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Pricing Parisians and barriers by hitting time simulation

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  • J. H. M. Anderluh

Abstract

Parisian options are not exchange traded, but there are various applications of Parisian optionality in the fields of real option theory, convertible bond valuation and credit risk. Especially the valuation of consecutive Parisian options is complicated and there exist no explicit formulas for these contracts. So far valuation can be done by numerically inverting Laplace transforms or by PDE methods. This paper develops a Monte Carlo method by exploiting the Markovian nature of the underlying value process. As a result, the Parisian option value can be written as an expression that can be solved by Monte Carlo integration, where the Parisian times are the random variables that need to be simulated. The Parisian times cannot be simulated directly as there exists no explicit distribution function. Therefore, these times are approximated by the simulation of hitting times in a special way. The quality of this approximation can be controlled and is a trade-off between accuracy and computation time.

Suggested Citation

  • J. H. M. Anderluh, 2008. "Pricing Parisians and barriers by hitting time simulation," The European Journal of Finance, Taylor & Francis Journals, vol. 14(2), pages 137-156.
    • Handle: RePEc:taf:eurjfi:v:14:y:2008:i:2:p:137-156
    DOI: 10.1080/13518470701705595
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    References listed on IDEAS

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    1. Franck Moraux, 2002. "Valuing corporate liabilities when the default threshold is not an absorbing barrier," Post-Print halshs-00077168, HAL.
    2. 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.
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    Cited by:

    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. 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.
    3. Deng, Jie & Qin, Zhongfeng, 2021. "On Parisian option pricing for uncertain currency model," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    4. An Chen & Markus Pelger & Klaus Sandmann, 2013. "New performance-vested stock option schemes," Applied Financial Economics, Taylor & Francis Journals, vol. 23(8), pages 709-727, April.

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