OIS Discounting







The term OIS Discounting is a misnomer.  We actually use the Effective Fed Funds Rates to revaluation of open swaps positions for collateral purposes.  LIBOR is still used for transaction purposes.  Before speaking about  OIS discounting, let’s review pricing an At Market Interest Rate Swap.


Illustration 1 shows a three year swap, resetting and paying annually.

The LIBOR curve is used to derive LIBOR forward rates.

The forward rates are then used to interpolate and solve for the fixed rate that brings all cash flows back to an NPV of zero.

The At-Market rate for our Swap is 7.445%; Specifically, the timeline diagram shows the counterparty

PAYING fixed @ 7.445% and RECEIVING 12 month LIBOR.


 N.B.: Timeline diagram: cash flows go up and in and down and out


To reprice the swap, the only change will be raising LIBOR 100 bps for each period.  All other variables will be left unchanged



Illustration 2 shows the repricing matrix using LIBOR rates, as we would normally do to revalue any LIBOR based swap.


Illustration 3 reprices our swap using  new LIBOR rates.

Note: The only variable changed has been LIBOR, which has been increased by 100 bps.

The counterparty has a profit on this swap of $16,233.44


Now we need to get the Effective Fed Funds Rates (a.k.a.: OIS discounting) to reprice this swap for collateral purposes.  The Fed Funds market is a short term market.   Therefore, the Overnight Index Swap (OIS) is used to extrapolate the Effective Fed Funds Curve.

Illustration 4 shows the Overnight Index Swap (OIS) below.  The OIS market is very active.



In our example below, we’ve used a 65 bps OIS swap for all three years.   The new LIBOR rates (up 100 bps) are then reduced by the OIS spread (65 bps).  The result will be the Effective Fed Funds rates to use to discount each cash flow.


Illustration 5 shows OIS discounting.

Notice the swap repriced using using Effective Fed Funds rates adjusted for an OIS rate of 65 bps

The swap’s new value of $16,585


Illustration 5 shows the comparison between the two discounting methods.

OIS discounting will be used for purposes of calculating collateral requirements.

LIBOR discounting will be used for revaluation and transaction purposes.


NOTE: With rates up 100 bps, the difference between LIBOR ($16,233.44) and OIS ($16,585) is $351.56.

With rates down 100 bps (and OIS at 65 bps), the difference between LIBOR and OIS is $148.29.  

Therefore we can summarize the impact of OIS discounting as one of negative convexity.

This quick overview of  OIS discounting and how it’s being used for collateral purposes is a useful primer.  We will come out with more advanced articles.

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