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 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 \phi (x){\bf 1}_{x   z} for smooth functions \phi 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 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 \phi (x){\bf 1}_{x  \geq{ z} for smooth functions \phi and z>0.