Deriving Long-Dated USD OIS Quotes from LIBOR Basis Swaps

Summary

The document asks how Bloomberg may derive USD overnight indexed swap quotes at maturities of seven years and longer from USD three-month LIBOR par swaps and LIBOR–federal funds basis swaps. It describes a synthetic fixed-for-floating federal funds swap: subtracting the basis spread from the LIBOR par swap rate, with adjustments for differing payment frequencies and day-count conventions.

The question focuses on which bid and ask sides should be combined when constructing the synthetic quote. The author argues that selling one leg of the basis swap might require using its ask, rather than subtracting bid from bid, and asks why the screen displays the latter. No answer or market evidence is provided, so the document frames a pricing and quote-convention question rather than resolving it. It is useful as an illustration of how basis swaps can be used to infer OIS rates, but does not establish the correct executable quote convention or explain Bloomberg’s specific methodology.

Key ideas

• A synthetic federal funds swap rate can be inferred from a LIBOR par swap and a LIBOR–federal funds basis spread.
• Payment frequency and day-count differences require adjustments when combining the rates.
• The document questions which bid and ask sides should be used to form an executable synthetic quote.
• It raises a Bloomberg quote-convention question but does not provide an answer.

Tags

# USD OIS curve. Why is the the bid bigger than the ask for maturities > 7 years?


# USD OIS curve. Why is the the bid bigger than the ask for maturities > 7 years?












I was wondering why the bid is larger than the ask for maturities bigger than or equal to 7 years?

If i export the screen to Excel i can see how the bid and ask swap rates are calculated. For the bid it is essentially just taking the bid Par swap rate for USD 3m LIBOR (=:K) and subtracting the bid par swap rate for a LIBOR-fed funds basis swap (=:s), with some adjustment for different payment frequencies and daycount conventions it creates a synthetic Federel funds fixed-for-floating swap i.e

(LIBOR- K) - (LIBOR-(FF+s)) = FF-(K-s)

```
 (bid)    -      (bid)     =  (bid)?
```

Bloomberg quotes (with some modifications) K-s on the screen in the 'bid' column for maturities bigger than 7. But why would you subtract bid for bid since you are 'selling' the LIBOR-ff basis swap. Shouldnt you take the bid from the Par swap and the ask from the LIBOR-ff basis swap to get:

(LIBOR- K) - (LIBOR-(FF+s)) = FF-(K-s)

```
 (bid)    -      (ask)    =  (bid)
```

Your help would appreciated.

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