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How Constant-Maturity and OIS Curves Differ in Construction

Article Quant Q&A · Author: sasha
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Summary

The document addresses whether constant-maturity swap (CMS) and overnight indexed swap (OIS) curves can be treated as the same when their reported values match. It explains CMS as a way to represent yields at fixed tenors over time, often using interpolation because traded bonds do not necessarily have exactly those maturities. It describes OIS rates as being derived from a series of futures and notes that OIS instruments are not bonds or notes with maturities that roll down over time.

The response concludes that the two curves should coincide on a given day, framing the issue as a terminology mix-up. That conclusion is presented without data, construction details, or discussion of market conventions, so it should not be taken as proof that CMS and OIS curves are generally interchangeable. The main practical lesson is to distinguish a constant-maturity representation from the instruments or rates used to construct a curve, and to investigate why two data series are identical before modeling them as equivalent.

Key ideas

  • A constant-maturity curve represents rates at fixed tenor points over time.
  • Interpolation can be needed because no traded instrument may match a target tenor exactly.
  • An OIS curve is described as deriving implied yields from a series of futures.
  • The response asserts that CMS and OIS curves coincide on a given day but offers no supporting data or construction specifics.

Tags

Fixed incomeFuturesStatistics
Full text
# Interest Rate Swap curve: CMS vs. OIS?


# Interest Rate Swap curve: CMS vs. OIS?












I'm working on a project where we're trying to create a database model where we can (daily) update collected data in order to make RPA predictions.

We received data from Interest Rate Curves called IR-CMS(Constant Maturity Swap?) in one file and IR-OIS (Overnight Indexed Swap?) in another.

You see, as the values are exactly the same, the person who started modelling assumed both curves are and behave the same.

From what I've learned, sorry if I'm a bit lost here but I'm new in this: if my understanding is right, aren't CMS and OIS different things? Or why is it safe to assume both curves behave the same way?

## Answer by JoshK (score -1)

https://quant.stackexchange.com/a/48750

I'm not sure what your exact situation is, nor what an RPA is, but I can at least explain to you OIS and CMS. I think you have terminology confusion.

CMS means "constant maturity". That is an interpolation between active issues to allow for consistency. For example, when looking at treasuries you are often looking at a small set of actively trading issues. But, how can you compare the yield on the 2yr note from 2 weeks ago to the yield now? There are different numbers of days. With high issuance, it could even be a different, new, note now.

Generating a CMS curve creates a set of points for each tenor point. That would allow us to see the implied 2 year maturity on any given day. On most days you will not have an instrument (bill or note or bond) that matures at that exact point - so you are relying on interpolation of some sort.

Now OIS is different because a series of futures is used to calculate the implied yield on any given day. There are no OIS bonds or notes, so you don't have to get rid of the optical confusion created by an X-year note that is really only [X-years - y-days] on any given day.

So really an OIS curve will be the same as a CMS curve on any given day.

Does that help?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.