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Occupation times of Lévy-driven Ornstein–Uhlenbeck processes with two-sided exponential jumps and applications

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  • Zhou, Jiang
  • Wu, Lan
  • Bai, Yang

Abstract

For an Ornstein–Uhlenbeck process driven by a double exponential jump diffusion process, we obtain formulas for the joint Laplace transform of it and its occupation times. The approach used is new and can be extended to investigate the occupation times of an Ornstein–Uhlenbeck process driven by a more general Lévy process. Besides, some applications to price occupation–time options are presented.

Suggested Citation

  • Zhou, Jiang & Wu, Lan & Bai, Yang, 2017. "Occupation times of Lévy-driven Ornstein–Uhlenbeck processes with two-sided exponential jumps and applications," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 80-90.
    • Handle: RePEc:eee:stapro:v:125:y:2017:i:c:p:80-90
    DOI: 10.1016/j.spl.2017.01.021
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    References listed on IDEAS

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    1. Giuseppe Campolieti & Roman N. Makarov & Karl Wouterloot, 2013. "Pricing Step Options under the CEV and other Solvable Diffusion Models," Papers 1302.3771, arXiv.org.
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    4. Alexander Novikov & R. E. Melchers & E. Shinjikashvili & N. Kordzakhia, 2003. "First Passage Time of Filtered Poisson Process with Exponential Shape Function," Research Paper Series 109, Quantitative Finance Research Centre, University of Technology, Sydney.
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    7. Ning Cai & Nan Chen & Xiangwei Wan, 2010. "Occupation Times of Jump-Diffusion Processes with Double Exponential Jumps and the Pricing of Options," Mathematics of Operations Research, INFORMS, vol. 35(2), pages 412-437, May.
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