Bootstrapping Treasury Spot Rates with Interpolation

Summary

The document asks how to bootstrap spot and forward curves from daily US Treasury yields when a coupon bond’s cash flows fall at maturities without quoted securities. For the two-year note, the missing one-and-a-half-year spot rate is needed alongside shorter rates. The response says an interpolation method is required and presents linear interpolation as the simplest starting point, while noting that it may not represent the curve’s curvature well. Splines are mentioned as a more flexible alternative.

The exchange identifies the practical issue of sparse maturity observations in curve construction, but does not work through the bootstrapping arithmetic or compare interpolation methods empirically. It points to an external guide for a fuller treatment. The choice of interpolation can affect the resulting spot and forward rates, so the brief answer does not establish which method is best for a particular curve or dataset.

Key ideas

• Bootstrapping coupon Treasury yields can require rates at maturities with no directly quoted security.
• Interpolation can supply the missing maturity rate needed to discount intermediate cash flows.
• Linear interpolation is a basic option, while splines can represent curve curvature more flexibly.
• The exchange provides no worked calculation or empirical comparison of interpolation methods.

Tags

# Bootstrapping spot rates from treasury yield curve


# Bootstrapping spot rates from treasury yield curve












I'm attempting to construct a spot rate and forward rate curve from the 2011 daily treasury yield curve rates provided by the US Treasury. All US Treasury securities (1m, 3m, 6m, 1y, 2y, 3y, 5y, 7y, 10y, 20y, 30y) are being taken into consideration.

Using the bootstrapping process, step 1 is to obtain all of the spot rates. In working through this step, I'm getting stuck when calculating the spot rate for the 2y Treasury Note. To get the spot rate for the 2y Treasury Note, I need the spot rates for the 6m, 1y, and 1.5y terms. The problem is that there is no observable 1.5y Treasury security.

How do I work through this? I've spent a great amount of time browsing the web trying to find the answer, and have come up empty. I found this topic while creating this post. Is linear interpolation the answer? Can someone point me to a good resource for learning this technique?

Thank you for your time.

## Answer by Kyle Balkissoon (score 2, accepted)

https://quant.stackexchange.com/a/3655

You are going to need to interpolate in some way shape or form....

Linear is the easiest and most basic, however it may not capture the curvature, you can use splines to better capture the curve.

A nice guide to doing so is here:

It's a guide to bootstrapping and it has all the components. http://www.business.mcmaster.ca/finance/deavesr/yieldcur.pdf

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.