IDEAS home Printed from https://ideas.repec.org/a/taf/quantf/v8y2008i5p461-469.html
   My bibliography  Save this article

Perpetual American options in incomplete markets: the infinitely divisible case

Author

Listed:
  • Vicky Henderson
  • David Hobson

Abstract

We consider the exercise of a number of American options in an incomplete market. In this paper we are interested in the case where the options are infinitely divisible. We make the simplifying assumptions that the options have infinite maturity, and the holder has exponential utility. Our contribution is to solve this problem explicitly and we show that, except at the initial time when it may be advantageous to exercise a positive fraction of his holdings, it is never optimal for the holder to exercise a tranche of options. Instead, the process of option exercises is continuous; however, it is singular with respect to calendar time. Exercise takes place when the stock price reaches a convex boundary which we identify.

Suggested Citation

  • Vicky Henderson & David Hobson, 2008. "Perpetual American options in incomplete markets: the infinitely divisible case," Quantitative Finance, Taylor & Francis Journals, vol. 8(5), pages 461-469.
  • Handle: RePEc:taf:quantf:v:8:y:2008:i:5:p:461-469
    DOI: 10.1080/14697680701400986
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/14697680701400986
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/14697680701400986?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. Hall, Brian J. & Murphy, Kevin J., 2002. "Stock options for undiversified executives," Journal of Accounting and Economics, Elsevier, vol. 33(1), pages 3-42, February.
    2. Thaleia Zariphopoulou, 2001. "A solution approach to valuation with unhedgeable risks," Finance and Stochastics, Springer, vol. 5(1), pages 61-82.
    3. Detemple, Jerome & Sundaresan, Suresh, 1999. "Nontraded Asset Valuation with Portfolio Constraints: A Binomial Approach," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 835-872.
    4. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    5. M. H. A. Davis & A. R. Norman, 1990. "Portfolio Selection with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 676-713, November.
    6. Carpenter, Jennifer N., 1998. "The exercise and valuation of executive stock options," Journal of Financial Economics, Elsevier, vol. 48(2), pages 127-158, May.
    7. Robert McDonald & Daniel Siegel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, Oxford University Press, vol. 101(4), pages 707-727.
    8. Bettis, J. Carr & Bizjak, John M. & Lemmon, Michael L., 2005. "Exercise behavior, valuation, and the incentive effects of employee stock options," Journal of Financial Economics, Elsevier, vol. 76(2), pages 445-470, May.
    9. Huddart, Steven & Lang, Mark, 1996. "Employee stock option exercises an empirical analysis," Journal of Accounting and Economics, Elsevier, vol. 21(1), pages 5-43, February.
    10. Vicky Henderson, 2005. "The impact of the market portfolio on the valuation, incentives and optimality of executive stock options," Quantitative Finance, Taylor & Francis Journals, vol. 5(1), pages 35-47.
    11. Ioannis Karatzas & (*), S. G. Kou, 1998. "Hedging American contingent claims with constrained portfolios," Finance and Stochastics, Springer, vol. 2(3), pages 215-258.
    12. Henderson, Vicky & Hobson, David, 2007. "Horizon-unbiased utility functions," Stochastic Processes and their Applications, Elsevier, vol. 117(11), pages 1621-1641, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Blog mentions

    As found by EconAcademics.org, the blog aggregator for Economics research:
    1. Optimal 10b5-1 Monetization
      by quantivity in Quantivity on 2011-09-27 12:02:52

    Citations

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


    Cited by:

    1. Anna Battauz & Marzia De Donno & Janusz Gajda & Alessandro Sbuelz, 2022. "Optimal exercise of American put options near maturity: A new economic perspective," Review of Derivatives Research, Springer, vol. 25(1), pages 23-46, April.

