On Bond Pricing with Jumps in Interest Rates

Abstract

The pricing of zero coupon bonds when the interest rate in the market is given by a jump-diffusion stochastic process of CIR-type is considered. The jump is assumed to be a Levy process of exponential type with no drift. Solving the associated partial integro-differential equation for the bond price, a semi-analytical expression, involving the Levy exponent, is obtained.Numerical experiments show that, with the same set of parameters, the bond price is higher with jump interest rate than with Gaussian interest rates.

Keywords: Levy process, zero coupon bond, characteristic exponent, variance gamma