Building the Very Short End of a Yield Curve
Summary
The document says short-horizon curve construction depends on the market and intended use. For a USD swap curve, builders can incorporate actively traded instruments with different maturities and frequencies, including monthly fed funds futures, short-dated OIS, quarterly Eurodollar futures, and basis swaps. Some curve builders fit most or all of these instruments simultaneously, using their market prices to shape the curve’s front end.
Government curves may be handled differently. The responses note that US Treasury curve builders may fit the sub-year sector separately, or use repo rates at the front end because Treasuries are financed in the repo market and repo can give more accurate forward rates. Another response describes flat-forward interpolation between Federal Reserve meeting dates for Treasury or OIS curves. These are market-specific practices rather than one universal default; the document does not compare methods quantitatively or give a detailed curve-building algorithm.
Key ideas
- Short-end interpolation choices depend on the market and the curve’s purpose.
- USD swap curves can use a range of actively traded instruments to constrain the front end.
- Some US Treasury curve builders fit the sub-year sector separately or use repo rates for front-end forwards.
- Flat-forward interpolation between central bank meeting dates is one suggested approach for the very short end.
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Full text
# Yield curve interpolation at (very) short horizons # Yield curve interpolation at (very) short horizons I'm struggling to find much information about yield curve interpolation for sub-yearly horizons. Say, one-two months. It seems to be the area where the curvature is usually nontrivial, while after that it's not that different from a straight line, oftentimes. Is there some method quants use for this task by default, as a simple yet effective estimate? Some industry standard? Or if it's more complicated than that, what literature should I read to get a good overview of existing methodologies? ## Answer by Helin (score 2) https://quant.stackexchange.com/a/22212 It depends on the market you're interested in and what the curve is used for. To build the USD swap curve, for example, you've got a ton of information available from actively traded market instruments – fed funds futures (monthly), OIS (even finer details at the front end), Eurodollar futures (quarterly), basis swap, etc. All of these should be incorporated into your curve building procedure. A lot of curve builders will fit most if not all of these available market instruments perfectly and simultaneously. For the government curve, it's a different story. In the US, most curve builders are not particularly concerned about fitting the front end of the Treasury curve all that well. In fact, 1) most of us are likely to fit the <1y sector by itself as a separate curve, 2) some of us use repo rates rather than Treasuries at the front end, since this gives more accurate forward rates (Treasuries are financed at repo rates). ## Answer by Kiwiakos (score 0) https://quant.stackexchange.com/a/22216 I assume that with 'yield curve' you mean US Treasury curve. The very short end is determined by the Fed rate, therefore one uses flat forward interpolation between Fed meeting dates (which are every 1.5 months). Same thing happens with OIS.
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