I am trying to apply SABR on EUR inflation caplets, with positive forward and negative strikes. Classical BS pricing is undefined, and so is SABR. I have read about the shifted SABR, which is supposed to accept negative strikes, but I was wondering whether anyone is aware of an existing implementation on Matlab for instance.
I have fitted the standard SABR parameters on positive strikes and modified some existing SABR code, adding the shift to the strike and the forward rate in the volatility equation. Now, I am feeding this modified volatility equation with my negative strikes and forward + the fitted SABR parameters, but nothing seems to have changed: it is still impossible to compute vols for negative strikes.
Do I have to feed the original strikes to the shifted model or the shifted strikes ? Do I have to shift the forward as well ? Is anyone aware of a better procedure for using the shifted SABR with negative rates?
Thanks a lot !