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OIS Curve Zero Rates: Day Counts, Compounding, and Curve Stripping

Article Quant Q&A · Author: Andrei Sultanov
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Summary

The document examines a small mismatch between a GBP overnight index swap market quote and a displayed zero rate. It calculates a one-week discount factor from the quoted rate using a simple day-count fraction, then converts that factor to a continuously compounded zero rate. The reported result is close to, but not identical to, the Bloomberg figure, prompting the question of how the curve is built.

The answer explains that the calculation is appropriate for the continuously compounded zero rate in one Bloomberg view, while another swap-pricing view may display rates using that swap’s day-count convention and compounding frequency. It also cautions that reproducing a stripped curve requires more than applying a formula: calendars and interpolation choices matter. The example is useful for distinguishing quote conventions and terminal displays, but it does not provide enough detail to replicate Bloomberg’s full curve construction.

Key ideas

  • A market quote can be converted to a discount factor and then to a continuously compounded zero rate.
  • Displayed rates may differ because screens use the underlying swap’s day-count convention and compounding frequency.
  • Curve replication also depends on calendars and interpolation choices.
  • The example explains a convention mismatch but does not specify a complete curve-stripping procedure.

Tags

Fixed incomeDerivatives pricingStatistics
Full text
# How does Bloomberg use the OIS curve to get the zero rates?


# How does Bloomberg use the OIS curve to get the zero rates?












I'm trying to reproduce the zero rates using the market rates, but I have not been able to. I read the Bloomberg's "Building the Interest Rate Curve" paper and followed the formulas exactly but that didn't help as well.

For example, for the 1-week GBP OIS: Discount factor = 1 / (1 + 3.42880% * 7 /365) = 0.999343 Zero rate = -365/7 * ln(0.999343) = 3.42767% (BBG zero rate 3.42816%)

Could anyone please help point any mistake here? Thank you in advance.

## Answer by AKdemy (score 2)

https://quant.stackexchange.com/a/76342

If you take screenshots, it helps if you do not cut off the important parts - or at least mention where the screenshot is from. Usually, `ICVS` is where one would look for details about interest rates.

However, I am almost certain your screenshot is actually from the `5) Curves` Tab of `SWPM`.

Your calculation is correct for the continuously compounded Zero rate as shown on ICVS. The dicount factor is computed from the zero rate.

However, if you hover over the value in SWPM, you will see that it uses the specific day-count convention and compound frequency of the swap itself.

The first set of values is relatively simple.

Overall, replicating curve stripping (not just Bloomberg) exactly is quite difficult. It is not only about knowing the correct method but also about taking into account all calendars, interpolation etc.

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.