Libor and Swap Market Models for the Pricing of Interest Rate Derivatives: An Empirical Analysis

Abstract

In this paper we empirically analyze and compare the Libor and Swap Market Models, developed by Brace, Gatarek and Musiela (1997) and Jamshidian (1997), using paneldata on prices of US caplets and swaptions. A Libor Market Model can directly be calibrated to observed prices of caplets, whereas a Swap Market Model is calibrated to a certain set of swaption prices. For both one-factor and two-factor models it is analyzed how well they price caplets and swaptions that were not used for calibration. We show that the Libor Market Models in general lead to better prediction of derivative prices that were not used for calibration than the Swap Market Models. A one-factor Libor Market Model that exhibits mean-reversion gives a reasonable fit of the derivative prices, and adding a second factor only decreases pricing errors to a small extent. Also, models that are chosen to exactly match certain derivative prices are overfitted. Regression tests reveal that all models are statistically rejected, and the pricing errors are correlated with the shape of the term structure of interest rates.

JEL Classification: G12, G13, E43