Before revision:  In the present work, a novel third-order approximation for close-to-the-money European option prices under the CGMY L\'{e}vy model is derived, and  extended to a model with an additional independent Brownian component.
After revision:  In the present work, a novel third-order approximation for close-to-the-money European option prices under an infinite-variation CGMY L\'{e}vy model is derived, and extended to a model with an additional independent Brownian component.