Hi, every one. I am doing the Monte Carlo of Heston Model. But I found that when I impletement the second SDE (actually it is CIR model)for the volatility dV(t)=k*(theta-V(t))*dt+sigma*sqrt(V(t))*dW. It will get negative number sometimes which is inconsistent with the fact that it can only be non-negative. Does any one know how to solve this problem? Thank you very much!yoki

take absolute value

QuoteOriginally posted by: SPAAGGtake absolute valueThank you, SPAAGG. Does it the usual way people do when this problem happens. At first I am also thinking about to set V=0 when it gets negative number, what do think about it? What I worry about is if I make such change, taking absolute value or setting 0, will it still consist with the SDE?

Hi,you've got two ways to solve this problem: 1. Use zero as absorbing barrier: if (volatility_t < 0) volatility_t :=02. Reflecting barrier: if (volatility_t < 0) volatility_t := -volatility_tIn my opinon, these are the common methods to deal with negative volatilities but I have to admit, that I don't know which one should be preferred. As far as I observed, this doesn't make much of a difference for the result of the simulation.Kind regards

I agree...

Increase the number of time steps per sample path. You will have to refit your volatility parameters though.

QuoteOriginally posted by: FiveEightsHi,you've got two ways to solve this problem: 1. Use zero as absorbing barrier: if (volatility_t < 0) volatility_t :=02. Reflecting barrier: if (volatility_t < 0) volatility_t := -volatility_tIn my opinon, these are the common methods to deal with negative volatilities but I have to admit, that I don't know which one should be preferred. As far as I observed, this doesn't make much of a difference for the result of the simulation.With all due respect, both suggestions are not totally ideal. The best way to handle this issue is to use (for time-stepping) a distribution that is non-negative, such as log-normal. Although in the case of the Heston model, a Gamma distribution is an even better choice. In either case it should be moment-matched to the actual moments of the Heston process. See Appendix A of this for details.

Vladimir,would you mind to elaborate a little bit on that?

QuoteOriginally posted by: AVtVladimir,would you mind to elaborate a little bit on that?hmmmnot sure what is it exactly that you want me to elaborate onIf on the use of a Gamma distribution vs lognormal, then here it goes. The Gamma distribution is a stationary distribution for the Heston model, and has tails that are more similar to the "real" transition density tails than the log-normal distribution. So you get a better approximation on each time step if you use the Gamma distribution, and that allows you to use coarse time steps. hope this helps-Vladimir

Hi, I also have a basic question regarding the Heston Model. If you are doing a Monte Carlo simulation then can you still simulate the stock price as the exact expression:S(t+1)=S(t)exp{[r-0.5*sigma*sigma]dt+sigma*Z*sqrt(dt)} or do you have to use an Euler discretization.Also is there is also a similar 'exact 'expression for the Heston Volatility rather than using Euler discretization?ThanksNewFinance

Could someone answer my question?ThanksNewFinance

Vladimir,Thank you, it helped somewhat ... i will have to find time to understand(A.2 & A.1) in that Andersen&Brotherton-Ratcliffe paper, especially howcorrelation has to be treated.Axel

Could anyone provide a pseudocode (algorithm) for the monte carlo of Heston? Anyone able to get reasonably good results for the simulation of SV?demian

Could anyone share some papers that talk about Monte Carlo approach to Heston model? In general, which scheme is more preferred, Euler or Milstein?I am new to this area, any hints are most appreciated.