A Tractable Heath Jarrow Morton Framework Based On Time Changed Levy Processes

In this paper we formulate a Heath-Jarrow-Morton framework based on time changed Levy processes. Our framework is based on the time changed Levy processes described in Carr and Wu (2004). Therefore, the framework allows us to capture stylized facts for interest rates, namely 1) non-normal innovations (through the use of Levy processes), 2) time in-homogeneous behavior (though a stochastic time varying activity rate (volatility)), and 3) finally dependence between the activity rate and the interest rate innovations. We derive a semi-analytical expression for the characteristic function of zero coupon bond prices, which allows for easy pricing of fixed income derivatives. Finally we show that our model encompasses known models for both forward rates and volatility.