Nothing Special   »   [go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v305y2017icp330-347.html
   My bibliography  Save this article

Pricing American-style Parisian down-and-out call options

Author

Listed:
  • Le, Nhat-Tan
  • Dang, Duy-Minh
Abstract
We propose an integral equation approach for pricing American-style Parisian down-and-out call options under the Black–Scholes framework. For this type of options, the knock-out feature is activated only if the underlying asset price continuously remains below a pre-determined barrier for a sufficiently long period of time. As such, the corresponding pricing problem becomes a three-dimensional (3-D) free boundary problem, instead of a two-dimensional (2-D) one as is the case of “one-touch” barrier options, and this poses a computational challenge. In our approach , we first reduce the 3-D problem to a 2-D one, and then, by applying the Fourier sine transform to the resulting 2-D problem, we can derive a pair of coupled integral equations governing the option price at any given time in terms of (i) the option price at the barrier and (ii) the optimal exercise boundary at that time. This pair of coupled integral equations can be solved using the Newton–Raphson iterative procedure, after which, the option price, the optimal exercise boundary, and the hedging parameters can be obtained in a straightforward manner. A complexity analysis of the method, together with numerical results, show that the proposed approach is robust and significantly more efficient than existing uniform finite difference methods with Crank–Nicolson timestepping, especially in dealing with spot prices near the barrier. Numerical results are also examined in order to provide new insight into several interesting properties of the option price and the optimal exercise boundary.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:305:y:2017:i:c:p:330-347
    DOI: 10.1016/j.amc.2017.02.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300317301194
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2017.02.015?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. Carl Chiarella & Andrew Ziogas, 2009. "American Call Options Under Jump-Diffusion Processes - A Fourier Transform Approach," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(1), pages 37-79.
    3. Marc Chesney & Laurent Gauthier, 2006. "American Parisian options," Finance and Stochastics, Springer, vol. 10(4), pages 475-506, December.
    4. Min Dai & Yue Kuen Kwok, 2004. "Knock‐in American options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 24(2), pages 179-192, February.
    5. Kim, In Joon, 1990. "The Analytic Valuation of American Options," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 547-572.
    6. Carl Chiarella & Adam Kucera & Andrew Ziogas, 2004. "A Survey of the Integral Representation of American Option Prices," Research Paper Series 118, Quantitative Finance Research Centre, University of Technology, Sydney.
    7. 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.
    8. Gerald H. L. Cheang & Carl Chiarella & Andrew Ziogas, 2013. "The representation of American options prices under stochastic volatility and jump-diffusion dynamics," Quantitative Finance, Taylor & Francis Journals, vol. 13(2), pages 241-253, January.
    9. 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.
    10. 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.
    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. Guo, Peidong & Zhang, Jizhou & Wang, Qian, 2020. "Path-dependent game options with Asian features," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    2. Klymak, Margaryta, 2023. "The trade effects of information provision about forced and child labor," World Development, Elsevier, vol. 167(C).
    3. Stiglitz, Joseph E., 2018. "Trump and Globalization," Journal of Policy Modeling, Elsevier, vol. 40(3), pages 515-528.
    4. Zaevski, Tsvetelin S., 2020. "Discounted perpetual game call options," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).

    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. Song-Ping Zhu & Nhat-Tan Le & Wen-Ting Chen & Xiaoping Lu, 2015. "Pricing Parisian down-and-in options," Papers 1511.01564, arXiv.org.
    2. 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.
    3. 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.
    4. Gongqiu Zhang & Lingfei Li, 2021. "A General Approach for Parisian Stopping Times under Markov Processes," Papers 2107.06605, arXiv.org.
    5. Hongzhong Zhang, 2018. "Stochastic Drawdowns," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 10078, August.
    6. Gorno, Leandro & Iachan, Felipe S., 2020. "Competitive real options under private information," Journal of Economic Theory, Elsevier, vol. 185(C).
    7. Pierangelo Ciurlia & Ilir Roko, 2005. "Valuation of American Continuous-Installment Options," Computational Economics, Springer;Society for Computational Economics, vol. 25(1), pages 143-165, February.
    8. Carl Chiarella & Andrew Ziogas, 2009. "American Call Options Under Jump-Diffusion Processes - A Fourier Transform Approach," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(1), pages 37-79.
    9. 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.
    10. Jonathan Ziveyi, 2011. "The Evaluation of Early Exercise Exotic Options," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 12, July-Dece.
    11. Chiarella, Carl & Ziogas, Andrew, 2005. "Evaluation of American strangles," Journal of Economic Dynamics and Control, Elsevier, vol. 29(1-2), pages 31-62, January.
    12. Xu Guo & Yutian Li, 2016. "Valuation of American options under the CGMY model," Quantitative Finance, Taylor & Francis Journals, vol. 16(10), pages 1529-1539, October.
    13. Ma, Jingtang & Yang, Wensheng & Cui, Zhenyu, 2021. "CTMC integral equation method for American options under stochastic local volatility models," Journal of Economic Dynamics and Control, Elsevier, vol. 128(C).
    14. Song-Ping Zhu & Xin-Jiang He & XiaoPing Lu, 2018. "A new integral equation formulation for American put options," Quantitative Finance, Taylor & Francis Journals, vol. 18(3), pages 483-490, March.
    15. Boda Kang & Christina Nikitopoulos Sklibosios & Erik Schlogl & Blessing Taruvinga, 2019. "The Impact of Jumps on American Option Pricing: The S&P 100 Options Case," Research Paper Series 397, Quantitative Finance Research Centre, University of Technology, Sydney.
    16. Han, Heejae & Jeon, Junkee & Kang, Myungjoo, 2016. "Closed form valuation of American chained knock-in options," Finance Research Letters, Elsevier, vol. 17(C), pages 176-185.
    17. 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.
    18. Rachel Kuske & Joseph Keller, 1998. "Optimal exercise boundary for an American put option," Applied Mathematical Finance, Taylor & Francis Journals, vol. 5(2), pages 107-116.
    19. João Nunes, 2011. "American options and callable bonds under stochastic interest rates and endogenous bankruptcy," Review of Derivatives Research, Springer, vol. 14(3), pages 283-332, October.
    20. 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.

    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:eee:apmaco:v:305:y:2017:i:c:p:330-347. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.