# simple SABR model & negative strikes

My goal is to calibrate a simple SABR model.

I do have $$tenor$$, $$expiry$$, $$forward$$ and "market volatilities for strike spread" ranging from -150 to 150 bps.

I think the model can only be calibrated for strike spreads greater than 0.

Is this correct?

I believe this to be true because: $$\log (f/K)$$ is only defined if $$K \gt 0$$ assuming $$f \gt 0$$

excerpt from Hagan et al (2002) paper link

Yes, the paper you are referring only works for non-negative strikes. In fact, the Taylor expansion does not converge when $$f$$ and $$K$$ have different signs. Hagan's formula is a short-term asymptotic approximation, meaning that the calibration error will increase with maturities and tenors. As an exercise, this is the easiest way to calibrate the standard SABR model. First fix the $$\beta$$ parameter to control the backbone of the volatility surface ($$\beta=0$$ for normal vol and $$\beta=1$$ for lognormal vol) and then fit the $$\alpha$$, $$\rho$$ and $$\nu$$ parameters to match the ATM market volatilities. Note that the asymptotic approximation for the ATM implied volatility must be consistent with the choice of $$\beta$$.