Hi all,should calendar spread no-arbitrage check hold for swaption vol surfaces?To be specific, should increasing option maturity for underlying constant maturity swaps, corresponds to increasing option premium?Thanks.

Can you be more specific? Do you mean "increasing option expiry"? And then, do you mean that the shape/slope of a swaption tail? Or do you mean the shape/slope of the early expiry volatility profile into a fixed expiry swap (think midcurve swaptions).Either way, the answer is no, the option premium is generally not an increasing function in either case. How do you think of this as an arbitrage? BTW, there is something very screwed up about the swaption market in general in the light of such consideration. The problem is the annuity factor of those instruments. There is a ton of 'rate curve' baked into these instruments. It makes it very difficult to think cleanly about volatility in either direction of the swaption grid. Ideally you would only want to ever reason in terms of single look CMS options. Alas, that product depends on the swaption skew and the swaption is a bit dysfunctinal concept (which moreover also bakes in a ton of 'rate curve', although this isn't the only problem...).