26 Pages Posted: 4 Jan 2009
Date Written: June 10, 2008
In this paper, we show how to calculate the price of zero-coupon bonds for many Gaussian and Levy one-factor and multi-factor models of r(t) using change of time method. These models include, in particular, Ornshtein-Uhlenbeck (1930), Vasicek (1977), Cox-Ingersoll-Ross (1985), continuous-time GARCH, Ho-Lee (1986), Hull-White (1990) and Heath-Jarrrow-Morton (1992) models and their various combinations. 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 interest rates r(t) described by various stochastic differential equations driven by alpha-stable Levy processes.
Keywords: stochastic interest rate derivatives, bond options, swaps, caps, floors, swaptions, captions, floortionschange of time methods, partial integro-differetial equations
JEL Classification: G1, E4, C5
Suggested Citation: Suggested Citation
Swishchuk, Anatoliy V., Levy-Based Interest Rate Derivatives: Change of Time Method and PIDEs (June 10, 2008). Available at SSRN: https://ssrn.com/abstract=1322532 or http://dx.doi.org/10.2139/ssrn.1322532