Consistent versus Non-Consistent Term Structure Models

Abstract

This article prices cap and swaptions in the Spanish market using the Vasicek, Cox, Ingersoll, and Ros and Hull and White (HW) models. Derivatives prices obtained with the Vasicek and CIR models estimated from time series data are very similar, but they differ substantially from the values given by the HW model fited to the term structureof interest rate swap yields (especially for at-the-money and out-of-the-money options). When the former models are estimated cross-sectionally, they produce option proces similar to those of the HW model. In samples of caps and swaptions, the Vasicek model estimated cross-sectionally, they produce option prices similar to those of the HW model. In samples of caps and swaptions, the Vasicek model estimated cross-sectionally outperforms the HW model. The Vasicek and CIR models estimated from time series produce very large pricing errors.