I apologize if this is too basic, but I am struggling with the volatility implied by the swaption skew and local volatility...Take for example we're looking at a 5y10y 200 bps OTM payer and the current ATMF is at 2%. Let's say the implied volatility (on a bpvol basis) backed out from someone's bid price is 80 bp vols. Does this mean that the person buying this swaption believes that when the ATMF is at 2%+200bps = 4%, that the normalized volatility will be 80 bp vols?? If not, how do I transform this implied volatility to reflect where implied volatility will be if the ATMF is at 4%....????

phoenixOmega,for an ATMF it is correct to assume that x bp norm implied vol means you can expect x bp of vol over the life of an option.But when looking at skew...it tells you the implied vol of Fwd+200 when ATMF = Fwd (local vol...d(vol)/d(moneyness))...when the ATMF becomes equal to Fwd + 200...your local itself will change and the skew will be different again (determined by SABR beta)For details I would recommend reading original SABR paper (Hagan et. al.)