Accruing the Floating Leg of an OIS Swap

Summary

The document explains how to calculate accrued interest on an overnight indexed swap’s floating leg before the accrual period ends, when the final cash flow is not yet known. Accrual is based on compounding the overnight rates observed so far: each rate is applied over its corresponding elapsed day count, and the resulting compounded growth is applied to the notional.

The answer gives a numerical illustration using three days of identical fixings and a notional amount, and identifies ACT/360 as the usual day-count convention. It notes that the interval between business days can span more than one calendar day, so the applicable day count must be reflected for each fixing. The calculation describes accrued floating-leg growth to date; it does not explain full swap valuation, payment conventions, projections for unfixed rates, or variations in market documentation. Those details may matter when implementing the calculation for a specific contract.

Key ideas

• OIS floating-leg accrual compounds the overnight fixings observed so far.
• The compounded factor is applied to the swap notional to determine accrued interest.
• Each fixing’s day-count interval matters, including intervals spanning multiple calendar days.
• ACT/360 is identified as the usual convention, though contract-specific details are not covered.

Tags

# how is accrual calculated on the floating leg of a OIS swap


# how is accrual calculated on the floating leg of a OIS swap












for Libor swaps, the accrual for the floating leg is easy as the cashflow is known already at accrual start day. The calculation would be similar to how the accrual of a bond is calculated.

How about the accrual of the floating leg of an OIS swap please? The cashflow is unknown until accrual end date.

## Answer by oronimbus (score 3, accepted)

https://quant.stackexchange.com/a/75140

The accrued is just the product of the OIS rates observed so far: $A=N\times\prod_{i=0}^t(1+r_i\frac{n}{360})-1$ for $n$ days elapsed between business days (usually 1 or 3), $N$ notional and $r_i$ is the reset rate observed. Usually the day count is ACT/360.

For example, if we've entered a swap three days ago and the OIS fixing was 4.83% on all days then our accrued on 10mm notional is around $4025: `=((1+4.83%/360)*(1+4.83%/360)*(1+4.83%/360)-1)*10000000`

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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