A BSDE approach for bond pricing under interest rate models with self-exciting jumps

Abstract

In this article, we consider zero-coupon bond pricing problems for the stochastic interest rate model with clustering effects of self-exciting jumps. We first develop the evolution of the interest rate model under the equivalent martingale measure. Then we characterize the bond price in terms of a backward stochastic differential equation (BSDE). Closed-form solution of the BSDE is expressed as an exponential affine function of the interest rate and the intensity of jumps when the coefficients of interest rate model have affine structures.