Hi All,I'm trying to calibrate the parameters of the Vasicek model from Euribor Rates (2008 - 2015, see attachment for the rates). I use a MLE technique (Matlab function from the Sitmo website: http://www.sitmo.com/article/calibratin ... eck-model/). Although when using the rates from that website it all works fine, when I'm using the Euribor Rates time series from the attachment I got weird parameters such as a very negative mean rate (lower than the lowes rate in the Euribor time series). I think this isn't possible and maybe it goes wrong due to the negative interest rates in the time series. Hopefully somebody can help me with this calibration issue.Thanks

The model is so badly mis-specified relative to actual market behavior that you should expect weird parameters. So your problem is probably not with the calibration per se.

So, which model would you use instead of the Vasicek model?

If you think about it, a short-rate model is kind of a weird thing. The short rate itself is a bit of an abstraction. I think of this class of models as kind of an academic enterprise.Further, it could be argued that the real purpose of such a model is to price a derivative (such as a bond option) - you don't really need a fancy model to tell you what zero coupon bonds cost, when you could just interpolate anyways. So I suppose one way to look at this is that your Vasicek model should be calibrated to an option price, not to a set of yields.If you must use a short rate model, you are probably better off using the so-called "G2++" model (i.e. a two-factor Hull-White model).My 2 cents, HTH [Edit - spelling]

Vasicek is just a historical stepping stone. It's a popular demo of applying risk-neutral pricing theory to interest rate derivatives. I don't think you would use it for anything other than teaching purposes. But multi-factor Vasicek, G2++ and then what culminated in the affine modeling framework is quite powerful. That the short rate is an abstraction need not matter too much actually if you have a realistic factor structure driving the model.

Thanks,Just found an interesting webinar on Mathworks (http://nl.mathworks.com/videos/calibrat ... 90140.html) about the G2++ model and its implementation. Haven't tried the model yet but do you think this model can handle the negative interest rates when I calibrate the model using historical time series?

This webinar show how to calibrate the model and thereafter how to simulate the model with a LinearGaussian2f function from matlab. Unfortunately I haven't the toolbox which can do that job. Anybody any advice (or code) which I can use to simulate the model after the calibration?Thanks.

Be careful, (unobservable) short rate and Euribor (EONIA?) overnight rates are not the same. Garatek et al (p. xiii) say that the overnight rate is a good proxy for the short rate butFilipovic (p.10) argues it is not ''because the motives and needs driving overnight borrowersare very different from those of borrowers who want money for a month or more''.In either case, even if you believe that the overnight rate is a good proxy for the short rate, you calibrate your model under historical measure (which may be needed for the risk management but is not suitable for the option valuation).If you have caps or swaptions data, you may try to calibrate Vasicek to them using QuantLib (this calibration is done under the risk-neutral measure).And have a look at my tutorial, likely, you will find some interesting stuff on Vasicekhttp://www.yetanotherquant.com/libor/tutorial.pdf