The Discrete-Time Framework of the Arbitrage-Free Nelson-Siegel Class of Term Structure Models

Linlin Niu and Gengming Zeng

No 2013-10-14, Working Papers from Wang Yanan Institute for Studies in Economics (WISE), Xiamen University

Abstract: We derive the discrete-time arbitrage-free Nelson-Siegel class of term structure models with an exact solution and proof of uniqueness. We design a fast and reliable estimation procedure based on reduced-dimension optimization with multistep embedded regressions. After an analytical illustration, we also show empirically that arbitrage-free restrictions have a bounded advantage for in-sample fit and out-of-sample forecast, compared to its reduced-form counterpart. However, the arbitrage-free model is a powerful tool for analysing risk premia associated with Level, Slope and Curvature factors. Our empirical results have interesting implications for both the US bond yield conundrum of 2004-05 and the recent financial crisis.

Date: 2013-10-14
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