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Nonlinearity, correlation and the valuation of employee stock options

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  • M. R. Grasselli

Abstract

We propose a discrete time algorithm for the valuation of employee stock options based on exponential indifference prices and taking into account both the possibility of partial exercise of a fraction of the options and the use of a correlated traded asset to hedge part of their risk. We determine the optimal exercise policy under this conditions and present numerical results showing how both effects can significantly change the value of the option for an employee, as well as its cost for the issuing firm.

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  • M. R. Grasselli, 2005. "Nonlinearity, correlation and the valuation of employee stock options," Papers math/0511234, arXiv.org.
    • Handle: RePEc:arx:papers:math/0511234
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    References listed on IDEAS

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    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. A. Oberman & T. Zariphopoulou, 2003. "Pricing early exercise contracts in incomplete markets," Computational Management Science, Springer, vol. 1(1), pages 75-107, December.
    3. 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.
    4. Carpenter, Jennifer N., 1998. "The exercise and valuation of executive stock options," Journal of Financial Economics, Elsevier, vol. 48(2), pages 127-158, May.
    5. Huddart, Steven, 1994. "Employee stock options," Journal of Accounting and Economics, Elsevier, vol. 18(2), pages 207-231, September.
    6. 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.
    7. L. C. Rogers & Jose A. Scheinkman, 2003. "Optimal Exercise of American Claims When Markets Are Not Complete," Levine's Working Paper Archive 506439000000000114, David K. Levine.
    8. J. Scheinkman & C. Rogers L., 2003. "Optimal Exercise of American Claims When," Princeton Economic Theory Working Papers 77e0e688f3178298289e06d42, David K. Levine.
    9. Marek Musiela & Thaleia Zariphopoulou, 2004. "A valuation algorithm for indifference prices in incomplete markets," Finance and Stochastics, Springer, vol. 8(3), pages 399-414, August.
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    Cited by:

    1. M. R Grasselli, 2006. "Getting real with real options," Papers math/0604302, arXiv.org.
    2. 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.
    3. 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.

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