Before revision:  In particular, a new type of transition phenomenon is uncovered in which the third order term exhibits two distinct asymptotic regimes depending on whether Y\in(1,3/2) or Y\in(3/2,2)  .
After revision:  In particular, a new type of transition phenomenon is uncovered in which the third order term exhibits two distinct asymptotic regimes depending on whether Y\in(1,3/2) or Y\in(3/2,2) . Unlike second order approximations, the expansions herein are shown to be remarkably accurate so that they can actually be used for calibrating some model parameters. For illustration, we calibrate the volatility \sigma of the Brownian component and the jump intensity C of the CGMY model to actual option prices .