How Overnight Index Swaps Compound Fixed-Rate Cash Flows

Summary

This short discussion addresses how to calculate the maturity amount for an overnight index swap over a short accrual period. It distinguishes a simple interest calculation over the full period from compounding a sequence of overnight rates. The answer says the appropriate treatment depends on the OIS market being considered and describes EUR and USD overnight swap rates as using compounding with rates updated overnight.

The example question specifies an ACT/365 day-count convention and asks about a period spanning several days without a weekend. The response points readers toward market-specific conventions rather than treating the quoted fixed rate as a universal formula. It gives no worked calculation, contract documentation, or detailed comparison of conventions, so it serves as a concise convention-level clarification. For an actual swap valuation, the relevant currency, accrual schedule, and product terms still need to be checked.

Key ideas

• OIS fixed-rate accrual conventions depend on the market and currency.
• The response describes EUR OIS rates as compounding overnight rates through the period.
• USD OIS rates are also described as using overnight compounding.
• The rates used in the compounding calculation are updated from night to night.
• The discussion offers a convention-level answer without a worked maturity calculation.

Tags

# OIS fixed rate compunding criteria


# OIS fixed rate compunding criteria












I have the following doubt: How should the OIS fixed rate be considered in computing principal+interests at the maturity of the swap? I mean, if i.e. the swap lasts 4 day (without w.e. in the middle), and the day count convention is ACT/365, I've found both: P*(1+OIS*4/365) (here) and P*(1+OIS/365)^4 (here)

Thanks!

## Answer by Jan Stuller (score 2)

https://quant.stackexchange.com/a/54917

Depends on which OIS you are referring to. For EUR OIS Swaps, the EONIA Swap rate is calculated via the usual compounding formula (notice that in the example below, the rate $r_i$ is updated every night):

Example is shown here:

For USD OIS Swaps, the link to Investopedia that you shared is correct: it is pretty much the same formula as for the EUR swap rate (compounded rates, updated on an overnight basis).

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