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

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  • Figueroa-López, José E.
  • Luo, Yankeng

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.

Suggested Citation

  • Figueroa-López, José E. & Luo, Yankeng, 2018. "Small-time expansions for state-dependent local jump–diffusion models with infinite jump activity," Stochastic Processes and their Applications, Elsevier, vol. 128(12), pages 4207-4245.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:12:p:4207-4245
    DOI: 10.1016/j.spa.2018.02.001
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    References listed on IDEAS

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    1. Yu, Jialin, 2007. "Closed-form likelihood approximation and estimation of jump-diffusions with an application to the realignment risk of the Chinese Yuan," Journal of Econometrics, Elsevier, vol. 141(2), pages 1245-1280, December.
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    3. Jos'e E. Figueroa-L'opez & Yankeng Luo & Cheng Ouyang, 2011. "Small-time expansions for local jump-diffusion models with infinite jump activity," Papers 1108.3386, arXiv.org, revised Jul 2014.
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