IDEAS home Printed from https://ideas.repec.org/a/taf/eurjfi/v14y2008i2p137-156.html
   My bibliography  Save this article

Pricing Parisians and barriers by hitting time simulation

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/13518470701705595
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/13518470701705595?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Deng, Jie & Qin, Zhongfeng, 2021. "On Parisian option pricing for uncertain currency model," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    3. 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.
    4. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Annabi, Amira & Breton, Michèle & François, Pascal, 2012. "Resolution of financial distress under Chapter 11," Journal of Economic Dynamics and Control, Elsevier, vol. 36(12), pages 1867-1887.
    3. Chang Shih-Chieh Bill & Lee Yen-Kuan, 2020. "Currency Uncertainty, Interest Guarantee, and Risk-Based Premiums in Life Insurance Guaranty Schemes," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 14(2), pages 1-30, July.
    4. Galai, Dan & Raviv, Alon & Wiener, Zvi, 2007. "Liquidation triggers and the valuation of equity and debt," Journal of Banking & Finance, Elsevier, vol. 31(12), pages 3604-3620, December.
    5. Maclachlan, Iain C, 2007. "An empirical study of corporate bond pricing with unobserved capital structure dynamics," MPRA Paper 28416, University Library of Munich, Germany.
    6. Huang, Fu-Wei & Chen, Shi & Lin, Jyh-Horng, 2022. "Free riding and insurer carbon-linked investment," Energy Economics, Elsevier, vol. 107(C).
    7. Reisz, Alexander S. & Perlich, Claudia, 2007. "A market-based framework for bankruptcy prediction," Journal of Financial Stability, Elsevier, vol. 3(2), pages 85-131, July.
    8. Dirk Broeders & An Chen & Birgit Koos, 2009. "An institutional evaluation of pension funds and life insurance companies," DNB Working Papers 227, Netherlands Central Bank, Research Department.
    9. Broeders, Dirk & Chen, An & Koos, Birgit, 2011. "A utility-based comparison of pension funds and life insurance companies under regulatory constraints," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 1-10, July.
    10. Moraux, Franck & Silaghi, Florina, 2014. "Inside debt renegotiation: Optimal debt reduction, timing, and the number of rounds," Journal of Corporate Finance, Elsevier, vol. 27(C), pages 269-295.
    11. Cheng, Chunli & Li, Jing, 2018. "Early default risk and surrender risk: Impacts on participating life insurance policies," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 30-43.
    12. Shi Chen & Jyh-Horng Lin & Wenyu Yao & Fu-Wei Huang, 2019. "CEO Overconfidence and Shadow-Banking Life Insurer Performance Under Government Purchases of Distressed Assets," Risks, MDPI, vol. 7(1), pages 1-25, March.
    13. 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.
    14. Lindset Snorre, 2008. "Risk-Based Pre-Funding of Guaranty Funds in Life Insurance," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 2(2), pages 1-10, March.
    15. Zbigniew Palmowski & José Luis Pérez & Budhi Arta Surya & Kazutoshi Yamazaki, 2020. "The Leland–Toft optimal capital structure model under Poisson observations," Finance and Stochastics, Springer, vol. 24(4), pages 1035-1082, October.
    16. Roman N. Makarov, 2016. "Modeling liquidation risk with occupation times," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(04), pages 1-11, December.
    17. Makarov, R. & Metzler, A. & Ni, Z., 2015. "Modelling default risk with occupation times," Finance Research Letters, Elsevier, vol. 13(C), pages 54-65.
    18. Bin Li & Qihe Tang & Lihe Wang & Xiaowen Zhou, 2014. "Liquidation risk in the presence of Chapters 7 and 11 of the US bankruptcy code," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 1(03), pages 1-19.
    19. Mao Hong & Wen Zhongkai, 2018. "Optimization of Price, Default Ratio and Capital under Regulatory Criterion of Maximizing Social Benefit," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 12(2), pages 1-15, July.
    20. Chen, An, 2008. "Loss analysis of a life insurance company applying discrete-time risk-minimizing hedging strategies," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1035-1049, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:eurjfi:v:14:y:2008:i:2:p:137-156. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/REJF20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.