Averaging Conventions for Federal Funds Basis Swap Legs

Summary

The discussion asks why the Federal Funds leg in a basis swap may use an arithmetic average, while a standard overnight indexed swap often compounds daily rates geometrically. The answer attributes the difference to market convention: the products developed with distinct terms and payment structures, so their floating-leg conventions need not match.

It offers a tentative rationale based on typical product structure. Shorter-dated OIS may have a single accrual period, making daily compounding a way to represent reinvestment through that period. Longer-dated Federal Funds–Libor basis swaps may have multiple periods and reset notional between them, which the respondent suggests makes arithmetic averaging reasonable. This explanation is explicitly framed as a guess, not a definitive account of market history or contract terms; actual conventions should be checked for the instrument being priced.

Key ideas

• Floating-rate averaging conventions can differ between OIS and basis swaps.
• The answer explains the distinction as a product-specific market convention.
• Daily geometric compounding represents reinvestment across an accrual period.
• The proposed link between multiple reset periods and arithmetic averaging is tentative.

Tags

# USD-Federal Funds for OIS swaps vs USD-Federal Funds for Basis swaps


# USD-Federal Funds for OIS swaps vs USD-Federal Funds for Basis swaps












Anyone knows why the OIS leg for basis swaps pays the average rate instead of the geometric average compounding rate as expected for a regular OIS swap leg?

## Answer by jaehyukchoi49 (score 4)

https://quant.stackexchange.com/a/32759

As far as I know, it's a market convention. The two products, namely OIS swap (fixed vs floating) and Fed Fund Libor basis swap, are developed differently, so they follow different conventions.

My only guess is that it's because of the difference in maturity and period: OIS swap is typically a single-period swap (i.e. zero coupon swap) on short-end (< 2 yrs) while FF Libor basis swap is multiple period swap on long-end (> 2 yrs). The geometric compounding is for mimicking the daily reinvestment, so it makes sense for the single period. However, the daily reinvestment is not in line with multiple period swap because the notional is reset at every period, so you don't have to stick to the geometric compounding. In fact, arithmetic averaging is a much simpler computing choice to layman.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.