IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1906.03562.html
   My bibliography  Save this paper

A Top-Down Approach for the Multiple Exercises and Valuation of Employee Stock Options

Author

Listed:
  • Tim Leung
  • Yang Zhou

Abstract

We propose a new framework to value employee stock options (ESOs) that captures multiple exercises of different quantities over time. We also model the ESO holder's job termination risk and incorporate its impact on the payoffs of both vested and unvested ESOs. Numerical methods based on Fourier transform and finite differences are developed and implemented to solve the associated systems of PDEs. In addition, we introduce a new valuation method based on maturity randomization that yields analytic formulae for vested and unvested ESO costs. We examine the cost impact of job termination risk, exercise intensity, and various contractual features.

Suggested Citation

  • Tim Leung & Yang Zhou, 2019. "A Top-Down Approach for the Multiple Exercises and Valuation of Employee Stock Options," Papers 1906.03562, arXiv.org, revised Sep 2019.
    • Handle: RePEc:arx:papers:1906.03562
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1906.03562
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    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. Wilmott,Paul & Howison,Sam & Dewynne,Jeff, 1995. "The Mathematics of Financial Derivatives," Cambridge Books, Cambridge University Press, number 9780521497893.
    4. 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.
    5. Carpenter, Jennifer N., 1998. "The exercise and valuation of executive stock options," Journal of Financial Economics, Elsevier, vol. 48(2), pages 127-158, May.
    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. 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. 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.
    11. Bettis, J. Carr & Bizjak, John M. & Lemmon, Michael L., 2001. "Managerial Ownership, Incentive Contracting, and the Use of Zero-Cost Collars and Equity Swaps by Corporate Insiders," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 36(3), pages 345-370, September.
    12. Tim Leung & Haohua Wan, 2015. "ESO Valuation with Job Termination Risk and Jumps in Stock Price," Papers 1504.08073, arXiv.org.
    13. Kay Giesecke & Lisa R. Goldberg & Xiaowei Ding, 2011. "A Top-Down Approach to Multiname Credit," Operations Research, INFORMS, vol. 59(2), pages 283-300, 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. 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. 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.
    3. 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.
    4. 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.
    5. repec:dau:papers:123456789/9550 is not listed on IDEAS
    6. Len, Angel & Vaello-Sebasti, Antoni, 2009. "American GARCH employee stock option valuation," Journal of Banking & Finance, Elsevier, vol. 33(6), pages 1129-1143, June.
    7. repec:dau:papers:123456789/13098 is not listed on IDEAS
    8. 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.
    9. Kimura, Toshikazu, 2010. "Valuing executive stock options: A quadratic approximation," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1368-1379, December.
    10. Tim Leung & Haohua Wan, 2015. "ESO Valuation with Job Termination Risk and Jumps in Stock Price," Papers 1504.08073, arXiv.org.
    11. Tang, Chun-Hua, 2012. "Revisiting the incentive effects of executive stock options," Journal of Banking & Finance, Elsevier, vol. 36(2), pages 564-574.
    12. Eikseth, Hans Marius & Lindset, Snorre, 2011. "Backdating executive stock options--An ex ante valuation," Journal of Economic Dynamics and Control, Elsevier, vol. 35(10), pages 1731-1743, October.
    13. 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.
    14. Klein, Daniel, 2018. "Executive turnover and the valuation of stock options," Journal of Corporate Finance, Elsevier, vol. 48(C), pages 76-93.
    15. Kamil Kladivko & Mihail Zervos, 2017. "Valuation of Employee Stock Options (ESOs) by means of Mean-Variance Hedging," Papers 1710.00897, arXiv.org.
    16. Susana Alvarez-Diez & J. Samuel Baixauli-Soler & Maria Belda-Ruiz, 2016. "Early Exercise Behaviour in Performance-vested Stock Option Grants," Annals of Economics and Finance, Society for AEF, vol. 17(1), pages 55-78, May.
    17. 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.
    18. Olaf Korn & Clemens Paschke & Marliese Uhrig-Homburg, 2012. "Robust stock option plans," Review of Quantitative Finance and Accounting, Springer, vol. 39(1), pages 77-103, July.
    19. Sautner, Zacharias & Weber, Martin, 2005. "Stock options and employee behavior," Papers 05-26, Sonderforschungsbreich 504.
    20. Gao, Huasheng, 2010. "Optimal compensation contracts when managers can hedge," Journal of Financial Economics, Elsevier, vol. 97(2), pages 218-238, August.
    21. Hamza Bahaji, 2018. "Are employee stock option exercise decisions better explained through the prospect theory?," Annals of Operations Research, Springer, vol. 262(2), pages 335-359, March.
    22. Philip Brown & Alex Szimayer, 2008. "Valuing executive stock options: performance hurdles, early exercise and stochastic volatility," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 48(3), pages 363-389, September.

    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:arx:papers:1906.03562. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.