Constructing Short-End Swap Curve Rates Below the Floating Reset Tenor
Summary
The document asks how very short maturities, such as overnight or one month, are represented on a curve built from swaps whose floating leg resets every three months. The responses emphasize that a one-month par swap referencing a three-month index is not generally a directly traded instrument. Short-end values may instead come from liquid instruments such as deposits, be derived from an existing curve by interpolation, or be produced through a model’s conversion or extrapolation conventions.
The discussion does not establish one universal construction. One response suggests interpolation from the three-month curve, another describes a possible model convention that changes payment frequency, and another points to deposits or extrapolation when no suitable market instrument is used. The choice depends on curve methodology and contract specifications; the thread gives possibilities rather than market data or a definitive calculation.
Key ideas
- A short maturity below the floating index reset period may not correspond to a directly traded par swap.
- Curve builders may use short-term instruments such as deposits to anchor short maturities.
- Interpolation or extrapolation can fill maturities without direct market quotes.
- Model conventions and contract specifications affect the resulting short-end curve values.
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Full text
# Swap curve and short maturities # Swap curve and short maturities Consider USD Libor 3M swap curve. There are different maturities: 2d, 1m, 3m, 6m, 9m, 1y, 18m etc. The values for 3m, 6m, 9m etc. time buckets are just swap rates for swaps with floating leg equal to 3m libor, settlements every 3 months and maturities 3m,6m, 9m etc. I wonder how the values for 2d or 1m are being calculated if the maturity is shorter than the settlement periods? ## Answer by MattR (score 1) https://quant.stackexchange.com/a/25120 Hy there, Well, the 3M Libor Curve is constructed most of the time with the 3M Ticker as the first point of the curve. Some people may include de O/N quote but it depends. But in this particular case i would say it may be obtained or calculated from an already derived curve. What is important is that the 1M Libor does not compound into the 3M Libor so i don't think that you can get a quote on the run for that specific tenor. I think it's just being interpolated from the 3M Libor Curve. ## Answer by dm63 (score 0) https://quant.stackexchange.com/a/25122 There's clearly no such thing as a one month par swap with a floating index of 3 months. So you're really just asking what a typical model kicks out of you ask for that rate. In my view the most likely answer is that it would convert the 3m rate into a monthly payment frequency, and that would be the rate given. Thus the rate would be slightly lower than the spot 3m rate. ## Answer by SmallChess (score 0) https://quant.stackexchange.com/a/25125 Obviously, you won't have a one-month swap with a 3m index. The shorter maturities are usually constructed by liquid short-term instruments such as: `deposits`. If those instruments are not used, you'll need an `extrapolation` scheme. This could be anything, like assuming a flat rate or some kind of equations. You'll need to find more from the contract specification.
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