Computing Arbitrage-Free Yields in Multi-Factor Gaussian Shadow Rate Term Structure Models

Abstract

This paper develops an approximation to arbitrage-free bond yields in Gaussian shadow rate term structure models. In this class of models, yields are constrained to be above an effective lower bound, thus rendering standard bond pricing methods inapplicable. I propose approximating the nonlinear relationship between yields and state variables using moments of the censored normal distribution. In an empirical application, this approximation technique is accurate to within a fraction of a basis point. As I show, minimizing the yield approximation error is crucial for model estimation as even seemingly small errors can lead to economically meaningful inference biases.