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

ISBN-13: 9781503223738 / Angielski / Miękka / 2014 / 36 str.

Federal Reserve Board

Opis

This paper develops a method to approximate arbitrage-free bond yields within a term structure model in which the short rate follows a Gaussian process censored at zero (a shadow-rate model as proposed by Black, 1995). The censoring ensures that model-implied yields are constrained to be positive, but it also introduces non-linearity that renders standard bond pricing formulas inapplicable. In particular, yields are not linear functions of the underlying state vector as they are in a ne term structure models (see Piazzesi, 2010). Existing approaches towards computing yields in shadow-rate models suffer from high computational burden or low accuracy. In contrast, I show that the technique proposed in this paper is sufficiently fast for single-step estimation of a three- factor shadow-rate term structure model, and sufficiently accurate to evaluate yields to within approximately half a basis point.