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Pricing executive stock options under employment shocks

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  • Carmona, Julio
  • León, Angel
  • Vaello-Sebastià, Antoni

Abstract

We obtain explicit expressions for the subjective, objective and market value of perpetual executive stock options (ESOs) under exogenous employment shocks driven by an independent Poisson process. Previously, we obtain the executive's optimal exercise policy from the subjective valuation that is necessary for the objective one, or fair value. The perpetual ESO is compared with the true finite maturity ESO finding that the approximation is reasonably good. To illustrate the usefulness of the objective valuation for accounting purposes, we analyze the statistical distribution of the fair value when there is uncertainty about the employment shock intensity. Finally, the role of ESOs in the design of executives' incentives is also discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:dyncon:v:35:y:2011:i:1:p:97-114
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    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    2. 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.
    3. John H. Cochrane & Jesus Saa-Requejo, 2000. "Beyond Arbitrage: Good-Deal Asset Price Bounds in Incomplete Markets," Journal of Political Economy, University of Chicago Press, vol. 108(1), pages 79-119, February.
    4. Jakša Cvitanić & Zvi Wiener & Fernando Zapatero, 2008. "Analytic Pricing of Employee Stock Options," Review of Financial Studies, Society for Financial Studies, vol. 21(2), pages 683-724, April.
    5. Tian, Yisong S., 2004. "Too much of a good incentive? The case of executive stock options," Journal of Banking & Finance, Elsevier, vol. 28(6), pages 1225-1245, June.
    6. Jonathan E. Ingersoll, Jr., 2006. "The Subjective and Objective Evaluation of Incentive Stock Options," The Journal of Business, University of Chicago Press, vol. 79(2), pages 453-488, March.
    7. Kahl, Matthias & Liu, Jun & Longstaff, Francis A., 2003. "Paper millionaires: how valuable is stock to a stockholder who is restricted from selling it?," Journal of Financial Economics, Elsevier, vol. 67(3), pages 385-410, March.
    8. 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.
    9. 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.
    10. Johnson, Shane A. & Tian, Yisong S., 2000. "Indexed executive stock options," Journal of Financial Economics, Elsevier, vol. 57(1), pages 35-64, July.
    11. Kevin J. Murphy & Brian J. Hall, 2000. "Optimal Exercise Prices for Executive Stock Options," American Economic Review, American Economic Association, vol. 90(2), pages 209-214, May.
    12. Chang, Charles & Fuh, Cheng-Der & Hsu, Ya-Hui, 2008. "ESO compensation: The roles of default risk, employee sentiment, and insider information," Journal of Corporate Finance, Elsevier, vol. 14(5), pages 630-641, December.
    13. Lambert, Ra & Larcker, Df & Verrecchia, Re, 1991. "Portfolio Considerations In Valuing Executive-Compensation," Journal of Accounting Research, Wiley Blackwell, vol. 29(1), pages 129-149.
    14. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    15. Carpenter, Jennifer N., 1998. "The exercise and valuation of executive stock options," Journal of Financial Economics, Elsevier, vol. 48(2), pages 127-158, May.
    16. Kim, In Joon, 1990. "The Analytic Valuation of American Options," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 547-572.
    17. 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.
    18. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    19. Lars Stentoft, 2004. "Convergence of the Least Squares Monte Carlo Approach to American Option Valuation," Management Science, INFORMS, vol. 50(9), pages 1193-1203, September.
    20. Peter Løchte Jørgensen, 2002. "American-style Indexed Executive Stock Options," Review of Finance, European Finance Association, vol. 6(3), pages 321-358.
    21. 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.
    22. 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.
    23. 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.
    24. A. Louis Calvet & Abdul H. Rahman, 2006. "The Subjective Valuation of Indexed Stock Options and Their Incentive Effects," The Financial Review, Eastern Finance Association, vol. 41(2), pages 205-227, May.
    25. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    26. Huddart, Steven, 1994. "Employee stock options," Journal of Accounting and Economics, Elsevier, vol. 18(2), pages 207-231, September.
    27. Lars Stentoft, 2004. "Assessing the Least Squares Monte-Carlo Approach to American Option Valuation," Review of Derivatives Research, Springer, vol. 7(2), pages 129-168, August.
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    Cited by:

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    2. 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.
    3. Wang, Xingchun, 2021. "The values and incentive effects of options on the maximum or the minimum of the stock prices and market index," The North American Journal of Economics and Finance, Elsevier, vol. 55(C).
    4. Sonia Oreffice & Climent Quintana, 2009. "Anthropometry and Socioeconomics in the Couple: Evidence from the PSID," Working Papers 2009-22, FEDEA.
    5. Xu, Guangli & Shao, Xinjian & Wang, Xingchun, 2019. "Analytical valuation of power exchange options with default risk," Finance Research Letters, Elsevier, vol. 28(C), pages 265-274.
    6. 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.
    7. Wang, Xingchun, 2018. "Valuing executive stock options under correlated employment shocks," Finance Research Letters, Elsevier, vol. 27(C), pages 38-45.

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    More about this item

    Keywords

    Executive stock options Risk aversion Undiversification Incentives FAS123R;

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G35 - Financial Economics - - Corporate Finance and Governance - - - Payout Policy
    • M52 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Personnel Economics - - - Compensation and Compensation Methods and Their Effects

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