IDEAS home Printed from https://ideas.repec.org/a/bla/mathfi/v19y2009i1p99-128.html
   My bibliography  Save this article

Accounting For Risk Aversion, Vesting, Job Termination Risk And Multiple Exercises In Valuation Of Employee Stock Options

Author

Listed:
  • Tim Leung
  • Ronnie Sircar

Abstract

We present a valuation framework that captures the main characteristics of employee stock options (ESOs), which financial regulations now require to be expensed in firms' accounting statements. The value of these options is much less than Black–Scholes prices for corresponding market‐traded options due to the suboptimal exercising strategies of the holders, which arise from risk aversion, trading and hedging constraints, and job termination risk. We analyze the combined effect of all of these factors along with the standard ESO features of multiple exercising rights, and vesting periods. This leads to the study of a chain of nonlinear free‐boundary problems of reaction‐diffusion type. We find that job termination risk, vesting, finite maturity and non‐zero interest rates are significant contributors to the ESO cost. However, we find that in the presence of vesting, the impact of allowing multiple exercise rights on ESO cost is negligible.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:mathfi:v:19:y:2009:i:1:p:99-128
    DOI: 10.1111/j.1467-9965.2008.00359.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9965.2008.00359.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9965.2008.00359.x?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
    ---><---

    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. Jakša Cvitanić & Zvi Wiener & Fernando Zapatero, 2008. "Analytic Pricing of Employee Stock Options," The Review of Financial Studies, Society for Financial Studies, vol. 21(2), pages 683-724, April.
    3. A. Oberman & T. Zariphopoulou, 2003. "Pricing early exercise contracts in incomplete markets," Computational Management Science, Springer, vol. 1(1), pages 75-107, December.
    4. Detemple, Jerome & Sundaresan, Suresh, 1999. "Nontraded Asset Valuation with Portfolio Constraints: A Binomial Approach," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 835-872.
    5. Hemmer, Thomas & Matsunaga, Steve & Shevlin, Terry, 1996. "The influence of risk diversification on the early exercise of employee stock options by executive officers," Journal of Accounting and Economics, Elsevier, vol. 21(1), pages 45-68, February.
    6. Carol A. Marquardt, 2002. "The Cost of Employee Stock Option Grants: An Empirical Analysis," Journal of Accounting Research, Wiley Blackwell, vol. 40(4), pages 1191-1217, September.
    7. Peter Carr & Vadim Linetsky, 2000. "The Valuation of Executive Stock Options in an Intensity-Based Framework," Review of Finance, European Finance Association, vol. 4(3), pages 211-230.
    8. Sircar, Ronnie & Xiong, Wei, 2007. "A general framework for evaluating executive stock options," Journal of Economic Dynamics and Control, Elsevier, vol. 31(7), pages 2317-2349, July.
    9. 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.
    10. René Carmona & Nizar Touzi, 2008. "Optimal Multiple Stopping And Valuation Of Swing Options," Mathematical Finance, Wiley Blackwell, vol. 18(2), pages 239-268, April.
    11. Carpenter, Jennifer N., 1998. "The exercise and valuation of executive stock options," Journal of Financial Economics, Elsevier, vol. 48(2), pages 127-158, May.
    12. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    13. 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.
    14. Dirk Becherer & Martin Schweizer, 2005. "Classical solutions to reaction-diffusion systems for hedging problems with interacting Ito and point processes," Papers math/0505208, arXiv.org.
    15. 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.
    16. 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.
    17. M. R. Grasselli, 2005. "Nonlinearity, correlation and the valuation of employee stock options," Papers math/0511234, arXiv.org.
    18. Huddart, Steven, 1994. "Employee stock options," Journal of Accounting and Economics, Elsevier, vol. 18(2), pages 207-231, September.
    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. 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. repec:dau:papers:123456789/9550 is not listed on IDEAS
    3. repec:dau:papers:123456789/13098 is not listed on IDEAS
    4. 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.
    5. 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.
    6. 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.
    7. Kimura, Toshikazu, 2010. "Valuing executive stock options: A quadratic approximation," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1368-1379, December.
    8. Len, Angel & Vaello-Sebasti, Antoni, 2009. "American GARCH employee stock option valuation," Journal of Banking & Finance, Elsevier, vol. 33(6), pages 1129-1143, June.
    9. Tang, Chun-Hua, 2012. "Revisiting the incentive effects of executive stock options," Journal of Banking & Finance, Elsevier, vol. 36(2), pages 564-574.
    10. Susana Álvarez-Díez & J. Baixauli-Soler & María Belda-Ruiz, 2014. "Are we using the wrong letters? An analysis of executive stock option Greeks," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 22(2), pages 237-262, June.
    11. Martin Widdicks & Jinsha Zhao, 2014. "A Model of Equity Based Compensation with Tax," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 41(7-8), pages 1002-1041, September.
    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. Tim Leung & Yang Zhou, 2020. "A Top-Down Approach For The Multiple Exercises And Valuation Of Employee Stock Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(02), pages 1-29, March.
    14. 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).
    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. Colwell, David B. & Feldman, David & Hu, Wei, 2015. "Non-transferable non-hedgeable executive stock option pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 161-191.
    17. 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.
    18. Tim Leung & Haohua Wan, 2015. "ESO Valuation with Job Termination Risk and Jumps in Stock Price," Papers 1504.08073, arXiv.org.
    19. 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.
    20. Sautner, Zacharias & Weber, Martin, 2005. "Stock options and employee behavior," Papers 05-26, Sonderforschungsbreich 504.
    21. 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.
    22. Klein, Daniel, 2018. "Executive turnover and the valuation of stock options," Journal of Corporate Finance, Elsevier, vol. 48(C), pages 76-93.

    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:bla:mathfi:v:19:y:2009:i:1:p:99-128. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0960-1627 .

    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.