Interpolating Treasury Par Yields and Fitting a Zero-Coupon Curve

Summary

The document discusses how to fill missing maturities in constant-maturity Treasury par-yield data before bootstrapping a zero-coupon curve. It describes the published CMT yields as par yields based on a cubic-spline model, where each quoted yield serves as both the yield to maturity and coupon rate for a theoretical bond priced at par. On that basis, one can interpolate par yields linearly or with a cubic spline, then bootstrap the resulting par curve.

The answer presents fitting a spline to a broader set of off-the-run Treasury securities as a better approach. It also points to the Svensson model and associated fitted yield-curve and zero-coupon data from Federal Reserve researchers. The document names practical alternatives but does not compare their accuracy, explain implementation details, or provide validation evidence. Any interpolation assumes the inserted observations represent par yields, and estimates depend on the selected securities and curve-fitting method.

Key ideas

• CMT observations are par yields, so interpolated values should also be treated as par yields when bootstrapping.
• Linear interpolation and cubic splines are options for filling missing tenors.
• Fitting a curve to a larger set of off-the-run Treasuries is suggested as a stronger alternative.
• The Svensson model is identified as another approach for estimating Treasury yield curves and zero-coupon rates.

Tags

# What techniques can be used to get the missing maturities from the CMT yields?


# What techniques can be used to get the missing maturities from the CMT yields?












I have constant maturity treasury data from the h15 release of the FED, from which I use 6 month, 1 year, 2, 3, 5, 7, 10, and 20 year yields. I want to strip the zero coupon curve, but am not sure about the best (most accurate) way to fill in the missing maturities for the CMT yields, which I need before I can bootstrap the zero coupon curve. Is there anyone that can provide me with some references on the different techniques that can be used, that are also understandable for application?

## Answer by Helin (score 3, accepted)

https://quant.stackexchange.com/a/28028

The CMT yields published by the Fed/US Treasury are par yields calculated using a cubic spline model. In other words, these are the yields to maturity as well as coupon rates on bonds whose theoretic prices are 100. With this information in mind, you can linearly interpolate between these yields, or use a cubic spline to fill in rates at other tenors, assuming the filled-in rates are also par yields, and bootstrap this resulting "par yield curve."

A better approach would be to use a large number of off-the-run Treasuries and fit a spline through them. Fed researchers provide an implementation of the Svensson model. The methodology, along with the fitted yield curve data (including zero coupon rates), are available here.

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.