Accounting for risk aversion, vesting, job termination risk and multiple exercised in valuation of employee stock options

Tim Leung, Ronnie Sircar

Research output: Contribution to journalArticle

50 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)99-128
Number of pages30
JournalMathematical Finance
Volume19
Issue number1
DOIs
StatePublished - Jan 1 2009

All Science Journal Classification (ASJC) codes

  • Accounting
  • Finance
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Applied Mathematics

Keywords

  • American options
  • Employee stock options
  • Reaction-diffusion equations
  • Risk aversion

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