A Finite Difference Model for Valuation of Employee Stock Options

Abstract

Employee stock option grants are a common incentive for employees and are a key remuneration device. These options differ from ordinary options in that they cannot be traded nor hedged. Nevertheless, the work of Carpenter enables one to price these options within a Black-Scholes framework, with one additional parameter calibrated from historical data. We develop a model where the price of the grant obeys the Black-Scholes differential equation with two additional parameters: one which controls the rate at which employees forfeit unvested options, and another which controls the rate at which employees exercise vested options. We implement a finite difference scheme for computation of the option values derived from this model.