Extending the Black-Scholes-Merton Model to Value Employee Stock Options
30 Pages Posted: 14 Jun 2006
This article develops an operationally useful contingent-claims model for valuing employee stock options (ESOs) that takes into account ESO vesting requirements, transfer restrictions, early exercise, and forfeiture. I extend the familiar Black-Scholes-Merton (BSM) model, which most firms use to value their ESOs. I treat the ESOs as a portfolio of European options with a representative set of discrete exercise dates between vesting and expiration, and model ESO exercise and forfeiture rates as meanreverting stochastic processes. The article furnishes ESO exercise and forfeiture data from 17 firms covering 156 separate ESO grants between 1981 and 2002 totaling more than 1.27 billion ESOs to identify the patterns of ESO exercise and forfeiture behavior. I show how to use historical data to calibrate my model. I compare the values obtained from my model to those from a trinomial lattice model and show that the two models provide consistent valuations. I explain how to use my model to calculate the cost of ESOs for financial reporting purposes.
JEL Classification: G39
Suggested Citation: Suggested Citation