Bond valuation under a discrete-time regime-switching term-structure model and its continuous-time extension

Abstract

Purpose – The purpose of this paper is to consider a discrete-time, Markov, regime-switching, affine term-structure model for valuing bonds and other interest rate securities. The proposed model incorporates the impact of structural changes in (macro)-economic conditions on interest-rate dynamics. The market in the proposed model is, in general, incomplete. A modified version of the Esscher transform, namely, a double Esscher transform, is used to specify a price kernel so that both market and economic risks are taken into account. Design/methodology/approach – The market in the proposed model is, in general, incomplete. A modified version of the Esscher transform, namely, a double Esscher transform, is used to specify a price kernel so that both market and economic risks are taken into account. Findings – The authors derive a simple way to give exponential affine forms of bond prices using backward induction. The authors also consider a continuous-time extension of the model and derive exponential affine forms of bond prices using the concept of stochastic flows.