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Pricing of Parisian Options for a Jump-Diffusion Model with Two-Sided Jumps

Author

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  • Hansjörg Albrecher
  • Dominik Kortschak
  • Xiaowen Zhou

Abstract

Using the solution of one-sided exit problem, a procedure to price Parisian barrier options in a jump-diffusion model with two-sided exponential jumps is developed. By extending the method developed in Chesney, Jeanblanc-Picqu� and Yor (1997; Brownian excursions and Parisian barrier options, Advances in Applied Probability , 29(1), pp. 165--184) for the diffusion case to the more general set-up, we arrive at a numerical pricing algorithm that significantly outperforms Monte Carlo simulation for the prices of such products.

Suggested Citation

  • Hansjörg Albrecher & Dominik Kortschak & Xiaowen Zhou, 2012. "Pricing of Parisian Options for a Jump-Diffusion Model with Two-Sided Jumps," Applied Mathematical Finance, Taylor & Francis Journals, vol. 19(2), pages 97-129, July.
    • Handle: RePEc:taf:apmtfi:v:19:y:2012:i:2:p:97-129
    DOI: 10.1080/1350486X.2011.599976
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    Cited by:

    1. Markus Leippold & Nikola Vasiljević, 2020. "Option-Implied Intrahorizon Value at Risk," Management Science, INFORMS, vol. 66(1), pages 397-414, January.
    2. Irmina Czarna & Zbigniew Palmowski, 2014. "Dividend Problem with Parisian Delay for a Spectrally Negative Lévy Risk Process," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 239-256, April.
    3. Gongqiu Zhang & Lingfei Li, 2021. "A General Approach for Parisian Stopping Times under Markov Processes," Papers 2107.06605, arXiv.org.
    4. Gongqiu Zhang & Lingfei Li, 2023. "A general approach for Parisian stopping times under Markov processes," Finance and Stochastics, Springer, vol. 27(3), pages 769-829, July.
    5. Czarna, Irmina & Palmowski, Zbigniew, 2017. "Parisian quasi-stationary distributions for asymmetric Lévy processes," Statistics & Probability Letters, Elsevier, vol. 127(C), pages 75-84.

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