Hi, We working on some interest rate model monte carlo simulation. We will start from simple one factor model such as Vasicek mean reversion and Cox Ingersoll Ross. We are not sure how to empirically estimate the parameters. And give the autocorrelation present in interest rate time series, how to use some econometric methods, ARCH and GARCH in the estimation. Does anyone here have some past experience? And what are some good two-factor models to recommend? Thank you!

The paper by Gibbons & Ramaswamy (Review of Financial studies, 1993 Vol 6) has some discussions on estimation of CIR parameters. Just google for it.

We did come up with parameter estimation, but are having difficulty annualizing the parameters as what we estimated are of monthly data.Any ideas?

Why do you want to use estimate the parameters using historical data ? Why not try to calibrate your model on the market itself ? (caplets, swaptions, CMS, etc...)

DcinvAre you still working on the interest rate model? I have the same situation as yours. Can I get some suggestion from you? Hope get your reply soon.Thanks

I believe this topic is discussed in Dixit and Pindyck's "Investment Under Uncertainty". Also, Aaron Brown responded to a similar question with this:The type of mean reversion will determine the annualization. If it's simple autocorrelation, that is tendency to the mean is linear in current deviation from the mean, the annual parameter = 1 - (1 - monthly parameter)^12. If the monthly parameter is small that's approximately 12*monthly parameter, but if it's large that approximation is bad. For other kinds of autocorrelation, other annualization formulae are appropriate. Hope this helps.