VALUING EMPLOYEE STOCK OPTIONS WITH EXOGENOUS AND ENDOGENOUS EARLY EXERCISE

Abstract

Journal of Derivatives AccountingVol. 02, No. 01, pp. 53-62 (2005) ARTICLESNo AccessVALUING EMPLOYEE STOCK OPTIONS WITH EXOGENOUS AND ENDOGENOUS EARLY EXERCISEYAN WU and ROBERT A. JONESYAN WUSchool of Business and Economics, Wilfrid Laurier University, Waterloo, ON, N2M 3C5, CanadaCorresponding author. Search for more papers by this author and ROBERT A. JONESDepartment of Economics, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada Search for more papers by this author https://doi.org/10.1142/S0219868105000306Cited by:1 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail AbstractThis paper examines how forfeiture, vesting, and early exercise affect the value of employee stock options. The forfeiture and exogenous exercise of the options are modeled as two Poisson processes with constant intensity. Rational exercise by the employee due to the option's American feature is modeled as endogenous exercise. The Crank–Nicholson numerical method is used to solve for the resulting value of employee stock options. Results are consistent with the findings that the employee stock options are worth substantially less than the Black–Scholes formula value. The model demonstrates that the option holder would rationally exercise the option early even when the underlying stock pays no dividend. The model also provides results on the expected time to exercise of employee stock options and the expected exercise price relative to strike price. The method used in this paper is proposed as an alternative to the Black–Scholes formula for measuring fair market value of employee stock options for accounting and regulation purposes.Keywords:Employee stock optionsvaluationaccountingearly exercise References J. N. Carpenter, Journal of Financial Economics 48, 127 (1998). Crossref, Google ScholarP. Carr and V. Linetsky, European Finance Review 4, 211 (2000). Crossref, Google ScholarC. Cuny and P. Jorion, Journal of Accounting and Economics 20, 193 (1995). Crossref, Google Scholar D. Duffie , Dynamic Asset Pricing Theory , 3rd edn. ( Princeton University Press , Princeton, NJ , 2001 ) . Google ScholarT. Foster, P. Koogler and D. Vickrey, The Accounting Review 68, 184 (1993). Google Scholar A. Friedman , Stochastic Differential Equations and Applications ( Academic Press , New York , 1975 ) . Google ScholarJ. M. Harrison and D. Kreps, Journal of Economic Theory 20, 381 (1979). Crossref, Google ScholarT. Hemmer, S. Matsunaga and T. Shevlin, Accounting Horizons 18, 207 (1994). Google ScholarS. Huddart and M. Lang, Journal of Accounting and Economics 21, 5 (1996). Crossref, Google Scholar Jones, RA (1995). Credit risk and credit rationing. Simon Fraser University working paper . Google Scholar N. Krylov , Controlled Diffusion Processes ( Springer-Verlag , New York , 1980 ) . Crossref, Google ScholarC. A. Marquardt, Journal of Accounting Research 40, 1191 (2002). Crossref, Google ScholarR. Merton, Journal of Financial Economics 3, 125 (1976). Crossref, Google Scholar W. H. Press et al. , Numerical Recipes: The Art of Scientific Computing , 2nd edn. ( Cambridge University Press , Cambridge , 1992 ) . Google Scholar V. Vemuri and W. J. Karplus , Digital Computer Treatment of Partial Differential Equations ( Prentice-Hall , Englewood Cliffs, NJ , 1981 ) . Google Scholar Wu, Y (2003). Employee stock option design and valuation. Unpublished doctoral dissertation, Simon Fraser University, Dept of Economics . Google Scholar FiguresReferencesRelatedDetailsCited By 1The incentive effect of repricing in employee stock optionsYan Wendy Wu20 Feb 2009 | Review of Accounting and Finance, Vol. 8, No. 1 Recommended Vol. 02, No. 01 Metrics History KeywordsEmployee stock optionsvaluationaccountingearly exercisePDF download