Some time back I did some work looking at getting a reasonable value for beta using historical swap rates. I found that beta was very different for different maturities, but I also found that it was different (substantially) when the period over which the maturities are analysed was increased from say 3 to 5 to 7 years. Why then do people tend to use a single value of beta (o.5 = cev is common)? Ispart of the reason because if everyone uses the same number in the market place, then we all agree? Your comments would be appreciated.

Not my market, but here is what I suspect. Thereare two ways to use the SABR process/formula. First,as simply a convenient interpolating formula for a smileat a fixed maturity. In that case, it's simply like fittingsome other nice function, say a quadratic, to a smile. Fix beta to some value if that is convenient. No problem -- it'sjust an interpolation.The second way is when people actually take the process seriouslyas a data generating process. That's what you did. Of course,you find the process is rejected. *All* time-homogenous dynamical models in finance will be rejected by a statistical test on real data. Whetheror not the process is still useful to you depends on your application.

Hi,Alan is absolutely correct. You can fit the market smile for any given beta value. Of course this leads to different vol-of-vol and correlation values.So if you just want to fit the smile, then make any choice of beta and select the vol-of-vol, correlation parameter and instantaneous vol (or ATMF vol) parameters that fit that smile.However, your delta hedging will be more accurate if your model resembles better the "real world". In that case, it makes a lot of difference to choose the correct value for beta. Therefore, if you think of capturing that extra volatility sold by delta hedging, then the correct model dynamics is essential.Cheers,