Calibration of Two Factor Vasicek and Hull-White Models with Contemporary Data

Abstract

The calibration attempts to understand the intricacies of interest rate dynamics by evaluating the effectiveness of three models: the Two-Factor Vasicek, the One-Factor Hull-White, and the Two-Factor Hull-White. Information from the U. S. Department of the Treasury was used for the estimation of the Two-Factor Vasicek model while the Hull-White models used Bloomberg data. The Vasicek model, based on two factors, is useful with regard to long-term movements in the rate but exhibits certain problems with regard to the calibration of convergence. The Hull-White model, with one-factor, is relatively good at short-term expectations. In contrast, the two-factor Hull-White model is a more sophisticated model that gives a more detailed picture of the behavior of interest rates at different maturities, but the calibration of which involves volatilities is difficult. Hence, regardless of the fact that simpler models may be adequate for some specific purposes, the results show that more complex models can indeed be more accurate if properly fine-tuned. This implies that the selection of a particular model depends on the type characteristics of the data and the application needs; thus, this work highlights the fact that financial modeling is a dynamic process.