IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-00776703.html
   My bibliography  Save this paper

Pricing Parisian options using Laplace transforms

Author

Listed:
  • Céline Labart

    (MATHFI - Financial mathematics - Inria Paris-Rocquencourt - Inria - Institut National de Recherche en Informatique et en Automatique - ENPC - École des Ponts ParisTech - UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12, CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique)

  • Jérôme Lelong

    (MATHFI - Financial mathematics - Inria Paris-Rocquencourt - Inria - Institut National de Recherche en Informatique et en Automatique - ENPC - École des Ponts ParisTech - UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12, CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École des Ponts ParisTech)

Abstract

In this work, we propose to price Parisian options using Laplace transforms. Not only do we compute the Laplace transforms of all the different Parisian options, but we also explain how to invert them numerically. We prove the accuracy of the numerical inversion.

Suggested Citation

  • Céline Labart & Jérôme Lelong, 2009. "Pricing Parisian options using Laplace transforms," Post-Print hal-00776703, HAL.
    • Handle: RePEc:hal:journl:hal-00776703
    Note: View the original document on HAL open archive server: https://hal.science/hal-00776703
    as

    Download full text from publisher

    File URL: https://hal.science/hal-00776703/document
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Joseph Abate & Ward Whitt, 1995. "Numerical Inversion of Laplace Transforms of Probability Distributions," INFORMS Journal on Computing, INFORMS, vol. 7(1), pages 36-43, February.
    2. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    3. 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.
    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. 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.
    2. Angelos Dassios & Junyi Zhang, 2020. "Parisian Time of Reflected Brownian Motion with Drift on Rays and Its Application in Banking," Risks, MDPI, vol. 8(4), pages 1-14, December.
    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. 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.
    5. Angelos Dassios & Shanle Wu, 2010. "Perturbed Brownian motion and its application to Parisian option pricing," Finance and Stochastics, Springer, vol. 14(3), pages 473-494, September.
    6. 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.

    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. 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.
    2. Dell'Era Mario, M.D., 2008. "Pricing of the European Options by Spectral Theory," MPRA Paper 17429, University Library of Munich, Germany.
    3. Chenxu Li, 2016. "Bessel Processes, Stochastic Volatility, And Timer Options," Mathematical Finance, Wiley Blackwell, vol. 26(1), pages 122-148, January.
    4. Jos� Carlos Dias & João Pedro Vidal Nunes & João Pedro Ruas, 2015. "Pricing and static hedging of European-style double barrier options under the jump to default extended CEV model," Quantitative Finance, Taylor & Francis Journals, vol. 15(12), pages 1995-2010, December.
    5. 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.
    6. 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.
    7. Marc N. Atlan & Hélyette Geman & Marc Yor, 2006. "Options on Hedge Funds under the High Water Mark Rule," Working Papers hal-00012382, HAL.
    8. Dell'Era Mario, M.D., 2008. "Pricing of Double Barrier Options by Spectral Theory," MPRA Paper 17502, University Library of Munich, Germany.
    9. 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.
    10. 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).
    11. Deng, Jie & Qin, Zhongfeng, 2021. "On Parisian option pricing for uncertain currency model," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    12. 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.
    13. Dmitry Davydov & Vadim Linetsky, 2003. "Pricing Options on Scalar Diffusions: An Eigenfunction Expansion Approach," Operations Research, INFORMS, vol. 51(2), pages 185-209, April.
    14. Dmitry Davydov & Vadim Linetsky, 2001. "Pricing and Hedging Path-Dependent Options Under the CEV Process," Management Science, INFORMS, vol. 47(7), pages 949-965, July.
    15. Hardy Hulley, 2009. "Strict Local Martingales in Continuous Financial Market Models," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 19, July-Dece.
    16. Hardy Hulley, 2009. "Strict Local Martingales in Continuous Financial Market Models," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2009.
    17. Ben Abdallah, Skander & Lasserre, Pierre, 2016. "Asset retirement with infinitely repeated alternative replacements: Harvest age and species choice in forestry," Journal of Economic Dynamics and Control, Elsevier, vol. 70(C), pages 144-164.
    18. Kau, James B. & Keenan, Donald C., 1999. "Patterns of rational default," Regional Science and Urban Economics, Elsevier, vol. 29(6), pages 765-785, November.
    19. Carol Alexandra & Leonardo M. Nogueira, 2005. "Optimal Hedging and Scale Inavriance: A Taxonomy of Option Pricing Models," ICMA Centre Discussion Papers in Finance icma-dp2005-10, Henley Business School, University of Reading, revised Nov 2005.
    20. William R. Morgan, 2023. "Finance Must Be Defended: Cybernetics, Neoliberalism and Environmental, Social, and Governance (ESG)," Sustainability, MDPI, vol. 15(4), pages 1-21, February.

    More about this item

    Statistics

    Access and download statistics

    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:hal:journl:hal-00776703. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.