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Pricing Parisian and Parasian options analytically

Author

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  • Zhu, Song-Ping
  • Chen, Wen-Ting

Abstract

In this paper, two analytic solutions for the valuation of European-style Parisian and Parasian options under the Black–Scholes framework are, respectively, presented. A key feature of our solution procedure is the reduction of a three-dimensional problem to a two-dimensional problem through a coordinate transform designed to combine the two time derivatives into one. Compared with some previous analytical solutions, which still require a numerical inversion of Laplace transform, our solutions, written in terms of double integral for the case of Parisian options but multiple integrals for the case of Parasian options, are both of explicit form; numerical evaluation of these integrals is straightforward. Numerical examples are also provided to demonstrate the correctness of our newly derived analytical solutions from the numerical point of view, through comparing the results obtained from our solutions and those obtained from adopting other standard finite difference approaches.

Suggested Citation

  • Zhu, Song-Ping & Chen, Wen-Ting, 2013. "Pricing Parisian and Parasian options analytically," Journal of Economic Dynamics and Control, Elsevier, vol. 37(4), pages 875-896.
    • Handle: RePEc:eee:dyncon:v:37:y:2013:i:4:p:875-896
    DOI: 10.1016/j.jedc.2012.12.005
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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. 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.
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    Citations

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    Cited by:

    1. 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.
    2. Song-Ping Zhu & Nhat-Tan Le & Wen-Ting Chen & Xiaoping Lu, 2015. "Pricing Parisian down-and-in options," Papers 1511.01564, arXiv.org.
    3. Gongqiu Zhang & Lingfei Li, 2021. "A General Approach for Parisian Stopping Times under Markov Processes," Papers 2107.06605, arXiv.org.
    4. Le, Nhat-Tan & Dang, Duy-Minh, 2017. "Pricing American-style Parisian down-and-out call options," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 330-347.
    5. Yangyang Zhuang & Pan Tang, 2023. "Pricing of American Parisian option as executive option based on the least‐squares Monte Carlo approach," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(10), pages 1469-1496, October.

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    More about this item

    Keywords

    Parisian options; Parasian options; Analytical solution; Laplace transform;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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