IDEAS home Printed from https://ideas.repec.org/a/wsi/jecxxx/v26y2018i03ns0219024918500620.html
   My bibliography  Save this article

Mathematical Properties Of American Chooser Options

Author

Listed:
  • SHI QIU

    (School of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, UK)

  • SOVAN MITRA

    (University of Liverpool, Brownlow Hill, Liverpool, L69 7ZX, UK)

Abstract

The American chooser option is a relatively new compound option that has the characteristic of offering exceptional risk reduction for highly volatile assets. This has become particularly significant since the start of the global financial crisis. In this paper, we derive mathematical properties of American chooser options. We show that the two optimal stopping boundaries for American chooser options with finite horizon can be characterized as the unique solution pair to a system formed by two nonlinear integral equations, arising from the early exercise premium (EEP) representation. The proof of EEP representation is based on the method of change-of-variable formula with local time on curves. The key mathematical properties of American chooser options are proved, specifically smooth-fit, continuity of value function and continuity of free-boundary among others. We compare the performance of the American chooser option against the American strangle option. We also conduct numerical experiments to illustrate our results.

Suggested Citation

  • Shi Qiu & Sovan Mitra, 2018. "Mathematical Properties Of American Chooser Options," Journal of Enterprising Culture (JEC), World Scientific Publishing Co. Pte. Ltd., vol. 21(08), pages 1-30, December.
    • Handle: RePEc:wsi:jecxxx:v:26:y:2018:i:03:n:s0219024918500620
    DOI: 10.1142/S0219024918500620
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024918500620
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024918500620?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. Deng, S.J. & Oren, S.S., 2006. "Electricity derivatives and risk management," Energy, Elsevier, vol. 31(6), pages 940-953.
    2. Chiarella, Carl & Ziogas, Andrew, 2005. "Evaluation of American strangles," Journal of Economic Dynamics and Control, Elsevier, vol. 29(1-2), pages 31-62, January.
    3. Goran Peskir & Farman Samee, 2011. "The British Put Option," Applied Mathematical Finance, Taylor & Francis Journals, vol. 18(6), pages 537-563, April.
    4. Aebi, Vincent & Sabato, Gabriele & Schmid, Markus, 2012. "Risk management, corporate governance, and bank performance in the financial crisis," Journal of Banking & Finance, Elsevier, vol. 36(12), pages 3213-3226.
    5. G. Alobaidi & R. Mallier, 2002. "Laplace transforms and the American straddle," Journal of Applied Mathematics, Hindawi, vol. 2, pages 1-9, January.
    6. 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.
    7. Wang, Xiao-Tian & Zhao, Zhong-Feng & Fang, Xiao-Fen, 2015. "Option pricing and portfolio hedging under the mixed hedging strategy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 424(C), pages 194-206.
    8. Detemple, Jérôme & Emmerling, Thomas, 2009. "American chooser options," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 128-153, January.
    9. Siim Kallast & Andi Kivinukk, 2003. "Pricing and Hedging American Options Using Approximations by Kim Integral Equations," Review of Finance, Springer, vol. 7(3), pages 361-383.
    10. Cornett, Marcia Millon & McNutt, Jamie John & Strahan, Philip E. & Tehranian, Hassan, 2011. "Liquidity risk management and credit supply in the financial crisis," Journal of Financial Economics, Elsevier, vol. 101(2), pages 297-312, August.
    11. Siim Kallast & Andi Kivinukk, 2003. "Pricing and Hedging American Options Using Approximations by Kim Integral Equations," Review of Finance, European Finance Association, vol. 7(3), pages 361-383.
    12. Hull, John & White, Alan, 2017. "Optimal delta hedging for options," Journal of Banking & Finance, Elsevier, vol. 82(C), pages 180-190.
    13. S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 1-14, April.
    Full references (including those not matched with items on IDEAS)

    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. Detemple, Jérôme & Emmerling, Thomas, 2009. "American chooser options," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 128-153, January.
    2. Fabozzi, Frank J. & Paletta, Tommaso & Stanescu, Silvia & Tunaru, Radu, 2016. "An improved method for pricing and hedging long dated American options," European Journal of Operational Research, Elsevier, vol. 254(2), pages 656-666.
    3. Doriana Ruffino & Jonathan Treussard, 2006. "Lumps and Clusters in Duopolistic Investment Games: An Early Exercise Premium Approach," Boston University - Department of Economics - Working Papers Series WP2006-044, Boston University - Department of Economics.
    4. 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.
    5. Minqiang Li, 2010. "Analytical approximations for the critical stock prices of American options: a performance comparison," Review of Derivatives Research, Springer, vol. 13(1), pages 75-99, April.
    6. Carl Chiarella & Jonathan Ziveyi, 2014. "Pricing American options written on two underlying assets," Quantitative Finance, Taylor & Francis Journals, vol. 14(3), pages 409-426, March.
    7. De Angelis, Tiziano & Kitapbayev, Yerkin, 2017. "Integral equations for Rost’s reversed barriers: Existence and uniqueness results," Stochastic Processes and their Applications, Elsevier, vol. 127(10), pages 3447-3464.
    8. Denis Veliu & Roberto De Marchis & Mario Marino & Antonio Luciano Martire, 2022. "An Alternative Numerical Scheme to Approximate the Early Exercise Boundary of American Options," Mathematics, MDPI, vol. 11(1), pages 1-12, December.
    9. Shen, Yang & Sherris, Michael & Ziveyi, Jonathan, 2016. "Valuation of guaranteed minimum maturity benefits in variable annuities with surrender options," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 127-137.
    10. Andrew Ziogas & Carl Chiarella, 2003. "McKean’s Method applied to American Call Options on Jump-Diffusion Processes," Computing in Economics and Finance 2003 39, Society for Computational Economics.
    11. Laminou Abdou, Souleymane & Moraux, Franck, 2016. "Pricing and hedging American and hybrid strangles with finite maturity," Journal of Banking & Finance, Elsevier, vol. 62(C), pages 112-125.
    12. Andrew Ziogas, 2005. "Pricing American Options Using Fourier Analysis," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2005, January-A.
    13. Andrew Ziogas & Carl Chiarella, 2004. "Pricing American Options on Jump-Diffusion Processes using Fourier-Hermite Series Expansions," Computing in Economics and Finance 2004 177, Society for Computational Economics.
    14. Jun Cheng & Jin Zhang, 2012. "Analytical pricing of American options," Review of Derivatives Research, Springer, vol. 15(2), pages 157-192, July.
    15. 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.
    16. Thomas Kruse & Philipp Strack, 2019. "An Inverse Optimal Stopping Problem for Diffusion Processes," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 423-439, May.
    17. Franck Moraux, 2009. "On perpetual American strangles," Post-Print halshs-00393811, HAL.
    18. Tsvetelin S. Zaevski, 2023. "American strangle options with arbitrary strikes," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(7), pages 880-903, July.
    19. Tiziano De Angelis, 2020. "Stopping spikes, continuation bays and other features of optimal stopping with finite-time horizon," Papers 2009.01276, arXiv.org, revised Jan 2022.
    20. 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.

    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:wsi:jecxxx:v:26:y:2018:i:03:n:s0219024918500620. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/jec/jec.shtml .

    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.