# SABR Calibration

I need to generate the Volatility Surface of call options on S&P500 index, my dataset contains implied volatilities regarding various expiration dates for various strike prices.

My doubt is, given beta in advance, in order to get a surface should I recalibrate the model parameters (alfa,rho,nu) for every different exipiration date or I have to run the LSQ non linear between the matrix containing the market volatilities and the volatilities by sabr all togheter? (So my surface will be based on a single set of parameters and not one for each maturity)

Thanks for the help

You are observing the same underlying $$S_t$$, therefore it has to be one set of parameters for all maturities. You could add a term structure to the parameters , however , since you are using SABR, I assume you use Hagan expansion to generate the implied vols, and for this approximation, the parameters must be constant.