Nelson-Siegel, arbitrage-free. The best of both worlds! Details: We derive the class of arbitrage-free affine dynamic term structure models that approximate the widely-used Nelson-Siegel yield-curve specification. Our theoretical analysis relates this new class of models to the canonical representation of the three-factor arbitrage-free affine model. Our empirical analysis shows that imposing the Nelson-Siegel structure on this canonical representation greatly improves its empirical tractability; furthermore, we find that improvements in predictive performance are achieved from the imposition of absence of arbitrage.
If Christensen-Diebold-Rudebusch (2007) is arbitrage-free Nelson-Siegel, then this paper is effectively arbitrage-free Svensson. The fourth factor in the Svensson model helps with its long-maturity fit (relative to three-factor Nelson-Siegel), but making it arbitrage-free is significantly more involved than with Nelson-Siegel. Indeed we show that there does not exist an arbitrage-free model with Svensson factor loadings. We also show, however, that a simple five-factor generalization (where the fifth factor has a natural interpretation as a second slope factor) solves the problem, achieving both freedom from arbitrage and good long-maturity fit in a Svensson-style environment.
The popular Nelson-Siegel (1987) yield curve is routinely fit to cross sections of intra-country bond yields, and Diebold and Li (2006) have recently proposed a dynamized version. In this paper we extend Diebold-Li to a global context, modeling a potentially large set of country yield curves in a framework that allows for both global and country-specific factors. In an empirical analysis of term structures of government bond yields for the Germany, Japan, the U.K. and the U.S., we find that global yield factors do indeed exist and are economically important, generally explaining significant fractions of country yield curve dynamics, with interesting differences across countries.
Do macroeconomic fundamentals help predict the yield curve? Does the yield curve help predict macroeconomic fundamentals? The answers are yes and yes, although the stronger direction of predictive causality seems to be from the macroeconomy to yields. The classic Nelson-Siegel curve, suitably dynamized and reinterpreted as a modern three-factor model of level, slope and curvature, forecasts bond yields surprisingly well, particularly at horizons between two and four quarters ahead.
New aspects of the macro/finance interface as embodied in yield curve modeling. The tension between current finance approaches that have the theoretically appealing property of freedom from arbitrage but forecast poorly, and traditional macroeconomic approaches that admit arbitrage but forecast well. A step toward resolving the tension: making Nelson-Siegel arbitrage-free.
More on the Diebold-Li approach to yield curve modeling and forecasting. The model is not affine, its risk factors appear to be priced, and bond portfolio risk management based on its generalized duration measure appears successful. |