Before revision: In the present work, a novel second-order approximation for ATM option prices is derived for a large class of exponential L\'evy models . Our method of proof is based on an integral representation of the option price involving the tail probability of the log-return process under the share measure and a suitable change of probability measure under which the pure-jump componentof the log-return process becomes a Y-stable process.
After revision: In the present work, a novel second-order approximation for ATM option prices is derived for a large class of exponential L\'evy models pure-jump componentof the log-return process becomes a Y-stable process.