Small-time expansions for state-dependent local jump–diffusion models with infinite jump activity

In this article, we consider a Markov process [Formula presented], which solves a stochastic differential equation driven by a Brownian motion and an independent pure jump component exhibiting both state-dependent jump intensity and infinite jump activity. A second order expansion is derived for the tail probability [Formula presented] in small time [Formula presented], where [Formula presented] is the initial value of the process and [Formula presented]. 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 [Formula presented] under the risk-neutral probability measure.