LEVY-BASED HEATH-JARROW-MORTON INTEREST RATE DERIVATIVES: CHANGE OF TIME METHOD AND PIDES

Abstract

In this paper, we show how to calculate the price of zero-coupon bonds Heath-Jarrow-Morton (HJM) L\'{e}vy model of forward interest rate $f(t,T)$ 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 L\'{e}vy processes.