Levy-Based Heath-Jarrow-Morton Interest Rate Derivatives: Change of Time Method and PIDEs

In this paper, we show how to calculate the price of zero-coupon bonds in a Heath-Jarrow-Morton (HJM) Lévy model of forward interest rates using the change of time method. We also derive partial integro-differential equations (PIDEs) for the values of swaps, caps, floors and options on them, swaptions, captions and floortions, respectively. We apply the change of time method to price the interest rate derivatives for the forward interest rates f(t, T) described by the stochastic differential equation driven by alpha-stable Lévy processes.     «

In this paper, we show how to calculate the price of zero-coupon bonds in a Heath-Jarrow-Morton (HJM) Lévy model of forward interest rates using the change of time method. We also derive partial integro-differential equations (PIDEs) for the values of swaps, caps, floors and options on them, swaptions, captions and floortions, respectively. We apply the change of time method to price the interest rate derivatives for the forward interest rates f(t, T) described by the stochastic differential equ...     »