On Calibrating an Extension of the Chen Model

Sammanfattning: There are many ways of modeling stochastic processes of short-term interest rates. One way is to use one-factor models which may be easy to use and easy to calibrate. Another way is to use a three-factor model in the strive for a higher degree of congruency with real world market data. Calibrating such models may however take much more effort. One of the main questions here is which models will be better fit to the data in question. Another question is if the use of a three-factor model can result in better fitting compared to one-factor models. This is investigated by using the Efficient Method of Moments to calibrate a three-factor model with a Lévy process. This model is an extension of the Chen Model. The calibration is done with Euribor 6-month interest rates and these rates are also used with the Vasicek and Cox-Ingersoll-Ross (CIR) models. These two models are calibrated by using Maximum Likelihood Estimation and they are one-factor models. Chi-square goodness-of-fit tests are also performed for all models. The findings indicate that the Vasicek and CIR models fail to describe the stochastic process of the Euribor 6-month rate. However, the result from the goodness-of-fit test of the three-factor model gives support for that model.