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The short-time asymptotic behavior of option prices for a variety of modelswith jumps has received much attention in recent years. In the present work, anovel second-order approximation for ATM option prices under the CGMY L\'evymodel is derived, and then extended to a model with an additional independentBrownian component. Our results shed light on the connection between both thevolatility of the continuous component and the jump parameters and the behaviorof ATM option prices near expiration. In case of an additional Browniancomponent, the second-order term, in time-t, is of the form $ d_{2}t^{(3-Y)/2}$, with the coefficient $d_{2}$ depending only on the overall jumpintensity parameter C and the tail-heaviness parameter Y. This extends theknown result that the leading term is $(\sigma/\sqrt{2\pi})t^{1/2}$, where$\sigma$ is the volatility of the continuous component. In contrast, under apure-jump CGMY model, the dependence on the two parameters C and Y is alreadyreflected in the leading term, which is of the form $d_{1} t^{1/Y}$.Information on the relative frequency of negative and positive jumps appearsonly in the second-order term, which is shown to be of the form $d_{2} t$ andwhose order of decay turns out to be independent of Y. The third-orderasymptotic behavior of the option prices as well as the asymptotic behavior ofthe corresponding Black-Scholes implied volatilities are also addressed. Ournumerical results show that in most cases the second-order term significantlyoutperform the first-order approximation.

High-order short-time expansions for ATM option prices under the CGMY model