Analytic Pricing of Employee Stock Options∗†

We introduce a model that captures the main properties that characterize employee stock options (ESO), in particular, the likelihood of early voluntary exercise and the obligation to exercise immediately if the employee leaves the firm, except if this happens before options are vested, in which case the options are forfeited. We derive an analytic formula for the price of the ESO and analyze its properties and sensitivity with respect to the model parameters. ∗We are grateful to Kevin Murphy for very useful preliminary conversations. Existing errors are our sole responsibility. †Patent pending. ‡Departments of Mathematics and Economics, USC, 3620 S Vermont Ave, MC 2532, Los Angeles, CA 90089. Ph: (213) 740-3794. Fax: (213) 740-2424. E-mail: [email protected]. §School of Business Administration, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem, 91905, Israel. Ph: (972) 2-588-3049. Fax: (972) 2-588-1341. E-mail: [email protected]. ¶FBE, Marshall School of Business, USC, Los Angeles, CA 90089-1427. Ph: (213) 740-6538. Fax: (213) 740-6650. E-mail: [email protected]. Analytic Pricing of Employee Stock Options We introduce a model that captures the main properties that characterize employee stock options (ESO), in particular, the likelihood of early voluntary exercise and the obligation to exercise immediately if the employee leaves the firm, except if this happens before options are vested, in which case the options are forfeited. We derive an analytic formula for the price of the ESO and analyze its properties and sensitivity with respect to the model parameters.