Building a Zero-Coupon Curve from Spot Rates and Market Instruments

Summary

The document explains how to obtain a zero-coupon yield curve and distinguishes observed spot rates from a curve calibrated to traded instruments. A curve can be interpolated from spot rates when they are available, but spot rates are generally not directly traded. Instead, practitioners infer rates at selected maturities from cash instruments in the near term, forward rate agreements and futures in the medium term, and swaps at longer maturities.

Interpolation and extrapolation then fill in rates between or beyond those instrument maturities. The answer identifies piecewise constant forward rates as a simple interpolation approach discussed by Hagan and West, and notes that a calibrated zero-rate curve can be sourced for a selected market. The response is concise and does not give bootstrapping equations, instrument conventions, or a comparison of interpolation methods; actual curve construction depends on market and calibration choices.

Key ideas

• Spot rates can be interpolated to form a zero-coupon curve when suitable rates are available.
• Spot rates are generally not directly traded, so curves are commonly inferred from traded instruments.
• Cash instruments, FRAs or futures, and swaps provide inputs across short, medium, and long maturities.
• Interpolation and extrapolation are used to estimate curve values at arbitrary maturities.
• Piecewise constant forward rates are presented as a simple interpolation scheme.

Tags

# Using Spot Rates to construct Zero-Coupon Bond Yield Curve


# Using Spot Rates to construct Zero-Coupon Bond Yield Curve












I am just trying to get an explanation as to why Spot Rates can't be used to create a yield curve for Zero-Coupon Bonds? Or if they can, would it involve Bootstrapping?

Thanks

## Answer by gt6989b (score 1, accepted)

https://quant.stackexchange.com/a/18287

If you want a zero coupon curve, you can interpolate it given the spot rates. This is typically not done, since spot rates are not traded on the market. Instead, cash instruments are used in the near term, FRAs and futures - in the medium-term, and swaps in the long term to imply rates at specific times, and an interpolation (and extrapolation) scheme is imposed to create the values for arbitrary points in time.

Hagan and West in a classic paper show that the simplest sane interpolation scheme is piecewise constant forwards.

As for where one may get a series of such rates, I would try the `CRVF` function on the Bloomberg for the specific country of interest. Just make sure you pick the calibrated zero rates curve.

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.