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

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  • 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
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    References listed on IDEAS

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    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, October.
    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.
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