BEHAVIOR OF LONG-TERM YIELDS IN A LÉVY TERM STRUCTURE

Abstract

We study the behavior of the long-term yield in a HJM setting for forward rates driven by Lévy processes. The long-term rates are investigated by examining continuously compounded spot rate yields with maturity going to infinity. In this paper, we generalize the model of Karoui et al. (1997) by using Lévy processes instead of Brownian motions as driving processes of the forward rate dynamics, and analyze the behavior of the long-term yield under certain conditions which encompass the asymptotic behavior of the interest rate model's volatility function as well as the variation of the paths of the Lévy process. One of the main results is that the long-term volatility has to vanish except in the case of a Lévy process with only negative jumps and paths of finite variation serving as random driver. Furthermore, we study the required asymptotic behavior of the volatility function so that the long-term drift exists.