  In this article, we consider a Markov process X, starting from x and solving
a stochastic differential equation, which is driven by a Brownian motion and an
independent pure jump component exhibiting state-dependent jump intensity and
infinite jump activity. A second order expansion is derived for the tail
probability P[X(t)>x+y] in small time t, for y>0. As an application of this
expansion and a suitable change of the underlying probability measure, a second
order expansion, near expiration, for out-of-the-money European call option
prices is obtained when the underlying stock price is modeled as the
exponential of the jump-diffusion process X under the risk-neutral probability
measure.

Probability;Mathematical Finance