Compounding Conventions for Interest Rate Basis Swaps
Summary
The discussion outlines conventions for basis swaps when the rates reset more often than the legs pay. It distinguishes ordinary daily compounding, a weighted average treatment for Federal Funds, and a special treatment described for Brazilian reset rates. It also raises how a spread is applied when both legs compound, noting that the leg receiving the spread matters for the payoff calculation.
The explanation is a brief answer to a market convention question rather than a complete specification. It says that for many overnight index swap periods longer than one day, the rate is applied linearly across the multi-day interval, while Brazilian reset rates compound each day. It further says Federal Funds conventionally use a day-count-weighted average, whereas SOFR versus Federal Funds is described as compounding both rates regularly. These statements are useful starting points, but the document supplies no authoritative convention sources or detailed product definitions, so actual pricing should be checked against the relevant market documentation.
Key ideas
- Basis swap legs may have reset intervals shorter than their payment intervals.
- The answer describes linear accrual across multi-day overnight reset intervals as a common convention.
- Brazilian reset rates are identified as an exception that compounds across days.
- Federal Funds swaps are described as using a day-count-weighted average rate.
- The placement of a spread affects the payoff and must be specified for pricing.
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Full text
# Two questions on Interest-Rate Basis Swap compounding # Two questions on Interest-Rate Basis Swap compounding I have 2 questions on Basis Swap compounding and market conventions. These obviously apply where the reset period is shorter than the payment period - Where both fixings have shorter reset period than payment period and there is a spread, and it is not a "compound without spread", does this, by convention, apply only to the first mentioned fixing rate? (The only one of which I know is SOFR vs Fed Funds which uses compound without spread so it doesn't apply yet, but as one who is programming pricing for these I need to know in a more general manner) - Where this is an IOS compounding and the reset period is more than 1 day, are the days compounded? That is the difference between (1+rd)^n and 1+rdn or using log1p, n(log1p(rd)) or log1p(rdn) where 'd' is the daycount fraction (or yearFraction) for a single day, r is the interest rate that is reset n days later (sometimes more than 1 due to weekends or holidays) ## Answer by CashCow (score 1) https://quant.stackexchange.com/a/49134 From what I have now read I can partially answer 2: It is normally (conventionally) 1+rdn or log1p(rdn) except on Brazilian reset rates which use (1+rd)^n or n(log1p(rd)). FED funds conventionally don't compound but use a weighted average rate over the period (weighted by daycount), and that is how they compound in Libor vs FED funds swaps. For SOFR vs FED Funds it appears both compound the same way, i.e. regular compounding. With regards spread, even if compounding without spread it is necessary to know to which side to apply the spread so which is mentioned first will have a big significance in that.
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