Treasury yield curve or treasury zero coupon yield curve is the term structures of treasury yields-to-maturity. The yield is also called the zero coupon rate or the implied forward rate.
Treasury yield curves are bootstrapped from treasury benchmark curves that contain the most actively traded treasury bills or bonds at some maturities.
There are four elements in interest rate: zero coupon rates (or zero rates), discount factor, par yields, and forward rates. The derivation of one of these element is conveniently sufficient for the determination of the other three elements. Each interest rate definition is derived from specific representations of bond price.
The zero coupon rate or zero rate, the most common form of interest rate, is the yield implied by the different between a zero coupon bond's current purchase price and the value it pays at maturity. A given zero rate applies only to a single point in the future and, as such, can only be used to discount cash flows occurring on this date. Zero rates can have different compoundings: continuously, semi-annually, annually, etc. The continuously compounded zero rate has the simplest expression and computation mathematically.
The discount factor for a corresponding term to maturity is equal to exp(-Z*T), where Z is the continuously compounded zero rate from 0 to T and T is the maturity date. The calculation of zero rates and their associated discount factors is essential for asset pricing.
Unfortunately both zero rates and discount factors prevailing in the market are not observable for all maturities. FinPricing bootstraps treasury benchmark curves to generate treasury yield curves (or treasury zero rate curves). All the yield curves generated by FinPricing are continuously compounded.
Treasury Yield Curve Data Sample
A treasury yield curve is shown below:
CurveName ValuationDate Tenor Value CAD_Treasury 2020-11-25 3/4/2021 0.0010898 CAD_Treasury 2020-11-25 5/13/2021 0.0015195 CAD_Treasury 2020-11-25 11/10/2021 0.002038 CAD_Treasury 2020-11-25 11/1/2022 0.0026914 CAD_Treasury 2020-11-25 9/1/2023 0.0030583 CAD_Treasury 2020-11-25 9/1/2024 0.0036062 CAD_Treasury 2020-11-25 9/1/2025 0.0045096 CAD_Treasury 2020-11-25 6/1/2026 0.0046731 CAD_Treasury 2020-11-25 6/1/2027 0.0051644 CAD_Treasury 2020-11-25 6/1/2028 0.0058674 CAD_Treasury 2020-11-25 6/1/2029 0.0064962 CAD_Treasury 2020-11-25 6/1/2030 0.0071914 CAD_Treasury 2020-11-25 6/1/2041 0.0113203 CAD_Treasury 2020-11-25 12/1/2051 0.0127914
References: