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Fitting Nelson–Siegel–Svensson Curves to Coupon Bonds and Zeroes

Article Quant Q&A · Author: Luks
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Summary

The document asks whether a Nelson–Siegel–Svensson sovereign zero-coupon yield curve can be calibrated using prices of both coupon-bearing and zero-coupon bonds. It explains that the fitting procedure can treat both instruments alike: a zero-coupon bond is equivalent to a coupon bond with a zero coupon rate, so both can contribute price observations to the parameter optimization.

The main caveat is market segmentation. Government coupon bonds and zero-coupon instruments such as STRIPS may trade with different liquidity and pricing patterns, and their implied yields can diverge across parts of the curve. Including both types may therefore produce a fitted curve between the curves implied by each market separately. The document offers this as a conceptual observation, not a quantitative comparison, and does not prescribe weighting, liquidity adjustments, or a preferred calibration sample.

Key ideas

  • Coupon bonds and zero-coupon bonds can be included in the same curve-fitting objective.
  • A zero-coupon bond is a coupon bond with a zero coupon rate.
  • Different liquidity and trading behavior can cause the two markets to imply different yields.
  • A fit using both instrument types may lie between the curves implied by either market alone.

Tags

Fixed incomeStatistics
Full text
# Constructing NS-Svensson parameters with zero coupon AND coupon bonds


# Constructing NS-Svensson parameters with zero coupon AND coupon bonds












I am in the process of calculating sovereign zero coupon yield curves using the NS-Svensson parameter for a number of countries. Due to data constraints, I would like to use the information from price data of both zero coupon and coupon bonds for the construction of the curves.

I had a look into different statistical packages (notably `termstrc` in R and `IRFunctionCurve.fitSvensson`in Matlab), where some appear to be able to cope with the optimization across the two asset classes and others restrict themselves to Coupon bonds.

Ignoring for now the question which packages dominates others in terms of implemention, is there any conceptual problem in optimizing the parameters of the model over both asset classes?

## Answer by Helin (score 1, accepted)

https://quant.stackexchange.com/a/19126

Nowadays, government yield curves are customarily built with only coupon bonds. Zero coupon bonds (i.e., STRIPS in the US) are much less liquid compared with coupon Treasuries, and tend to trade very differently. If you plot a zero curve implied by coupon Treasuries vs yields of STRIPS, you'll notice that they can differ quite a bit in certain parts of the curve. If you include both coupon bonds and zeros, you'd get an "in-between" curve between the two very segmented markets.

Mechanically, as @Physcs Envy mentioned, there's no point in differentiating the two though. The curve fitting process can proceed with both in exactly the same fashion. After all, zero coupon bonds are simply coupon bonds with coupon rate of 0%.

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.