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Choosing Yield Curve Inputs for the Nelson–Siegel Model

Article Quant Q&A · Author: RndmSymbl
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Summary

This note asks whether Nelson–Siegel should be estimated from Treasury par yields or from spot rates bootstrapped from those yields. The accepted response recommends fitting the model directly to bond prices when those prices are available. If working with the published Daily Treasury Yield Curve Rates, it explains that these are already fitted par yields, derived from on-the-run and selected off-the-run Treasury securities using a cubic spline.

Because par yields can be treated as coupon rates for hypothetical bonds priced at par, the response says they can be supplied to the model on that basis. The note gives no empirical comparison of fitting approaches, implementation details for a particular R package, or discussion of how estimation results differ across inputs. Its guidance is therefore limited to the described Treasury data and relies on the characterization of those published rates as fitted par yields.

Key ideas

  • When Treasury bond prices are available, the response recommends fitting Nelson–Siegel directly to the prices.
  • The published Daily Treasury Yield Curve Rates are described as fitted par yields.
  • Par yields can be treated as coupon rates for hypothetical bonds priced at par.
  • The note does not compare the estimation performance of par yields and bootstrapped spot rates.

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Fixed incomeStatistics
Full text
# Does Nelson-Siegel require adjustments to yield curve input data?


# Does Nelson-Siegel require adjustments to yield curve input data?












I am attempting to gain a better understanding of the limitations of the Nelson-Siegel model as described in Estimating the Yield Curve Using the Nelson-Siegel Model.

As I have been playing around with the data I started to wonder whether the inputs to the Nelson-Siegel model are correct. I am using Daily Treasury YieldCurve Rates and estimating the model through the R YieldCurve package. It has been my understanding that spot rates need to be derived from observable par yields before applying any modelling. This understanding, I believe, has been confirmed at a separate discussion. But documentation of the relevant R packages fails to mention which rates should be supplied.

Should the input to the Nelson-Siegel model, in general and with respect to the R package, be the Daily Treasury YieldCurve Rates or should one bootstrap the spot rates before applying the model?

## Answer by Helin (score 6, accepted)

https://quant.stackexchange.com/a/15260

The NS model should be fit directly to bond prices. If you have the prices of all the Treasuries, you should use those directly. See this paper for how the Fed does it http://www.federalreserve.gov/pubs/feds/2006/200628/200628pap.pdf

The "Daily Treasury Yield Curve Rates" are already fitted par yields (they're fitted using a cubic spline model to on-the-run and select off-the-run Treasuries). Since these are par yields, you can assume that they represent the coupon rates of Treasuries with prices of 100, and feed them into the NS model.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.