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Someone told me that mean reversion can be implied by the different valuations of bermudan swaptions when using different methods for volatility calibration. Does anyone know what this means?

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The question is so vague that it doesn't deserve an answer IMO. Define first mean reversion, the dynamics of your model and what vanillas you are using in your calibration portfolio. –  TheBridge Aug 9 '11 at 19:37
The model that is used is the Quadratic Gaussian Model (wilmott.com/messageview.cfm?catid=4&threadid=83920). But the answer should be independent of the model, no? It is more the concept that I don't understand, not the exact application to this specific model. –  Financial Economist Aug 10 '11 at 8:24
ok we have the model, now what it is mean-reversion mathematically speaking ? –  TheBridge Aug 11 '11 at 22:36
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1 Answer

Bermudan swaptions (often on interest rates) are typically valued with a model that incorporates mean-reversion parameters. This might be as naive as Black-Karasinski, but more often is somewhat more sophisticated, for example Generalized Vasicek.

Calibrating the model involves choosing model parameters that "best" fit the observed bermudan swaption prices. Since one of those parameters is a mean reversion term ($\mu$), after your fitting process you end up with a market-implied risk-neutral estimate of mean reversion rate $\mu$ within that model.

You will find that $\mu$'s magnitude will correlate highly with other measures of mean reversion (say from time series analysis), but that outside your original model framework $\mu$'s actual level is only qualitatively valuable .

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Brian B, thank you for your answer. This is pretty much what I had in mind. But, could you please tell me how different methods of volatility calibration can imply mean reversion? I suspect that it has to do with coterminal vs vfit vol calibration but not sure exactly how this could give me the mean reversion. –  Financial Economist Aug 14 '11 at 19:12
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