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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 !

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I would say that SABR is overkill for inflation options, because due to the scarcity of prices for inflation options, there isn't enough information to fit all the SABR parameters. It is probably better to adopt a simple Normalized model of inflation rates, which you can calibrate by looking at historical normalized volatility. This will also take care of your negative rates problem.

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