Article2009

ACCOUNTING FOR RISK AVERSION, VESTING, JOB TERMINATION RISK AND MULTIPLE EXERCISES IN VALUATION OF EMPLOYEE STOCK OPTIONS

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Stochastic processes and financial applications Accounting Theory and Financial Reporting Financial Reporting and Valuation Research

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.

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References

1969Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case 1998Methods of Mathematical Finance 2002Stock options for undiversified executives 1995The Mathematics of Financial Derivatives 1998Methods of Mathematical Finance 2000The Minimal Entropy Martingale Measure and the Valuation Problem in Incomplete Markets 1996Employee stock option exercises an empirical analysis 1998The exercise and valuation of executive stock options

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