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Monte Carlo methods for pricing discrete Parisian options

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  • Carole Bernard
  • Phelim Boyle

Abstract

The paper develops an efficient Monte Carlo method to price discretely monitored Parisian options based on a control variate approach. The paper also modifies the Parisian option design by assuming the option is exercised when the barrier condition is met rather than at maturity. We obtain formulas for this new design when the underlying is continuously monitored and develop an efficient Monte Carlo method for the discrete case. Our method can also be used for the case of multiple barriers. We use numerical examples to illustrate the approach and reveal important features of the different types of options considered. Some performance-based executive stock options include different tranches of discretely monitored Parisian options and we illustrate this with a practical example.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:eurjfi:v:17:y:2011:i:3:p:169-196
    DOI: 10.1080/13518470903448473
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    References listed on IDEAS

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    1. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
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    6. Broadie, Mark & Detemple, Jerome, 1996. "American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods," The Review of Financial Studies, Society for Financial Studies, vol. 9(4), pages 1211-1250.
    7. Boyle, Phelim & Broadie, Mark & Glasserman, Paul, 1997. "Monte Carlo methods for security pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1267-1321, June.
    8. Jin-Chuan Duan & Evan Dudley & Geneviève Gauthier & Jean-Guy Simonato, 1999. "Pricing Discretely Monitored Barrier Options by a Markov Chain," CIRANO Working Papers 99s-15, CIRANO.
    9. Peter Carr & Vadim Linetsky, 2000. "The Valuation of Executive Stock Options in an Intensity-Based Framework," Review of Finance, European Finance Association, vol. 4(3), pages 211-230.
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    Cited by:

    1. Carole Bernard & Olivier Le Courtois, 2012. "Performance Regularity: A New Class of Executive Compensation Packages," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 19(4), pages 353-370, November.
    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. 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.
    4. 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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