First order Euler discretization is straightforward: generate a normal variable z1 to simulate V first and then generate another independent normal variable z2 and factor in the correlation by doing [z1+(1-Rho^2)]^0.5*z2 to simulate S.I understand that I can use non Central Chi square distribution to simulate (exact) the Variance process since the transition density of square root process is known. So what I do first is simulating a value of V by sampling from non central Chi square. Next, I want to use first order Euler to simulate S.Here is my question. How I'm going to sample S based on simulated V? Do I need to back out an implied z1 from simulated V (based on first order Euler discretization on process V) and used the implied z1 and independently simulated z2 and the correlation formula of z1+(1-Rho^2)^0.5*z2 to simulate S? Or put it in another way, I can use Non Central Chi Square to simulate the exact V but how do I simulate S which is correlated with V?I feel confused.Thanks.Wondering

Have u looked at mark Broadie's paper on exact simulation of heston model,he has a detailed discussion there showing you steps how u simulate S from non central chi-squared distributed V!

Thanks a whole lot. I found the paper in case anyone else is interested in the exact simulation of Heston.http://finmath.stanford.edu/seminars/do ... roadie.pdf

Efficient Simulation of the Heston Stochastic Volatility Model LEIF B.G. ANDERSEN Banc of America Securities --------------------------------------------------------------------------------October 29, 2006Keywords: Heston model, Monte Carlo simulation, SDE discretization, bias reduction, affine square-root models http://papers.ssrn.com/sol3/papers.cfm? ... _id=946405

Coincidently, I'm trying to implement Andersen's schemes and wondered how I would go about testing my code (rather than calibrate the model)? As a novice to this I'm at a bit of a loss as to how to proceed - apart from trying to replicate his results are there any other tests I could perform (I was thinking along the lines of checking put-call parity)? Any ideas or pointers to papaers/books would be appreciated.

Try matching the values in this threadregards,