Quasi-Cubic Hermite Spline Treasury Yield Curve Methodology

(Discontinued 12/6/2021)

Treasury Yield Curve Methodology


This description was revised and updated on May 20, 2020.

The Treasury's yield curve is derived using a quasi-cubic hermite spline function. Our inputs are indicative, bid-side market quotations (not actual transactions) for the on-the-run securities obtained by the Federal Reserve Bank of New York at or near 3:30 PM each trading day. Because the on-the-run securities typically trade close to par, those securities are designated as the knot points in the quasi-cubic hermite spline algorithm and the resulting yield curve is considered a par curve.  However, Treasury reserves the option to make changes to the yield curve as appropriate and in its sole discretion.  Such changes may include but are not necessarily limited to adding, removing or modifying inputs, and making changes to the methodology for deriving the yield curve.  For example, prior to the re-introduction of the 20-year Treasury bond on May 20, 2020, the yield curve had used additional inputs that were composites of off-the-run bonds in the 20-year range that reflected market yields available in that time tranche.  Also, at various times in the past, Treasury has used other inputs, such as interpolated yields and rolled down securities deemed necessary for deriving a good fit for the quasi-cubic hermite spline curve.

The current inputs are the most recently auctioned 4-, 8-, 13-, 26-, and 52-week bills; the most recently auctioned 2-, 3-, 5-, 7-, and 10-year notes; and the most recently auctioned 20- and 30-year bonds. The inputs for the five bills are their bond equivalent yields.

Between August 6, 2004 and June 2, 2008, to reduce volatility in the 1-year Treasury Constant Maturity (CMT) rate, and due to the fact that there were no on-the-run issues between 6-months and 2-years, Treasury used an additional input to insure that the 1-year CMT rate was consistent with on-the-run yields on either side of its maturity range. Thus, Treasury interpolated between the secondary bond equivalent yield on the most recently auctioned 26-week bill and the secondary market yield on the most recently auctioned 2-year note and inputted the resulting yield as an additional knot point for the derivation of the daily Treasury Yield Curve. The result of that step was that the 1-year CMT was generally the same as the interpolated rate during that time period. As of June 3, 2008, the interpolated yield was dropped as a yield curve input and the on-the-run 52-week bill was added as an input knot point in the quasi-cubic hermite spline algorithm and resulting yield curve.

Between December 3, 2007 and November 7, 2008, due to Treasury's discontinuance of 3-year notes, we added a composite rate in the 3-year range based on an average of off-the-run securities in that time tranche.  This composite was replaced on November 10, 2008 with the on-the-run 3-year note upon its reintroduction. Treasury does not provide the computer formulation of our quasi-cubic hermite spline yield curve derivation program. However, we have found that most researchers have been able to reasonably match our results using alternative cubic spline formulas.

Treasury reviews its yield curve derivation methodology on a regular basis and reserves the right to modify, adjust or improve the methodology at its option. If Treasury determines that the methodology needs to be changed or updated, Treasury will revise the above description to reflect such changes.

Yield curve rates are usually available at Treasury's interest rate web sites by 6:00 PM Eastern Time each trading day, but may be delayed due to system problems or other issues. Every attempt is made to make this data available as soon as possible.

Office of Debt Management
Department of the Treasury