Employee Stock Options: Accounting for Optimal Hedging, Suboptimal Exercises, and Contractual Restrictions

Abstract:     
Employee stock options (ESOs) have become an integral component of compensation in the U.S. In view of their significant cost to firms, the Financial Accounting Standards Board (FASB) has mandated expensing ESOs since 2004. The main difficulty of ESO valuation lies in the uncertain timing of exercises, and a number of contractual restrictions of ESOs further complicate the problem.

We present a valuation framework that captures the main characteristics of ESOs. Specifically, we incorporate the holder's risk aversion, and hedging strategies that include both dynamic trading of a correlated asset and static positions in market-traded options. Their combined effect on ESO exercises and costs are evaluated along with common features like vesting periods, job termination risk and multiple exercises. This leads to the study of a joint stochastic control and optimal stopping problem. We find that ESO values are much less than the corresponding Black-Scholes prices due to early exercises, which arise from risk aversion and job termination risk; whereas static hedges induce holders to delay exercises and increase ESO costs.

Keywords: employee stock options, American options, risk aversion, reaction-diffusion equations

JEL Classifications: M41, M44, J33, G13

Working Paper Series