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

36 Pages Posted: 6 Nov 2013

See all articles by Marcel Priebsch

Marcel Priebsch

Board of Governors of the Federal Reserve System

Date Written: September 24, 2013

Abstract

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 affine 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.

Keywords: Shadow-rate model, zero lower bound, dynamic term structure model

JEL Classification: E43, G12, C63

Suggested Citation

Priebsch, Marcel, Computing Arbitrage-Free Yields in Multi-Factor Gaussian Shadow-Rate Term Structure Models (September 24, 2013). FEDS Working Paper No. 2013-63, Available at SSRN: https://ssrn.com/abstract=2350873 or http://dx.doi.org/10.2139/ssrn.2350873

Marcel Priebsch (Contact Author)

Board of Governors of the Federal Reserve System ( email )

20th Street and Constitution Avenue NW
Washington, DC 20551
United States

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