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A simulation-based algorithm for American executive stock option valuation


  • León, Angel
  • Vaello-Sebastià, Antoni


We present an algorithm that merges a certainty-equivalence framework with the least-squares Monte Carlo algorithm to obtain the executive stock option (ESO) value for a risk-averse and undiversified agent. We account for the difference between executive's value and firm cost of the ESO. We show how early-exercise decisions depend on executive's preferences and its diversification degree. Because of the algorithm flexibility, it allows for multiple state-variables. As an example, we consider the case of indexed ESOs revealing a significant improvement in terms of executive's discount respect to fixed strike ESOs.

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  • León, Angel & Vaello-Sebastià, Antoni, 2010. "A simulation-based algorithm for American executive stock option valuation," Finance Research Letters, Elsevier, vol. 7(1), pages 14-23, March.
  • Handle: RePEc:eee:finlet:v:7:y:2010:i:1:p:14-23

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    References listed on IDEAS

    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. Michael W. Brandt & Amit Goyal & Pedro Santa-Clara & Jonathan R. Stroud, 2005. "A Simulation Approach to Dynamic Portfolio Choice with an Application to Learning About Return Predictability," Review of Financial Studies, Society for Financial Studies, vol. 18(3), pages 831-873.
    3. Longstaff, Francis A, 2001. "Optimal Portfolio Choice and the Valuation of Illiquid Securities," Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 407-431.
    4. 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.
    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. 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.
    7. 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.
    8. Johnson, Shane A. & Tian, Yisong S., 2000. "Indexed executive stock options," Journal of Financial Economics, Elsevier, vol. 57(1), pages 35-64, July.
    9. 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.
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    Cited by:

    1. Carmona, Julio & León, Angel & Vaello-Sebastià, Antoni, 2012. "Does stock return predictability affect ESO fair value?," European Journal of Operational Research, Elsevier, vol. 223(1), pages 188-202.
    2. 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.


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