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Pricing Parisian-Style Options With A Lattice Method

Author

Listed:
  • MARCO AVELLANEDA

    (Department of Mathematics, Courant Institute of Mathematical Sciences, New York University, 251 Mercer St, New York, NY 10012, USA and Morgan Stanley, New York, USA)

  • LIXIN WU

    (Department of Mathematics, HKUST, Clear Water Bay, Kowloon, Hong Kong, China)

Abstract

A Parisian-style barrier option expires if the price of the underlying asset remains above or below some level(s) continuously over a specified period of time (the "window"). A trinomial-lattice scheme is developed for calculating the price and the sensitivities of such options. Monte–Carlo simulation of hedging events using the resulting deltas show errors which are of the same magnitude as for hedging vanilla options, confirming the validity of proposed scheme. We use these results to price callable and convertible bonds with this "window" feature.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijtafx:v:02:y:1999:i:01:n:s0219024999000029
    DOI: 10.1142/S0219024999000029
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    Citations

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    Cited by:

    1. Marc Chesney & Laurent Gauthier, 2006. "American Parisian options," Finance and Stochastics, Springer, vol. 10(4), pages 475-506, December.
    2. Chen, An & Suchanecki, Michael, 2006. "Default Risk, Bankruptcy Procedures and the Market Value of Life Insurance Liabilities," Bonn Econ Discussion Papers 8/2006, University of Bonn, Bonn Graduate School of Economics (BGSE).
    3. 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.
    4. Chen, An & Suchanecki, Michael, 2007. "Default risk, bankruptcy procedures and the market value of life insurance liabilities," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 231-255, March.
    5. Deng, Jie & Qin, Zhongfeng, 2021. "On Parisian option pricing for uncertain currency model," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    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.
    7. Dassios, Angelos & Zhang, You You, 2016. "The joint distribution of Parisian and hitting times of the Brownian motion with application to Parisian option pricing," LSE Research Online Documents on Economics 64959, London School of Economics and Political Science, LSE Library.
    8. Céline Labart & Jérôme Lelong, 2009. "Pricing Parisian options using Laplace transforms," Post-Print hal-00776703, HAL.
    9. Broeders, Dirk & Chen, An, 2010. "Pension regulation and the market value of pension liabilities: A contingent claims analysis using Parisian options," Journal of Banking & Finance, Elsevier, vol. 34(6), pages 1201-1214, June.
    10. Marcellino Gaudenzi & Antonino Zanette, 2017. "Fast binomial procedures for pricing Parisian/ParAsian options," Computational Management Science, Springer, vol. 14(3), pages 313-331, July.
    11. Yuh-Dauh Lyuu & Cheng-Wei Wu, 2010. "An improved combinatorial approach for pricing Parisian options," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 33(1), pages 49-61, May.
    12. Gongqiu Zhang & Lingfei Li, 2021. "A General Approach for Parisian Stopping Times under Markov Processes," Papers 2107.06605, arXiv.org.
    13. Nicholas Sharp & Paul Johnson & David Newton & Peter Duck, 2009. "A New Prepayment Model (with Default): An Occupation-time Derivative Approach," The Journal of Real Estate Finance and Economics, Springer, vol. 39(2), pages 118-145, August.
    14. Angelos Dassios & You You Zhang, 2016. "The joint distribution of Parisian and hitting times of Brownian motion with application to Parisian option pricing," Finance and Stochastics, Springer, vol. 20(3), pages 773-804, July.
    15. 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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