Saturday, April 4, 2015

stochastic volatility - 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?




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