Around 10 years ago, while reading the excellent paper of Etore and Gobet on stochastic Taylor expansions for the pricing of vanilla options with discrete (cash) dividends, I had the idea of a small improvement, by using a more precise proxy for the Taylor expansion. More recently, I applied the idea to approximate arithmetic Asian options prices by using the geometric Asian option price as a proxy (with some adjustments). This worked surprisingly well, and is competitive with the best implement
