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

José E. Figueroa-López*, Yankeng Luo

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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.

Original languageEnglish
Pages (from-to)4207-4245
Number of pages39
JournalStochastic Processes and their Applications
Issue number12
Publication statusPublished - Dec 2018
Externally publishedYes


  • Local jump–diffusion Markov models
  • Option pricing
  • Short-time asymptotics
  • Stochastic differential equations with jumps


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