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Parisian option pricing: a recursive solution for the density of the Parisian stopping time

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  • Dassios, Angelos
  • Lim, Jia Wei

Abstract

In this paper, we obtain the density function of the single barrier one-sided Parisian stopping time. The problem reduces to that of solving a Volterra integral equation of the first kind, where a recursive solution is consequently obtained. The advantage of this new method as compared to that in previous literature is that the recursions are easy to program as the resulting formula involves only a finite sum and does not require a numerical inversion of the Laplace transform. For long window periods, an explicit formula for the density of the stopping time can be obtained. For shorter window lengths, we derive a recursive equation from which numerical results are computed. From these results, we compute the prices of one-sided Parisian options.

Suggested Citation

  • 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.
    • Handle: RePEc:ehl:lserod:58985
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    References listed on IDEAS

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    1. Céline Labart & Jérôme Lelong, 2009. "Pricing Parisian options using Laplace transforms," Post-Print hal-00776703, HAL.
    2. Joseph Abate & Ward Whitt, 1995. "Numerical Inversion of Laplace Transforms of Probability Distributions," INFORMS Journal on Computing, INFORMS, vol. 7(1), pages 36-43, February.
    3. Céline Labart & Jérôme Lelong, 2009. "Pricing Double Barrier Parisian Options Using Laplace Transforms," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(01), pages 19-44.
    4. J. Anderluh & J. Weide, 2009. "Double-sided Parisian option pricing," Finance and Stochastics, Springer, vol. 13(2), pages 205-238, April.
    5. Marco Avellaneda & Lixin Wu, 1999. "Pricing Parisian-Style Options With A Lattice Method," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 2(01), pages 1-16.
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    Cited by:

    1. Angelos Dassios & Jia Wei Lim & Yan Qu, 2020. "Azéma martingales for Bessel and CIR processes and the pricing of Parisian zero‐coupon bonds," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1497-1526, October.
    2. 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.
    3. Dassios, Angelos & Lim, Jia Wei & Qu, Yan, 2020. "Azéma martingales for Bessel and CIR processes and the pricing of Parisian zero-coupon bonds," LSE Research Online Documents on Economics 101765, London School of Economics and Political Science, LSE Library.
    4. Gongqiu Zhang & Lingfei Li, 2021. "A General Approach for Parisian Stopping Times under Markov Processes," Papers 2107.06605, arXiv.org.
    5. Angelos Dassios & Jia Wei Lim, 2018. "An Efficient Algorithm for Simulating the Drawdown Stopping Time and the Running Maximum of a Brownian Motion," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 189-204, March.
    6. 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

    Parisian option; Brownian excursion; Volterra equation;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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