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Identifying the Stub LIBOR Rate in Floating-Rate Discount Margins

Article Quant Q&A · Author: Deane Yang
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Summary

The document asks which LIBOR observations are used for the stub rate when calculating a floater’s discount margin. It refers to a formula reproduced from a credit-spread paper and proposes that a Bloomberg yield-analysis page’s index-to-next-coupon field may represent an interpolated rate. The central unresolved detail is the maturity and observation date of the LIBOR rates used to construct that stub.

No formula for the stub rate or answer to the question is provided, and the referenced formula image is not present in the text. As a result, the document does not establish how to interpolate the rate, what conventions apply to the next coupon period, or how the calculation handles current benchmarks. Its value is as a narrowly framed fixed-income question about aligning an index rate with a short coupon interval; resolving it would require the source formula and the applicable market or terminal conventions.

Key ideas

  • The question concerns the stub index rate used in a floater’s discount margin calculation.
  • The author suspects the relevant rate is interpolated to the next coupon date.
  • The document leaves unspecified which LIBOR maturities and observation dates provide the interpolation inputs.
  • It supplies no explicit stub-rate formula or resolution, so benchmark and coupon conventions remain unclear.

Tags

Fixed incomeDerivatives pricingStatistics
Full text
# LIBOR rate used for computing discount margin


# LIBOR rate used for computing discount margin












A formula for computing the discount margin of a floater is provided in an image displayed in this answer as well as below. The image below comes from page 14 of the paper "Credit Spreads Explained" by O'Kane and Sen in 2004.

However, no precise definition or formula is provided for $L_{\operatorname{stub}}$. I believe that on the Bloomberg YAS page this is the Index To (next coupon date) and that it is an interpolated rate. But which LIBOR rates (maturity and date) are used?

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.