IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v22y2019i06ns0219024919500353.html
   My bibliography  Save this article

American Options And Incomplete Information

Author

Listed:
  • ERIK EKSTRÖM

    (Department of Mathematics, Uppsala University, Box 480, 75106 Uppsala, Sweden)

  • MARTIN VANNESTÅL

Abstract

We study the optimal exercise of American options under incomplete information about the drift of the underlying process, and we show that quite unexpected phenomena may occur. In fact, certain parameter values give rise to stopping regions very different from the standard case of complete information. For example, we show that for the American put (call) option it is sometimes optimal to exercise the option when the underlying process reaches an upper (lower) boundary.

Suggested Citation

  • Erik Ekström & Martin Vannestål, 2019. "American Options And Incomplete Information," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(06), pages 1-14, September.
    • Handle: RePEc:wsi:ijtafx:v:22:y:2019:i:06:n:s0219024919500353
    DOI: 10.1142/S0219024919500353
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024919500353
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024919500353?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. Kristoffer Glover & Goran Peskir & Farman Samee, 2010. "The British Russian Option," Research Paper Series 269, Quantitative Finance Research Centre, University of Technology, Sydney.
    2. Pavel V. Gapeev, 2012. "Pricing Of Perpetual American Options In A Model With Partial Information," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 1-21.
    3. Lakner, Peter, 1995. "Utility maximization with partial information," Stochastic Processes and their Applications, Elsevier, vol. 56(2), pages 247-273, April.
    4. Pavel V. Gapeev, 2012. "Pricing Of Perpetual American Options In A Model With Partial Information," World Scientific Book Chapters, in: Matheus R Grasselli & Lane P Hughston (ed.), Finance at Fields, chapter 14, pages 327-347, World Scientific Publishing Co. Pte. Ltd..
    5. Bing Lu, 2013. "Optimal Selling of an Asset with Jumps Under Incomplete Information," Applied Mathematical Finance, Taylor & Francis Journals, vol. 20(6), pages 599-610, December.
    6. Manuel Klein, 2009. "Comment on “Investment Timing Under Incomplete Information”," Mathematics of Operations Research, INFORMS, vol. 34(1), pages 249-254, February.
    7. Stephane Villeneuve, 1999. "Exercise regions of American options on several assets," Finance and Stochastics, Springer, vol. 3(3), pages 295-322.
    8. Jean-Paul Décamps & Thomas Mariotti & Stéphane Villeneuve, 2005. "Investment Timing Under Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 30(2), pages 472-500, May.
    9. Stéphane Villeneuve, 2007. "On the Threshold Strategies and Smooth-Fit Principle For Optimal Stopping Problems," Post-Print hal-00173165, HAL.
    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. Tiziano De Angelis & Erik Ekstrom & Kristoffer Glover, 2018. "Dynkin games with incomplete and asymmetric information," Papers 1810.07674, arXiv.org, revised Jul 2020.
    2. Vicky Henderson & Kamil Klad'ivko & Michael Monoyios & Christoph Reisinger, 2017. "Executive stock option exercise with full and partial information on a drift change point," Papers 1709.10141, arXiv.org, revised Jul 2020.
    3. Erik Ekstrom & Juozas Vaicenavicius, 2015. "Optimal liquidation of an asset under drift uncertainty," Papers 1509.00686, arXiv.org.
    4. Glover, Kristoffer, 2022. "Optimally stopping a Brownian bridge with an unknown pinning time: A Bayesian approach," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 919-937.
    5. Juozas Vaicenavicius, 2017. "Asset liquidation under drift uncertainty and regime-switching volatility," Papers 1701.08579, arXiv.org, revised Jan 2019.
    6. Gapeev, Pavel V., 2022. "Discounted optimal stopping problems in continuous hidden Markov models," LSE Research Online Documents on Economics 110493, London School of Economics and Political Science, LSE Library.
    7. Xing, Jie & Ma, Jingtang & Yang, Wensheng, 2023. "Optimal entry decision of unemployment insurance under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 110(C), pages 31-52.
    8. Th'eo Durandard & Matteo Camboni, 2024. "Under Pressure: Comparative Statics for Optimal Stopping Problems in Nonstationary Environments," Papers 2402.06999, arXiv.org.
    9. Décamps, Jean-Paul & Mariotti, Thomas & Villeneuve, Stéphane, 2000. "Investment Timing under Incomplete Information," IDEI Working Papers 115, Institut d'Économie Industrielle (IDEI), Toulouse, revised Apr 2004.
    10. Jean-Paul Décamps & Thomas Mariotti & Stéphane Villeneuve, 2005. "Investment Timing Under Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 30(2), pages 472-500, May.
    11. J. Michael Harrison & Nur Sunar, 2015. "Investment Timing with Incomplete Information and Multiple Means of Learning," Operations Research, INFORMS, vol. 63(2), pages 442-457, April.
    12. Tiziano Angelis, 2020. "Optimal dividends with partial information and stopping of a degenerate reflecting diffusion," Finance and Stochastics, Springer, vol. 24(1), pages 71-123, January.
    13. Salvatore Federico & Giorgio Ferrari & Neofytos Rodosthenous, 2021. "Two-sided Singular Control of an Inventory with Unknown Demand Trend (Extended Version)," Papers 2102.11555, arXiv.org, revised Nov 2022.
    14. Federico, Salvatore & Ferrari, Giorgio & Rodosthenous, Neofytos, 2021. "Two-Sided Singular Control of an Inventory with Unknown Demand Trend," Center for Mathematical Economics Working Papers 643, Center for Mathematical Economics, Bielefeld University.
    15. Thomas Dangl & Youchang Wu, 2016. "Corporate Investment over the Business Cycle," Review of Finance, European Finance Association, vol. 20(1), pages 337-371.
    16. Manuel Guerra & Cláudia Nunes & Carlos Oliveira, 2021. "The optimal stopping problem revisited," Statistical Papers, Springer, vol. 62(1), pages 137-169, February.
    17. Wang, Xiao-Tian & Li, Zhe & Zhuang, Le, 2017. "European option pricing under the Student’s t noise with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 848-858.
    18. Carmine De Franco & Johann Nicolle & Huyên Pham, 2019. "Dealing with Drift Uncertainty: A Bayesian Learning Approach," Risks, MDPI, vol. 7(1), pages 1-18, January.
    19. Guidolin, Massimo & Timmermann, Allan, 2007. "Properties of equilibrium asset prices under alternative learning schemes," Journal of Economic Dynamics and Control, Elsevier, vol. 31(1), pages 161-217, January.
    20. Abdelali Gabih & Hakam Kondakji & Jorn Sass & Ralf Wunderlich, 2014. "Expert Opinions and Logarithmic Utility Maximization in a Market with Gaussian Drift," Papers 1402.6313, arXiv.org.

    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:ijtafx:v:22:y:2019:i:06:n:s0219024919500353. 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/ijtaf/ijtaf.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.