Employee Stock Option Valuation with an Early Exercise Boundary

Many companies are recognizing that the Black–Scholes formula is inappropriate for employee stock options (ESOs) and are moving toward lattice models for accounting or decision-making purposes. In the most influential of these models, the assumption is that employees exercise voluntarily when the stock price reaches a fixed multiple of the strike price, effectively introducing a “horizontal” exercise boundary into the lattice. In practice, however, employees make a trade-off between intrinsic value captured and the opportunity cost of time value forgone. The model proposed here explicitly recognizes and accounts for this reality and is intuitively appealing, easily implemented, and compliant with U.S. accounting standards.Employee stock options (ESOs) must be valued for accounting and economic purposes, but increasing numbers of companies are recognizing that variants of the Black–Scholes formula are inappropriate for this purpose. They are moving toward the use of lattice models—for example, the binomial option-pricing model. The most influential lattice model for option pricing assumes that employees exercise voluntarily when the stock price reaches a fixed multiple, M, of the strike price. Conceptually, this approach introduces a “horizontal” voluntary exercise boundary into the lattice. Empirical evidence suggests, however, that employees make a trade-off between intrinsic value captured and the opportunity cost of time value forgone. So, the stock must be at a relatively high multiple of the strike price to induce voluntary exercise early in the ESO life, whereas later on, employees are willing to exercise at relatively low multiples of the strike price. We propose a model that explicitly recognizes and accounts for this reality. We assume that employees exercise voluntarily when the “moneyness” of the option reaches a fixed proportion, which we term μ, of its remaining Black–Scholes value. This approach results in an intuitively appealing downward-sloping voluntary exercise boundary. Our μ model is compliant with Statement of Financial Accounting Standards No. 123 (revised), Share-Based Payment, is easily implemented, and readily encompasses such ESO characteristics as vesting restrictions, forfeiture, and forced early exercise as a result of employment termination.We show why our model may be less prone to bias than both the M model and the modified Black–Scholes model when parameter inputs are calculated from historical observations of voluntary exercise behavior. Given the known early exercise trade-off made by employees, a company that has enjoyed rapid stock price growth will probably have experienced ESO exercises at somewhat high multiples of strike price (and early in the ESO lives), so using these historical observations to calibrate an M model leads to high ESO valuations (but using the modified Black–Scholes model leads to low values). Conversely, a company that has experienced sluggish stock price growth will have experienced ESO exercises at comparatively low multiples of strike price (and later in the ESO lives), so an M model will produce low ESO values (and a Black–Scholes model will produce high valuations). To the extent that our exercise boundary better describes the exercise decisions of employees than do other models, our model is less susceptible to the biases caused by atypical stock price histories. We illustrate this comparison analytically by simulating stock price paths with a well-known utility-based model of employee exercise as a benchmark.Our results have implications for compensation committees and consultants who need to understand the potential economic cost of ESO awards to executives and employees. The results are also relevant to practitioners who are selecting ESO valuation models for accounting disclosure purposes. Academic researchers and other users of financial statements will find our results important for understanding the sensitivity of the disclosed data to the choice of valuation model and to the estimation of parameter values—which are themselves dependent on the chosen historical dataset.Editor’s Note: The paper on which this article is based won the Second Annual “Best Conference Research Paper Award” from the Canadian Finance Executives Research Foundation at the 2008 Financial Executives International (FEI) Canada conference.