I want to make sure that the variances are identical. So in other words: How do I match the variances between Hestons density and the Black-Scholes density?Thanks.P.S. I DON'T know how to calculate the variance in Hestons model.

Aaron · January 24th, 2003, 2:25 pm

I think there is an on-line calculator that does this for you. Thispapershows how to calculate the moments.

pi314 · February 6th, 2005, 5:26 pm

Hi,I dont find exactly the same results with Heston's paper 93.Particularly, For a vol of 7.10 %, I have BS(S=100,K=100,t=.5,r=0, ss= 0.071)= 2.00266269808066and I have BS(S=100,K=100,t=.5,r=0, ss=0.1)= 2.82036033043281Heston(S=100,K=100,t=.5,r=0,... ) = 2.79682791225110Someone have alreday found this results ?My Heston values are OK (check with the pricer of this forum).thanks

AVt · February 8th, 2005, 3:34 pm

Tropp: the was a thread on Monte Carlo for Heston with a nice Excel sheet done by ds (i forgot where and it is several month ago), try a search.pi314: yes, i get 2.7968290406871452 and 2.7840573872793896 for corr= + 0.5 and - 0.5 with vol = 0.099165 and 0.098712 respectively using Maple

pi314 · March 15th, 2005, 8:29 pm

Hi,I have a little problem with Heston(93)'s paper.He writes (Figure 2) p337:.... BS with equal volatility to option maturity.I dont see how he can get the volatility at T (maturiity) whereas the volatility Vt is stochastic ??????Thanks a lot for your ideas!