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

26 Pages Posted: 4 Jan 2009  

Anatoliy V. Swishchuk

University of Calgary

Date Written: June 10, 2008

Abstract

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

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

Anatoliy V. Swishchuk (Contact Author)

University of Calgary ( email )

University Drive
Calgary, Alberta T2N 1N4
Canada

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