Re: [Quantlib-dev] Heston.cpp Alan Lewis decorrelation for Heston

[Klaus S. <kl...@sp...>]

Hi

> In Hestonprocess.cpp there is a switch on Exact Variance Simulation where
> it's said that one uses Alan Lewi's trick to decorrelate equity and
> variance process.


If the equity process and the variance process are not correlated in the 
Heston model one can use an exact sampling method for the variance process, 
which is a "square root" process. (see e.g. Glasserman, Monte Carlo Methods 
in Finance). This removes one main source for the bias of Monte-Carlo 
Sampling methods for the Heston model, namely the variance process can not 
get negative values using this discretization method. 

To achieve zero correlation for a "normal" Heston model one should transform 
the equity process x(t)=ln(S(t)) using Ito's Lemma and 

y(t)=x(t)-\frac{rho}{sigma}\nu(t). 

This removes the correlation between y(t) and the variance and one can use 
exact sampling for the variance process and Euler discretization for y(t). 

This schema might be better than the other discretization schemes if \sigma is 
large.

regards

 Klaus