    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. Grasselli, Matheus & Henderson, Vicky, 2009. "Risk aversion and block exercise of executive stock options," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 109-127, January.
    2. Carpenter, Jennifer N. & Stanton, Richard & Wallace, Nancy, 2010. "Optimal exercise of executive stock options and implications for firm cost," Journal of Financial Economics, Elsevier, vol. 98(2), pages 315-337, November.
    3. Hodder, James E. & Jackwerth, Jens Carsten, 2011. "Managerial responses to incentives: Control of firm risk, derivative pricing implications, and outside wealth management," Journal of Banking & Finance, Elsevier, vol. 35(6), pages 1507-1518, June.
    4. Tim Leung & Ronnie Sircar, 2009. "Accounting For Risk Aversion, Vesting, Job Termination Risk And Multiple Exercises In Valuation Of Employee Stock Options," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 99-128, January.
    5. repec:dau:papers:123456789/9550 is not listed on IDEAS
    6. Jackwerth, Jens Carsten & Hodder, James E., 2008. "Managerial responses to incentives: Control of firm risk, derivative pricing implications, and outside wealth management," CoFE Discussion Papers 08/07, University of Konstanz, Center of Finance and Econometrics (CoFE).
    7. repec:dau:papers:123456789/13098 is not listed on IDEAS
    8. Tang, Chun-Hua, 2012. "Revisiting the incentive effects of executive stock options," Journal of Banking & Finance, Elsevier, vol. 36(2), pages 564-574.
    9. Carmona, Julio & León, Angel & Vaello-Sebastià, Antoni, 2011. "Pricing executive stock options under employment shocks," Journal of Economic Dynamics and Control, Elsevier, vol. 35(1), pages 97-114, January.
    10. Bahaji, Hamza & Casta, Jean-François, 2016. "Employee stock option-implied risk attitude under Rank-Dependent Expected Utility," Economic Modelling, Elsevier, vol. 52(PA), pages 144-154.
    11. Brian J. Hall & Thomas A. Knox, 2002. "Managing Option Fragility," NBER Working Papers 9059, National Bureau of Economic Research, Inc.
    12. Hamza Bahaji, 2009. "Contribution à l'analyse des déterminants du comportement d'exercice des porteurs de stock options : une étude empirique sur le marché Américain," Working Papers halshs-00512840, HAL.
    13. Gao, Huasheng, 2010. "Optimal compensation contracts when managers can hedge," Journal of Financial Economics, Elsevier, vol. 97(2), pages 218-238, August.
    14. Brian J. Hall & Thomas A. Knox, 2004. "Underwater Options and the Dynamics of Executive Pay‐to‐Performance Sensitivities," Journal of Accounting Research, Wiley Blackwell, vol. 42(2), pages 365-412, May.
    15. Abudy, Menachem & Benninga, Simon, 2013. "Non-marketability and the value of employee stock options," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 5500-5510.
    16. Zacharias Sautner & Martin Weber, 2009. "How Do Managers Behave In Stock Option Plans? Clinical Evidence From Exercise And Survey Data," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 32(2), pages 123-155, June.
    17. Kimura, Toshikazu, 2010. "Valuing executive stock options: A quadratic approximation," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1368-1379, December.
    18. Randall A. Heron & Erik Lie, 2017. "Do Stock Options Overcome Managerial Risk Aversion? Evidence from Exercises of Executive Stock Options," Management Science, INFORMS, vol. 63(9), pages 3057-3071, September.
    19. Miao, Jianjun & Wang, Neng, 2007. "Investment, consumption, and hedging under incomplete markets," Journal of Financial Economics, Elsevier, vol. 86(3), pages 608-642, December.
    20. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    21. Abdoh, Hussein, 2023. "Rivals risk-taking incentives and firm corporate policy," The Quarterly Review of Economics and Finance, Elsevier, vol. 90(C), pages 106-123.
    22. Kevin F. Hallock & Craig A. Olson, 2010. "New Data for Answering Old Questions Regarding Employee Stock Options," NBER Chapters, in: Labor in the New Economy, pages 149-180, National Bureau of Economic Research, Inc.

    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:quantf:v:8:y:2008:i:5:p:461-469. 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/RQUF20 .

    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.