How a Five-Year OIS Rate Relates to Overnight Compounding

Summary

The document introduces the interpretation of a longer-tenor overnight indexed swap (OIS) rate. An OIS exchanges a fixed cash flow against a floating leg based on daily overnight rates; the cited answer identifies the Federal Funds Effective Rate and an ACT/360 day-count convention for the floating side. Thus a five-year quote belongs to a swap extending over that horizon, rather than being a single overnight rate applied unchanged for five years.

The fixed leg follows an agreed payment schedule, and the fair swap rate is associated with a transaction whose present value is zero at inception. The text does not provide the full compounding formula, discounting convention, payment schedule, or a derivation showing precisely how to infer expected future overnight rates from the quoted rate. It is therefore a basic market description, with conventions that may vary by contract and market, rather than a complete guide to constructing or interpreting an OIS curve.

Key ideas

• An OIS exchanges fixed cash flows for a floating leg linked to daily overnight rates.
• The floating overnight rate is accrued using the contract’s day-count convention, identified here as ACT/360.
• The fixed leg can follow an agreed payment schedule.
• A fair swap is entered with zero present value under the applicable valuation conventions.
• The explanation omits detailed compounding and curve construction conventions.

Tags

# What does 5 year OIS actually mean?


# What does 5 year OIS actually mean?












I am aware that OIS is the new reference/risk-free rate for collateralized cashflows. OIS is by definition an overnight rate (annualized, I assume). So once I have constructed my OIS yield curve, what does it actually mean as I go along the different tenors.

For example, would the yield at 5yr represent the fair swap rate indexed against the expected overnight lending rates for the next 5 years. How is interest even calculated on the overnight lending? Would it simply be expected rate*(1/360)?

Just curious about how to view OIS rate that is dated beyond overnight, i.e. longer maturity

## Answer by JoshK (score 6, accepted)

https://quant.stackexchange.com/a/47478

When people say OIS swap they mean an exchange of some sort of fixed cash flow and in return the receipt of daily OIS based on the "Fed Effective Rate" (FEDL01 Index on Bloomberg).

The floating side is always fed effective daily (ACT/360). The fixed side can be any schedule you want, but the default I think is ACT/360 (money market).

The PV of the swap should be 0 (otherwise why would anyone engage in the transaction?)

Here's a screen shoot from Bloomberg:

I can get you more details if you need, just let me know.

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.