Choosing Instruments and Methods for Yield Curve Construction
Summary
The document considers whether short Treasury bills and coupon-bearing bonds should feed one yield curve or separate curves. Its central guidance is to decide first whether the instruments belong to the same product market and should share a curve. In the U.S. Treasury market, bills and short remaining maturities on coupon securities are generally treated as part of one curve; arbitrage activity can push anomalous yields back toward it. The response also notes that liquidity and demand can justify separating on-the-run from off-the-run Treasury securities at longer maturities.
A second answer outlines a construction workflow: bootstrap coupon bonds into discount factors or zero-coupon equivalents, interpolate where maturities are missing, and derive spot rates. It mentions parametric fitting such as Nelson–Siegel as another approach, and favors linear interpolation on log discount factors for simplicity while noting that it is not continuous. These are suggested approaches, not a universal prescription: market conventions, tax treatment, and instrument comparability can differ across countries, with Mexico and Brazil given as examples where bill and bond yields need not converge.
Key ideas
- Decide whether instruments belong on the same curve before fitting a curve.
- In the U.S. Treasury market, bills and short-maturity coupon securities are generally viewed as sharing a curve.
- Liquidity effects can motivate separate on-the-run and off-the-run curves.
- Bootstrapping coupon bonds creates discount factors, while interpolation fills maturity gaps.
- Market conventions and taxation can make a single curve inappropriate in some countries.
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Full text
# Construct yield curve using bonds and bills or bonds only? # Construct yield curve using bonds and bills or bonds only? I have: - 3M,6M,1Y,2Y,3Y....bonds - 1W,2W,1M,2M,3M.... bills To build the yield curve what is better: - build a single curve using bonds+bills - build 2 separate yield curves, 1 to price bonds made out of bonds only, and to price bills, bill only curve - something else? EDIT just to clarify, I am concerned about whether I should use bill rates in building the bond curve? Will it improve or distort my result? ## Answer by Dimitri Vulis (score 2, accepted) https://quant.stackexchange.com/a/74018 before you get to curve fitting, you need to decide whether these instruments are on the same curve or not. And that's not a quantitative finance question, but a product question. For example, in the U.S., they generally are. U.S. treasury sells zero-coupon T-bills with maturities up to 1 year. And there are lots of coupon-paying notes and bonds that U.S. treasury issued years ago and that have less than 1 year left to maturity. Many market participants watch their yields like hawks and, whenever an instruments trades at an anomalous yield different from this single curve, will pounce and make free mouney from arbitrage until the anomaly goes away. Tangentially to your question, beyond the maturity of U.S. T-bills, for technical reasons, there is more demand for on-the-run coupon-paying notes and bonds, so some people split off the on-the-run and off-the-run curves. But other markets differ, for example, in their taxation, so betting that the yields of their zero-coupon instruments would converge with coupon-paying instruments would not necessarily pay out. I can think of Mexico (cetes and mbonos) and Brazil as good examples. ## Answer by LvM_ (score 0) https://quant.stackexchange.com/a/74010 As a student, this is how I would have done it. - Using bootstrapping methodology, convert Coupon Bond into zero coupon bond so you have zero coupon bond for all maturities. - you will find that you have some "missing Data". e.g. you don't have the zero coupon bond for certain Coupon date. You can address this issue by choosing an appropriate interpolation methodology [1] - Convert your Zero coupon bond (discount rate) into spot rate then plot your curve. Basic idea / principle used: No arbitrage e.g. a bond with coupon C that matures in 3 years (even if it was issued 5 years ago), must have the same price as a 3 years bond (with same coupon) issued today that has the same maturity.[2] Please note: Zero coupon Bond and Discount factor are the same thing. Another approach you might want to consider are Curve fitting, using for example the Nelson Siegel Model (or the extended version). I.e. we assume that the discount factor is a function of maturity T (i.e. Z(0,T)). I hope this help, but I want to emphasis that I don't know what are best practices, I just shared my view on how I would do it if I was still a student. Best, Jules [1] Great paper from Patrick S. Hagan and Graeme West. You have a summary on page 10 which compare all methodology. I personally like Raw (linear on log of discount) as it is simple to implement. Draw back being: Not continuous. http://web.math.ku.dk/~rolf/HaganWest.pdf [2]Fixed Income securities - Pietro Veronesi || p62
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