# SABR beta range

I am thinking of using SABR for non-rate underlyings (eg FX and equity underlyings).

Typically one finds the beta via a regression of historical implied vols vs forwards, since $$\ln(\textrm{atm vol}) = \ln(\alpha) - (1-\beta) \times \ln(\textrm{forward}).$$ However for FX and equity underlyings, it is not uncommon to find a resulting beta either negative or above 1.

My question : is the SABR model still valid for beta values outside the typical [0,1] range?

• Just because other values for $\beta$ don't represent a special case that we attached a label to doesn't mean they are not admissible. – LocalVolatility Mar 13 '17 at 17:40
• @LocalVolatility Is it necessarily the case that the SDEs that define SABR have the same kind of solution as the usual solution when $\beta$ is between 0 and 1? I don't know, but it would be relevant I would imagine. Either way, not a huge fan of using SABR for smile dynamics - it has a major inherent flaw in that the stochastic volatility does not have a mean reverting component. – FinanceGuyThatCantCode Apr 12 '17 at 20:19