SABR model with extra param controlling the volofvol smile

doublebarrier2000 · July 22nd, 2010, 11:08 am

HiI am using pre-calibrated SABR parameters to compute Black Swaption vols for certain expiry/tenor pairs at various strikes in the usual way, however, an extra parameter is present (lets call it VS). VS is described as controlling how fast the volofvol (nu) parameter decays as the strike moves away from the fwd.I am trying to backwards-engineer the actual maths, however, it is a slow process.For example, for EUR swaptions, VS is set to 0.001 but for EUR caps/floors it is set to 0.01.Is anyone aware of any documentation regarding this tweaked SABR approach?

doublebarrier2000 · July 28th, 2010, 9:30 pm

you will be glad to know that I have solved my problem.Given the SABR model, Nu changes by strike in this way:Nu' = Nu * (min(F,K)/max(F,K))^b3 whereF is the forwardK is the Cap/Floor/Swaption strikeb3 is the VS parameter andNu is the volofvol SABR parameter

Soorma · August 5th, 2010, 2:29 pm

I dont have much idea about swaptions but i assume the vol of vol increases when time to expiration decreases just because there is a jump risk for short term options. So i did not understand what decay are you talking about . Vol of vol may come down when the atm vol increases . Also would this make you use different vol of vol for different strikes on the same maturity/tenor?