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Bounding One-Week LIBOR Forwards Without a Tradable Curve

Article Quant Q&A · Author: Math
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Summary

The document asks how to construct a one-week LIBOR curve when no commonly traded instruments are available to bootstrap it, and how to estimate the short first coupon of a forward-starting swap that references one-week LIBOR. The answer says a dedicated one-week curve cannot be bootstrapped from traded instruments in the described market setting.

As a workaround, it proposes bounding the one-week forward rate between overnight federal funds and one-month LIBOR, calculating the rates at those bounds from curves that can be bootstrapped. This provides a range rather than a directly observed or uniquely determined one-week rate, so it does not specify a point estimate or a full interpolation model. The discussion is brief and reflects the market context described in the source; it provides no calibration data or evidence on how tight the bounds are in practice. Users would need to consider whether the instruments and rate conventions remain appropriate for their valuation date and market.

Key ideas

  • The answer reports that traded instruments do not support bootstrapping a standalone one-week LIBOR curve in the setting discussed.
  • A one-week forward rate can be bounded using overnight federal funds and one-month LIBOR forwards.
  • The bounding rates can be obtained from curves that are supported by traded instruments.
  • The proposed range does not supply a unique rate or a complete method for valuing the short swap coupon.

Tags

Fixed incomeDerivatives pricing
Full text
# One week LIBOR?


# One week LIBOR?












Are there any commonly traded instruments that would allow one to bootstrap a one week LIBOR curve?

If not, is there some alternate way to value forward starting swaps with a short first period that use interpolation between one week LIBOR and 1M LIBOR for the coupon of the first floating payment?

## Answer by dm63 (score 2, accepted)

https://quant.stackexchange.com/a/31796

There are no traded instruments that would allow a 1w libor curve to be bootstrapped. If you need to calculate a forward rate for 1week libor in the current environment, I would suggest that it can be bounded as follows : overnight fed funds < 1 week libor < 1 month libor. The forward rates on the bounds can be calculated from bootstrapped curves.

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.