We consider a stochastic volatility model with L\'evy jumps for a log-return
process $Z = (Z_t)_{t\ge 0}$ of the form $Z = U+X$, where $U = (U_t)_{t\ge 0}$
is a classical stochastic volatility process and $X = (X_t)_{t\ge 0}$ is an
independent L\'evy process with absolutely continuous L\'evy measure $\nu$.
Small-time expansions, of arbitrary polynomial order in time $t$, are obtained
for the tails $\bbp(Z_t \ge z)$, $z >0$, 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 de