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

José E. Figueroa-López and Yankeng Luo

Stochastic Processes and their Applications, 2018, vol. 128, issue 12, 4207-4245

Abstract: In this article, we consider a Markov process {Xt}t⩾0, 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 P[Xt⩾x+y] in small time t, where x is the initial value of the process and 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 {Xt}t⩾0 under the risk-neutral probability measure.

Keywords: Short-time asymptotics; Local jump–diffusion Markov models; Stochastic differential equations with jumps; Option pricing (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304414918300164
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:128:y:2018:i:12:p:4207-4245

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spa.2018.02.001

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().