How is mean reversion implied by different valuations of Bermudan swaptions?

Question

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?

Answer 1

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 .