I have heard that the SABR volatility model was not good at pricing a constant maturity swap (CMS). How is that?

  • $\begingroup$ Hi Al Khawarizmi, welcome to quant.SE. Do you have a source you can cite for your assertion? $\endgroup$ Sep 27, 2011 at 15:13
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    $\begingroup$ That was a question @ a BNP Paribas interview. I have to admit that I had no clue about the answer although I see the advantages of the SABR dynamics and the way it improved the delta hedging (as explained in the "founding" article). I still remember the interviewer mentioning higher rates and maturities though $\endgroup$
    – Averroes
    Sep 27, 2011 at 15:29

3 Answers 3


Here's a research note devoted to pricing of CMS by means of a stochastic volatility model. The authors indicate in the Introduction that

an analysis of the coupon structure leads to the conclusion that CMS contracts are particularly sensitive to the asymptotic behavior of implied volatilities for very large strikes. Market CMS rates actually drive the option market in extreme strike regions and indicate that implied volatilities flatten out and converge asymptotically to a constant. This behavior is not consistent with the rapidly diverging asymptotics which are implied by SABR.

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    $\begingroup$ The link is broken. Is it possible to update it? $\endgroup$
    – Gordon
    Apr 13, 2016 at 16:47
  • $\begingroup$ The link is broke. Could you please update it? Also, could you please write out the title and author of the paper so that in case the link is broke people can search for it? $\endgroup$
    – Hans
    Jan 9, 2018 at 3:05
  • $\begingroup$ I think they mean A Stochastic Volatility Model for Bermuda Swaptions and Callable CMS Swaps by Claudio Albanese and Manlio Trovato. pdfs.semanticscholar.org/4f87/… $\endgroup$ Jun 3, 2020 at 2:05

The SABR model has an overly fat right tail. If you do the CMS replication using cash-settled swaptions you find that you need ridiculously high strikes.

  • $\begingroup$ What you say is true (I experienced that) nevertheless using those ridiculous high strike swaptions, CMS Swaplet, Caplet, Floorlet using Hagan's type replication argument, this works quite well in practice (at least for my needs over EURIBOR products). How to interpret that and what model to use instead of SABR ? Best Regards $\endgroup$
    – TheBridge
    Jan 17, 2012 at 9:09

Late to the game here and an already well-answered question, but an important one nonetheless. In a nutshell, stochastic volatility models are generally a weak solution for products that depend mainly on the terminal distribution (and CMS is a ubiquitous case of this) because of poor fitting of the vol surface (especially on wing strikes). Terminal swap rate models (linear, exponential ...etc) are usually a much better option.


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