Inferring an OIS Swap Rate from IRS and Basis Quotes

Summary

The note explains how to estimate an overnight indexed swap rate from a fixed rate on an interest rate swap and a matching-tenor Fed Funds versus Libor basis spread. When the relevant swap schedules align—including dates, payment frequency, day-count convention, and business-day rules—the OIS quote can be approximated by subtracting the basis spread, converted from basis points to percentage points, from the IRS rate.

For accurate valuation when schedules differ, the document recommends bootstrapping the term structures, potentially together because they may depend on one another. It also flags a USD-specific complication: OIS rates reflect compounding, whereas the Fed Funds rate is averaged arithmetically. The explanation gives no worked numerical example or empirical validation, so the simple subtraction is a conditional shortcut rather than a generally exact conversion.

Key ideas

• When IRS and basis swap schedules match, subtract the basis spread from the IRS rate after converting units.
• Schedule alignment includes dates, frequency, day-count convention, and business-day adjustment.
• Different schedules require bootstrapping the relevant curves, potentially in a joint process.
• USD OIS and Fed Funds conventions differ because one compounds while the other uses an arithmetic average.

Tags

# Derive OIS rate from IRS rate and Fed Funds/Libor basis spread


# Derive OIS rate from IRS rate and Fed Funds/Libor basis spread












For example I have 7Y interest rate swap rate and 7Y Fed funds/Libor basis spread. What is the step-by-step procedure to derive OIS rate from these two?

## Answer by MattBecker82 (score 2, accepted)

https://quant.stackexchange.com/a/19482

If you're lucky enough that the payment schedules (start/end dates, frequency, day count, business day adjustment etc.) are the same between the fixed leg of the interest rate swap and the "spread" leg of the basis swap, then you can simply use:

OIS rate (%) = IRS Rate (%) - 0.01 * (basis spread (bps))

Otherwise, to do it accurately, you'll need to do a bootstrap the two term structures (possibly simultaneously if there is mutual dependence between them).

[In fact, in the USD case, there is an added complication that comes from the OIS rate being a compounding rate, while the FedFunds rate is an arithmetic average.]

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.