Valuing Employee Stock Options with Exogenous and Endogenous Early Exercise

This 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