A Finite Difference Model for Valuation of Employee Stock Options
12 Pages Posted: 6 Oct 2007 Last revised: 13 Mar 2009
Date Written: January 14, 2009
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.
Keywords: Employee stock option, early exercise, finite difference scheme
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