Hi all,I am trying to calibrate SABR for Cap floor and swaptions.For Beta Initial guess as per G.West paper Log-log plot can be used to derive beta value using historical data.But i use a method where in SABR Expansion i restrict corelation and volvol to Zero.I think it becomes local vol model there. Using remaining terms i get guess of Beta.Still not sure that both ways are similar for initial guess of beta & 2nd way has some inaccuracies involved.Please advise on 2nd way whether it is accurate way to guess Beta.Regards,Qmatringale

Well, I think you are right when you say setting correl and volvol to zero you get a local vol model with alpha and beta. If your estimate beta from this is theoretically ok - depends on how you do it. For e.g. if you use the current smile to fit alpha and beta (if it is possible at all), that would not be correct, but if you use this "local vol" model to fit beta using only atm vol, that should be correct (and this is what essentially the log-log plot method do).

Thanks Prodipto,i use deduced LV ( so called CEV) for beta and retain same initial vol in CEV & SABR.Then calibrate correlation and volvol . But recently while benchmarking with bloomberg realised that they dont use corelation in VCUB-SABR. I mean they use correlation=0 across all time points. Any info/thoughts on Bloomberg aspect will be helpful.

Hi,I realised that there are to ways for Beta calibration across time maturities1.Calibrate beta using either Log-log plot or LV, on each and every time point.Thus we might have different values of all four parameters in SABR calibration on each and every time point.2.But some brokers calibrate Beta and retain same value of beta across all tenor points and then change remaining three parameters for matching skew on each and every tenor point.First way is quite labourious and slows down whole calibration.For second way i am not quite sure which tenor points Beta guess is used across all tenor points and whether approximations involved( same beta for all tenor points) are more beneficial ( lesser time required for calibration-less data involved)than inaccuracies as compared to first way?Need views on this.

well, I think both methods have merits, the point is what is the purpose of calibration. If it is for a market making purpose, i would say I would rather have my beta marked at some "reasonable" fixed values and calibrate other parameters, and hope to choose the beta such that my delta hedges are most stable. And my efforts will also depend on what is my major book-level exposure. Intuitively, shorter the maturity, more it should behave like log-normal and higher the tenor more chance of "normal" behavior. using a CEV method and/ or log-log plot is good if you have some kind of "relative value" trades in mind and want to see how atm vols moves w.r.t the underlying (CEV-> how market currently price the relationship, log-log -> how it has been in the past). Also I would prefer a "real" calibration of beta more for short maturities (where the realized parameters matters for your PnL) than a long-dated one. The fact is whichever way you estimate beta, it will not be stable (like all other params!!). The point is do you really believe in the SABR dynamics totally, or (as I guess most folks would have this stance) just use it mostly for interpolating the vols