Valuing Multiple Employee Stock Options Issued by the Same Company

Abstract

Stock options issued to employees has become a significant component of total compensation in many firms. Although option pricing technology has evolved remarkably over the years, valuing employee stock options (ESOs) still presents numerous challenges, and there is no model that is generally accepted in practice. Simply treating ESOs as if they were plain vanilla (American) stock options fails to take proper account of a number of their particular features. Along with vesting rules and the uncertainty they entail, these features include the fact that the equity of existing stockholders will be diluted when the ESOs are exercised. In that sense they resemble warrants rather than traded option contracts. Also, the fact that ESOs are issued on a regular basis means there are typically a number of outstanding ESOs with differing maturities and strike prices, which introduces interaction among them in valuation and in optimal exercise strategy. In this article, Dennis and Rendleman present a lattice technique to value ESOs that takes account of the effects of dilution and optimal exercise for a firm that has a diverse set of ESOs outstanding. Their approach increases computational efficiency substantially over the standard solution technique for a lattice model, but realistic problems still can become intractable as the number of time steps and options grows. Fortunately, the results indicate that in most cases, the effect of dilution and interaction among exercise decisions is present but relatively small.