Before revision: In the present work, a novel second-order approximation for ATM option prices under an exponential tempered stable model, a rich class of L\'evy processes with desirable features for financial modeling, is derived and, then, extended to a model with an additional independent Brownian component .
After revision: In the present work, a novel second-order approximation for ATM option prices under an exponential tempered stable model, a rich class of L\'evy models .