Valuing Employee Stock Options: Does the Model Matter?

Abstract

In this numerical analysis of models for valuing employee stock options, the focus is on the impact of a model on the resulting option prices and the sensitivity of pricing differences between models with respect to changes in the parameters. For most models, the price reduction relative to standard options is uniquely determined by the expected life of the option. In fact, with the exception of the Financial Accounting Standards Board 123 model, pricing differences are negligible if the models are calibrated to the same expected life of the option. Consequently, the application of models with several hard-to-estimate parameters, such as the utility-maximizing model, can be greatly simplified by calibration, because expected life is easier to estimate than utility parameters.

Employee stock options differ from standard options in significant ways, and several researchers have noted the shortcomings of using traditional option formulas to value employee stock options. Although several pricing models for employee stock options have been proposed, no standard model has yet been accepted. As a contribution to the ongoing model discussion, we present a comparative analysis of current models for valuing employee stock options and propose a new model that accounts for suboptimal exercise because of nontradability by a simple adjustment of the exercise price. We analyze the impact of each model on the resulting option prices and investigate the sensitivity of pricing differences between models with respect to changes in the parameters.

In particular, we investigate a utility-maximizing model, a recent Hull-White model, the model proposed by the Financial Accounting Standards Board (called “FASB 123”), and our model, which we call the “Enhanced American” model because of its similarity to modeling the price of a standard American option. In addition, we compare all the models with a standard Black-Scholes option-pricing model and the model for valuing American-style options.

We show that, with the exception of the FASB 123 model and the standard Black-Scholes and American models, the models produce virtually identical option prices (differences in the range of −0.4 percent to +0.4 percent) if they are calibrated to the same expected life of the option. (The expected life of a set of employee stock options is defined as the length of time that options remain unexercised, on average, given that they vest.) In fact, for most models, after premature exercise of the option is accounted for, the expected life is a sufficient parameter to determine the price of an employee stock option relative to a standard option. In other words, even though the models tested derive their exercise policies in completely different approaches, the pricing effect of the exercise schemes is negligible as long as the expected life of the option is the same. As a consequence, dependence on unobservable and hard-to-estimate parameters, such as risk aversion, expected return, and nonoption wealth in the utility-maximizing model, can be overcome by using expected life, which is much easier to estimate, to calibrate the model. Expected life can replace the utility parameters because any combination of utility parameters implying the same expected life for the option produces the same option price.

Furthermore, we show that modeling a time-varying employee exit rate can increase the value of the option if one assumes that the exit rate decreases during the vesting period for an option that is in the money. Hence, valuation models that use constant exit rates tend to underestimate the value of employee stock options.

We would like to thank Bernd Brommundt, Michael Genser, Stephan M. Kessler, Peter Raupach, Michael Verhofen, and Rico von Wyss for their helpful comments.