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What are the approaches available to price a swaption (either European or American style)? So far it seems Black method is the only one used. Thanks!

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  • $\begingroup$ Please improve your question by adding a few references and links. You should develop a bit more. $\endgroup$ – SRKX Jan 14 '13 at 11:19
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The question should not be about the swaption pricing formula, its well established and widely accepted and utilized every single day. The question you SHOULD be asking, however, is which underlying volatility model you are using. Its idential to you questioning the use of B-S in transforming vols -> prices, and prices -> vols in the equity world while you should be asking how to model volatility. In general, you should be thinking about the Brownian motion variables and not deterministic ones when modeling and choosing which model to select in pricing derivatives.

Current going practice to price swaptions is to use the Stochastic Apha, Beta, Rho (SABR) model and its derivatives (such as dynamic SABR,...).

Here is the wiki: http://en.wikipedia.org/wiki/SABR_volatility_model

But more importantly here is the original Hagan paper:

http://www.wilmott.com/pdfs/021118_smile.pdf

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  • $\begingroup$ The Hagan paper's link is dead... Also, I think it is worth mentioning that Bachelier model can be used as well, and is used by providers (e.g. Bloomberg) to quote ATM swaptions normal volatilities (vs Black volatilties). $\endgroup$ – JejeBelfort Oct 10 '17 at 12:21
  • $\begingroup$ Hagan kindly uploaded the original SABR paper to researchgate.net/publication/235622441_Managing_Smile_Risk $\endgroup$ – Dimitri Vulis 2 days ago

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