Let's consider the swaption ATM (normal) volatility dynamics when the forward moves (the backbone). In the SABR model (0<beta<1) the vol moves up when the forward moves up? What about the market? The objective is to calibrate the SABR beta to capture the market backbone dynamics hence optimizing the hedging for let's say normal market conditions. Recently for example the forwards went down (EUR) with ATM volatilities going up.

From past experience, you set beta at a fixed number and tweak from there..however ....

Yes. Just thinking about improving this slighlty. For example it would be interesting to identify the market behavior, under which conditions the backbone is correclty predicted by SABR, normal and lognormal market regimes etc.

you are referring to what is commonly known and done in practice as shadow hedging. i.e. completely ignore the SABR backbone and hedge what you believe is the right backbone. it is tricky to answer the question you are asking. that said it is going into the right direction, i.e. as opposed to what the great masters of ad hoc models of stochastic calculus here are trying to achieve you are pointing into the empirical direction. it is tricky to figure this out though. you would have to run historical regressions and a big backtesting exercise in order to figure this out. I think that the problem in finance is often one of small sample, in that if you make available to yourself all historical skew data you can possibly get, you might still find it tricky to conclude on what the best backbone dynamics is. hence a lot of (buy side) firms don't even bother.QuoteOriginally posted by: ZhuLiAnYes. Just thinking about improving this slighlty. For example it would be interesting to identify the market behavior, under which conditions the backbone is correclty predicted by SABR, normal and lognormal market regimes etc.

maybe a simple first step would be to work with simulated data... how does hedging performance change if you are a) delta and b) vega hedged when the "real model" has one set of value of rho / beta whereas you hedge with wrong values but such that the models agree on option pricealong lines of this paperhttp://papers.ssrn.com/sol3/papers.cfm?abstract_id=1031927

Exaclty. As a simple check I compared the stability of the lognornal vol vs. normal vol using recent historical data (forwards and swaption volatility) and the conclusion is that forwards have a normal dynamics.