December 2nd, 2007, 5:55 pm
With SABR, you calibrate (sigma, alpha, beta, rho) using market quoted vols (whatever you have). Once you calibrate to those vols and fit the smile, than you have to believe each price/vol from the model is right, including implied vols that are not explicitly quoted.In some cases, you might have to extrapolate the smile for better calibration, but generally SABR calibrates well with few data points (that is one reason why it is popular for rates). The market gives you the smile and the price. What it does not give you are the hedges you need for a particular instrument. So SABR ensures that you can recover vol quotes and prices from the market and in addition gives you the right hedges (insofar as you believe the model is right.)