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Bootstrapping a USD Zero Curve from Money-Market, FRA, and Swap Rates

Article Quant Q&A · Author: Under
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Summary

The document asks how to build a USD zero-rate curve from short LIBOR tenors, forward rate agreements, and interest-rate swaps. The response recommends bootstrapping: first infer discount factors or zero rates at the short maturities, then use those results to solve for rates at maturities implied by the FRAs and swaps. Each instrument contributes a maturity point to the curve.

This is an iterative construction rather than a single closed-form formula. The response says a root-finding solver is needed to match instrument-implied cash flows and points to a reference on single-curve construction, while recommending QuantLib as a practical implementation option. The excerpt does not give instrument conventions, interpolation choices, market-data adjustments, or a worked example, so those details must be specified before building a production curve.

Key ideas

  • Construct the zero curve by bootstrapping market instruments in maturity order.
  • Infer short-end rates from money-market inputs before using FRAs and swaps for later maturities.
  • Use a root solver to find rates that satisfy each instrument's pricing relationship.
  • The excerpt omits conventions, interpolation choices, and a worked construction example.

Tags

Fixed incomeStatisticsDerivatives pricing
Full text
# Zero-rate USD Curve


# Zero-rate USD Curve












Good day, I have inputs: Libor 1D, 1M, 2m, 3m. FRA 3x6, 3x9, 3x12 IRS 2Y, 30Y.

What formula should I use to construct zero rate curve?

Thanks

## Answer by SmallChess (score 1)

https://quant.stackexchange.com/a/25042

You'll need to bootstrap a zero curve from your market data. This process is iterative in the sense that the implied zero rates for your short-term LIBOR rates are calculated before using those rates to bootstrap your zero rates implied by your FRAs. You will need to bootstrap for each time-point defined by your instruments.

A good reference for you would be (no multi-curve) Methods for Constructing a Yield Curve.

There is no easy formula, you will need a root-solver for the construction. I recommend the QuantLib library.

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.