Term Structure Models Driven by General Lévy Processes

Abstract

As a generalization of the Gaussian Heath-Jarrow-Morton term structure model, we present a new class of bond price models that can be driven by a wide range of L'evy processes. We deduce the forward and short rate processes implied by this model and prove that, under certain assumptions, the short rate is Markovian if and only if the volatility structure has either the Vasicek or the Ho-Lee form. Finally, we compare numerically forward rates and European call option prices in a model driven by a hyperbolic L'evy motion with those in the Gaussian model. Keywords: term structure models, martingale modelling, L'evy process, hyperbolic L'evy motion, Markov property, Vasicek model 1 Introduction Models of the term structure of interest rates are important for many problems in economics, in particular for the valuation of contingent claims depending on interest rate sensitive assets. In the Heath-Jarrow-Morton (1992) setting, one assumes that there is a complete set of zero coupon bonds w..