Parameters in a CIR model

kimkc84 · August 15th, 2007, 2:20 pm

Hi all- I'm working on building a LIBOR interest rate model to forecast long-term 10YR LIBOR rates. I'm trying to use a CIR model, but having a hard time estimating the parameters such as the mean reversion speed and sigma, the variance rate. Do you have any suggestions as to how to approach this problem? I thought about running a simple regression, but the volatility part is correlated with the rate, and so the regression won't work unless I use the Vasicek model. Thanks.

Edwyn · August 20th, 2007, 1:28 pm

Looks like you are talking about calibration to the historical data. I guess there are two possibilities:1) the rate in the CIR is a non-centralised chi-square distribution, so if you are able to find the pdf of this one then you can use the (quasi) MLE to find the parameters;2) alternatively you can discretize the CIR process and the "shock" will be in a conditional Normal term (google Alfonsi and discretization), I suppose you can then use the much simpler QMLE for the Normal distribution for calibration