Accounting for Risk Aversion, Vesting, Job Termination Risk and Multiple Exercises in Valuation of Employee Stock Options

Abstract

We present a valuation framework that captures the main characteristics of employee stock options (ESOs), which financial regulations now require to be expensed in firms' accounting statements. The value of these options is much less than Black-Scholes prices for corresponding market-traded options due to the suboptimal exercising strategies of the holders, which arise from risk aversion, trading and hedging constraints, and job termination risk. We analyze the combined effect of all of these factors along with the standard ESO features of multiple exercising rights, and vesting periods. This leads to the study of a chain of nonlinear free-boundary problems of reaction-diffusion type. We find that job termination risk, vesting, finite maturity and non-zero interest rates are significant contributors to the ESO cost. However, we find that, in the presence of vesting, the impact of allowing multiple exercise rights on ESO cost is negligible.

Keywords: employee stock options, reaction-diffusion equations, indifference pricing

JEL Classification: M41, M44, J33, G13