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

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  • Jos'e E. Figueroa-L'opez
  • Yankeng Luo

Abstract

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.

Suggested Citation

  • Jos'e E. Figueroa-L'opez & Yankeng Luo, 2015. "Small-time expansions for state-dependent local jump-diffusion models with infinite jump activity," Papers 1505.04459, arXiv.org, revised Dec 2015.
    • Handle: RePEc:arx:papers:1505.04459
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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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    5. 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.
    6. Paul Glasserman & S. G. Kou, 2003. "The Term Structure of Simple Forward Rates with Jump Risk," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 383-410, July.
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