Extending OIS Discount Curves with Interest Rate and Basis Swaps

Summary

The document asks how market participants built long-maturity OIS discount curves when long-dated OIS swaps were not yet liquidly quoted. The accepted response describes constructing the curve by combining interest-rate swap rates with Fed Funds versus LIBOR basis swap rates. In its example, a ten-year swap rate of 2.0% and a basis of minus 35 basis points imply a ten-year OIS rate of 1.65% under the stated calculation.

The response says basis swaps had been liquid for decades, making this approach available even without direct long-term OIS quotes. It links the widespread move from LIBOR discounting to OIS discounting to the widening of the Fed Funds/LIBOR basis after 2008. The exchange gives a brief historical explanation and a single illustrative calculation; it does not spell out curve bootstrapping, interpolation, collateral assumptions, or how the method varies across currencies and periods.

Key ideas

• Interest-rate swap rates and Fed Funds/LIBOR basis swap rates can be combined to infer OIS rates.
• Liquid basis swaps provided market inputs even when long-dated OIS quotes were unavailable.
• The example derives an OIS rate by adjusting the interest-rate swap rate by the basis.
• The response connects wider Fed Funds/LIBOR basis spreads after 2008 with the shift to OIS discounting.

Tags

# How were OIS discount curves built before long-term OIS were liquid?


# How were OIS discount curves built before long-term OIS were liquid?












Many sources put the switch from LIBOR discounting to OIS discounting at some point in 2008, or perhaps a little earlier (the earliest I have seen is August 2007). It seems that this may be optimistic, and that the switch did not happen until a couple of years later, some time around 2010.

As far as I can tell, 10Y OIS were not often quoted until mid-2008 (Bloomberg has prices from 6th July) and longer term OIS were not quoted until the end of 2011 (Bloomberg has 15Y+ OIS quotes from 27th Sep 2011).

There is some overlap when the market built OIS discount curves, but long-term OIS swaps were not liquidly traded. What techniques were used to build the discount curve in the absence of OIS quotes?

## Answer by dm63 (score 5, accepted)

https://quant.stackexchange.com/a/31313

The ois curves were (and still are) primarily build from adding together (a) interest rate swap rates and (b) Fed Funds/Libor basis swaps. For example, if 10yr swaps are 2.0%, and 10yr fF/libor is -35bp, the 10yr ois is 1.65%.

The basis swaps have been liquid for decades, so this calculation has always been possible. However, participants didn't discount swaps at ois until after 2008, when the FF/Libor basis widened dramatically.

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.