# LIBOR 3M and 1M from Vasicek model

I would like to discuss my approach toward modelling of interest rates with respect to its downsides and advantages.

My problem is to forecast daily LIBOR 3M and LIBOR 1M over a particular time horizon, let say 10Y.

I was thinking about applying Vasicek interest rate dynamics and treating realized historical LIBORS for 3M and 1M as instaneous rates and calibrating the model to them via regression approach.

This simplified apprach won't be used for any derivative valuations, therefore I am accepting some limitations, like no fit to current interest rate curve.

Do you think that my approach is acceptable in the light of the aim of this analysis?

Thanks, Bart

## 1 Answer

"Calibrating the model to them via regression"... Vasicek has just three parameters: $\sigma$ (vol), $r_L$ (long rate) and $a$ (mean reversion) and a time-dependent short rate $r_0$. Can you specify what you are thinking of in terms of a regression model to estimate these? Obviously $r_0$ will not be a stable parameter. If you want to estimate $\sigma$, $r_L$and $a$, you have to contend with the fact that actual yield curves & dynamics are not well explained by a one factor model (here $r_0(t)$ parameterizes the factor), so it's going to be tricky to use regression without having the fact that the model is wrong mess up the estimates. E.g., if you do cross-sectional regressions, the apparent values of $a$ and $\sigma$ will be much larger than the ones that do a good job of describing time-series dynamics. And $r_L$ won't be easy to stably estimate with small values of $a$ and $\sigma$ corresponding to the apparent time-series behavior.

• Thanks for your answer. I am aware of the fact that the actual yield curve will not be reflected in this approach, nevertheless that is a limitation I agree with. The aim is to have a simple (i.e. as simple as possible) forecasting model for 3M libor and 1M libor. I was thinking of regression approach as specified here: sitmo.com/article/calibrating-the-ornstein-uhlenbeck-model. My main question is if my approach (two models, calibration to historical LIBOR) is acceptable? – Bart D. May 6 '16 at 7:06