Hi All,I would like to know the inference of the SABR parameters. For example:Beta: The BS model assumes S to follow lognormal distribution, but in reality we don't observe stock prices to follow normal distribution rather to follow a distribution which has fat tails. because of fat tails, smile comes into picture in the market. and the SABR beta captures this smile. whereas the BS assumes the smile to be flat.Similarly i would like to know the idea about rho, alpha.I do know that rho captures the skewness of the curve. But could somebody please help me in connecting this skewness to black scholes or real market just like done above for beta.Regards...

Well, the whole point of SABR is to capture the smile and beta is not the only one to be involved.Beta enables to move from lognormal to normal distributions (if you assume beta in [0,1], which is not always the case). Beta's role is actually not trivial, it controls the backbone of the smile.Sigma captures the overall level of the slope (kind of sigma in BS)Rho captures the skewness/slope of the smile (not possible in BS, you have to consider shifted BS)Alpha captures the convexity (volatility of volatility).Pierre-Yves and I have written a paper on the subject where we show the impact of each parameter: nothing fancy but it helps in getting a clear picture of SABR parameters.