Before revision:  Small-time expansions, of arbitrary polynomial order, in time-t, are obtained for the tails \bbp(Z_{t}\geq z), z>0, and for the call-option prices \bbe(e^{z+Z_{t}}-1)_{+}, z\neq 0, assuming smoothness conditions on the L\'evy density {\PaleGrey  away from the origin and a small-time large deviation principle on U. Our approach allows for a unified treatment of general payoff functions of the form \varphi (x){\bf 1}_{xz} for smooth functions \varphi and z>0.
After revision:  Small-time expansions, of arbitrary polynomial order, in time-t, are obtained for the tails \bbp(Z_{t}\geq z), z>0, and for the call-option prices \bbe(e^{z+Z_{t}}-1)_{+}, z\neq 0, assuming smoothness conditions on the L\'evy density {\PaleGrey away from the origin and a small-time large deviation principle on U. Our approach allows for a unified treatment of general payoff functions of the form \varphi (x){\bf 1}_{xz} for smooth functions \phi and z>0.