I have a S&P500 implied vol surface backed out from vannila. I'm pricing 1 yr Arithmetic Asia Option (monthly average price, fixed strike). To get a good approximation, I'm using Turnbull (Edgeworth expansion). Which implied vol I should plug in that formula? I tried using the average implied vol of maturities from 1 months to 12 months with the same strike of Asian, the pricing results actually looks quite good. Is this just a coincident or it makes some sense?Do I need to have stochastic vol model for Asian options? I understand that local vol is no good since the forward smile dynamic is wrong (BTW, would this impact Asia a whole lot?)Any sight is appreciated. Thanks.Wondering