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Interpolating an Initial Floating-Rate Stub from Money-Market Rates

Article Quant Q&A · Author: vara
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Summary

The document describes a simple linear interpolation for estimating an initial stub rate in a floating-rate note or swap. Given one-month and two-month reference rates, it weights the difference between them according to where the stub period falls between those tenors, then adds that adjustment to the one-month rate. The example uses an ACT/ACT day-count convention and a stub running from December 1 to January 13, with the interpolation based on its position between the one-month and two-month dates.

The answer supplies a numerical result for the example, but it does not explain Bloomberg’s implementation in detail or establish that this approach matches every product setup. Conventions, calendar adjustments, fixing dates, and the definition of the relevant tenors may affect a production calculation. The method is therefore a useful basic money-market approximation, while the example alone does not establish Bloomberg’s full pricing methodology.

Key ideas

  • Linear interpolation can estimate a stub rate from neighboring money-market tenors.
  • The example weights the one-to-two-month rate difference by the stub’s position between those maturities.
  • The stated day-count convention for the example is ACT/ACT.
  • Product conventions and date adjustments can matter beyond the simple interpolation shown.

Tags

Fixed incomeDerivatives pricingStatistics
Full text
# How does Bloomberg arrive at stub rate for swaps/floaters?


# How does Bloomberg arrive at stub rate for swaps/floaters?












I'm trying to interpolate initial stub rate ( 'Index to' in the image ) for the following FRN pricing example.

- Fixes on 2016/11/30

- 1m : 0.623670

- 2m : 0.742500

- 3m : 0.93417

Please be as specific as possible ( particularly day count convention ).

## Answer by rrg (score 3, accepted)

https://quant.stackexchange.com/a/31617

Basic money markets arithmetic. Using day count convention ACT/ACT,

`01 Dec 2016 to 13 Jan 2017 is 43 days,`

`(43-30)/(60-30)*(2m Libor - 1m Libor)+(1m Libor)`

`= 0.675163`

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.