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Interpreting LIBOR–OIS Spreads as Bank Borrowing Costs

Article Quant Q&A · Author: Vol_Smile
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Summary

The document explains how a bank’s LIBOR borrowing rate can be compared with the overnight indexed swap rate to describe its funding spread. In the example, three-month LIBOR is 2.10 percent and the corresponding OIS rate is 2 percent, giving a 10-basis-point difference. OIS references an overnight rate; in the US example, that rate is federal funds.

The answer interprets the quoted borrowing cost as the OIS rate plus the spread, rather than as an assumed initial loan at the federal funds rate. A bank seeking to remove LIBOR exposure could receive LIBOR and pay the OIS rate plus a spread in a swap; the example’s spread is 10 basis points. This explanation assumes the swap is entered at zero present value and simplifies the quoted statement. It does not discuss credit, funding, collateral, or tenor-basis risks that may affect actual borrowing costs.

Key ideas

  • The example LIBOR rate exceeds the comparable OIS rate by 10 basis points.
  • In the US context described, the overnight index underlying OIS is the federal funds rate.
  • Receiving LIBOR and paying OIS plus a spread can offset LIBOR exposure on a LIBOR-funded loan.
  • The spread interpretation assumes a fair swap entered at zero present value.

Tags

Fixed incomeDerivatives pricingUS markets
Full text
# Basic question on LIBOR-OIS swap


# Basic question on LIBOR-OIS swap












I'm just starting a pricing class and am a little confused by a statement in a class reading (a fed report). It goes something like this:

"A bank borrowing at the 3-month LIBOR rate of 2.10 percent that enters into a swap to receive at the 3-month OIS rate of 2 percent has a borrowing cost equal to the effective federal funds rate plus 10 basis points."

I'm not sure how does the fed funds rate come into the picture here. Is it assumed that the bank initially borrows the principal at fed funds rate and now has to pay a net 10 bps interest in this swap deal which adds up to a total effective borrowing cost of fed funds rate + 10 bps?

Could someone please clarify? Any input would be appreciated.

Thanks in advance.

## Answer by Rostock (score 5)

https://quant.stackexchange.com/a/15493

Vol_smile. The sentence as you quote it doesn't make much sense, but my guess as to what they mean is this:

OIS stands for Overnight Index Swap. In the US the overnight rate is called Fed Funds as 'experequite' mentioned (in the Euro-zone it is Eonia). The bank is borrowing at 3m Libor, which in this example is currently 2.10%. If 3m Fed Funds OIS is at 2%, then the bank is borrowing 10bps above 3m Fed Funds OIS (2.1% - 2%). If the bank then doesn't want to have any dependency on Libor they could enter a 3m swap in which they receive Libor and pay Fed Funds + X bps. since this swap will have 0 PV at the moment of execution (otherwise either they or the counterpart wouldn't do it) X = 10bps.

Hope that helps. Must be quite an old report if 3m Libor is 2.1%. Wonder how long it'll be till we see those rates again.

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