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How arbitrage-free is the Nelson-Siegel Model?

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  • Coroneo, Laura
  • Nyholm, Ken
  • Vidova-Koleva, Rositsa

Abstract

We test whether the Nelson and Siegel (1987) yield curve model is arbitrage-free in a statistical sense. Theoretically, the Nelson-Siegel model does not ensure the absence of arbitrage opportunities, as shown by Bjork and Christensen (1999). Still, central banks and public wealth managers rely heavily on it. Using a non-parametric resampling technique and zero-coupon yield curve data from the US market, we find that the no-arbitrage parameters are not statistically different from those obtained from the NS model, at a 95 percent confidence level. We therefore conclude that the Nelson and Siegel yield curve model is compatible with arbitrage-freeness. To corroborate this result, we show that the Nelson-Siegel model performs as well as its no-arbitrage counterpart in an out-of-sample fore-casting experiment. JEL Classification: C14, C15, G12

Suggested Citation

  • Coroneo, Laura & Nyholm, Ken & Vidova-Koleva, Rositsa, 2008. "How arbitrage-free is the Nelson-Siegel Model?," Working Paper Series 874, European Central Bank.
    • Handle: RePEc:ecb:ecbwps:2008874
    Note: 120728
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    References listed on IDEAS

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    More about this item

    Keywords

    Affine term structure models; Nelson-Siegel model; No-arbitrage restrictions; non-parametric test;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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