Hello everybody,I am trying to use the SABR model on the cap market. I have two questions:1. According to Hagan's paper one can choose arbitrarily the beta parameter and find the alpha parameter thanks to the ATM vol. Which leaves only two parameters to calibrate...As cap volatilities are not consistents, I have built a caplet vols surface. By doing so, to find my caplet ATM vol, I have to do some kind of interpolation. This comes from the fact that the ATM strike for caps is a swap rate while the ATM strike for caplets is the forward rate, isn't it?My issue is the following one: I am trying to estimate my SABR alpha parameter with an interpolated ATM vol. As a matter of fact, my results will highly depend on the quality of my interpolation. What do you think about it? Is there another way to proceed?2. Still in Hagan's paper, an approximation of the black implied vol is given (formula 3.1a). How does he go from formula 2.17 to 3.1?Thanks.

Could you precise you data ?Which kind of data do you have ?Do you have (strike, volatility) or only ATM vol ?

I have strike & vol

The basic calibration is: beta by time serie calibration.rho and volvol and alpha are calibrated by fitting the smile.Least square error.

What if I only have an ATM implied vol swaption matrix (maturities and swap tenor). I have access to bloomberg but I assume bloomberg does not provide any implied vols for a given (example, 1y1y) swaption over different strikes?Any ideas how to get those data? Otherwise I dont see how I can fit the smile. Thanks.