A note on high-order short-time expansions for ATM option prices under the CGMY model

The short-time asymptotic behavior of option prices for a variety of models with jumps has received much attention in recent years. In the present work, a novel third-order approximation for ATM option prices under the CGMY L evy model is derived, and extended to a model with an additional independent Brownian component. Our results shed new light on the connection between both the volatility of the continuous component and the jump parameters and the behavior of ATM option prices near expiration. In particular, a new type of transition phenomenon is uncovered in which the third order term exhibits two district asymptotic regimes depending on whether 1 < Y < 3=2 or 3=2 < Y < 2.