My understanding is that TurnballTurnbull & Wakeman derived an approximation formula for continous arithmetic Asian option using Edgeworth series by matching the first two moments.
However, in the book Mathematical Models of Financial Derivatives, after a few pages of proof on the approximation, it writes "Besides the Edgeworth expansion method, .... Turnbull and Wakeman (1991) ..."
So the idea of Edgeworth approximation didn't come from Turnbull and Wakeman and possibly somebody else?