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

30 Pages Posted: 17 Jan 2009

See all articles by Tim Leung

Tim Leung

University of Washington - Department of Applied Math

Ronnie Sircar

Princeton University - Department of Operations Research and Financial Engineering

Multiple version iconThere are 2 versions of this paper

Date Written: 2007-08

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 BlackScholes 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.

Suggested Citation

Leung, Tim and Sircar, Ronnie, Accounting for Risk Aversion, Vesting, Job Termination Risk and Multiple Exercises in Valuation of Employee Stock Options (2007-08). Mathematical Finance, Vol. 19, Issue 1, pp. 99-128, January 2009. Available at SSRN: https://ssrn.com/abstract=1327438 or http://dx.doi.org/10.1111/j.1467-9965.2008.00359.x

Tim Leung (Contact Author)

University of Washington - Department of Applied Math ( email )

Lewis Hall 217
Department of Applied Math
Seattle, WA 98195
United States

HOME PAGE: http://faculty.washington.edu/timleung/

Ronnie Sircar

Princeton University - Department of Operations Research and Financial Engineering ( email )

Princeton, NJ 08544
United States

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