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Building a USD Libor Zero Curve from Cash, Futures, and Swaps

Article Quant Q&A · Author: Under
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Summary

The document explains why a handful of short-term USD Libor quotes cannot define a full zero-rate curve. It outlines a typical instrument sequence: use cash or deposit rates for the short end, Eurodollar futures to extend the curve through the intermediate maturities, and par fixed-floating swaps for longer maturities. The precise instruments and available quotes depend on the curve being built and the market convention being followed.

A second response describes the construction process in stages: assemble an interest-rate curve from cash, forward-rate agreements or futures, and swaps; derive discount factors; then convert those factors into zero rates. Futures can make the initial rate inputs discontinuous, so a continuous discount-factor curve is needed for cash-flow calculations. The discussion gives no market quotes beyond the question’s short-end inputs, nor a bootstrapping formula, interpolation method, day-count conventions, or treatment of collateral and curve basis. It is therefore a high-level map of the required data and steps, rather than a complete implementation recipe.

Key ideas

  • Short-term Libor observations alone do not supply enough instruments for a full USD zero curve.
  • Cash rates, futures or forward-rate agreements, and swaps typically cover successive maturity segments.
  • Curve construction proceeds from market rates to discount factors and then to zero rates.
  • Interpolation and market conventions are necessary implementation details that the discussion does not specify.

Tags

Fixed incomeFuturesStatistics
Full text
# Zero rate curve USD Libor


# Zero rate curve USD Libor












Good day, I gave following inputs of Libor rates :

ON 0.3731 1W 0.3939 1M 0.4265 2M 0.5148 3M 0.6176 6M 0.8655 1Y 1.1336

How can I build zero-rate curve ?

## Answer by Todd Page (score 1)

https://quant.stackexchange.com/a/23238

The short answer is - you need more data.

If you want to build a full zero-rate swap curve, typically these curves go out to 30 years.

In general, the front of the curve is made from LIBOR rates, which you have. Typically you don't see practitioners use anything past the 3M point but some will use up to the 6M point.

For the 2nd part of the curve, from 6M to at least 2-years, you will need to imply rates from Eurodollar futures. There are a few places to get contract prices for these (CME and Quandl being two of them).

The the final part of the curve you will need to imply zero rates using par (at the money) fixed-float swaps. I don't know of a great place to get these rates other than bloomberg, although Quandl (mentioned above) may have a datasource.

Once you have data, there are many answers to curve-building questions such as this.

## Answer by D V Rakesh (score 0)

https://quant.stackexchange.com/a/34301

To construct a zero rate curve the first step needed is to build a IR curve using Cash,FRAs/Future,Swap rates. Second step is to form a Discount factor curve from these rates which is continuous(as the IR curve built is non continuous due to Future). Third step is to compute Zero curve from this discount curve which will be continuous in nature and ca be used for generating cash flows.

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.