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An analytical solution for the two-sided Parisian stopping time, its asymptotics and the pricing of Parisian options

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  • Dassios, Angelos
  • Lim, Jia Wei

Abstract

In this paper, we obtain a recursive formula for the density of the two-sided Parisian stopping time. This formula does not require any numerical inversion of Laplace transforms, and is similar to the formula obtained for the one-sided Parisian stopping time derived in Dassios and Lim [6]. However, when we study the tails of the two distributions, we find that the two-sided stopping time has an exponential tail, while the one-sided stop- ping time has a heavier tail. We derive an asymptotic result for the tail of the two-sided stopping time distribution and propose an alternative method of approximating the price of the two-sided Parisian option.

Suggested Citation

  • Dassios, Angelos & Lim, Jia Wei, 2017. "An analytical solution for the two-sided Parisian stopping time, its asymptotics and the pricing of Parisian options," LSE Research Online Documents on Economics 60154, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:60154
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    File URL: http://eprints.lse.ac.uk/60154/
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    References listed on IDEAS

    as
    1. Carole Bernard & Phelim Boyle, 2011. "Monte Carlo methods for pricing discrete Parisian options," The European Journal of Finance, Taylor & Francis Journals, vol. 17(3), pages 169-196.
    2. Dassios, Angelos & Lim, Jia Wei, 2013. "Parisian option pricing: a recursive solution for the density of the Parisian stopping time," LSE Research Online Documents on Economics 58985, London School of Economics and Political Science, LSE Library.
    3. J. Anderluh & J. Weide, 2009. "Double-sided Parisian option pricing," Finance and Stochastics, Springer, vol. 13(2), pages 205-238, April.
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    Cited by:

    1. Gongqiu Zhang & Lingfei Li, 2021. "A General Approach for Parisian Stopping Times under Markov Processes," Papers 2107.06605, arXiv.org.
    2. Sirovich, Roberta & Testa, Luisa, 2019. "On the first positive and negative excursion exceeding a given length," Statistics & Probability Letters, Elsevier, vol. 150(C), pages 137-145.
    3. 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.

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    More about this item

    Keywords

    Brownian excursion; double-sided Parisian options; tail asymptotics;
    All these keywords.

    JEL classification:

    • F3 - International Economics - - International Finance
    • G3 - Financial Economics - - Corporate Finance and Governance

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