Statistics methods applied in employee stock options

Abstract

This study presents model-based and compensation-based approaches to determining the price-subjective value of employee stock options (ESOs). In the model-based approach, we consider a utility-maximizing model in which the employees allocate their wealth among company stock, a market portfolio, and risk-free bonds, and then we derive the ESO formulas, which take into account illiquidity and sentiment effects. By using the method of change of measure, the derived formulas are simply like those of the market value with altered parameters. To calculate the compensation-based subjective value, we group employees by hierarchical clustering with a K-means approach and back out the option value in an equilibrium competitive employment market. Further, we test illiquidity and sentiment effects on ESO values by running regressions that consider the problem of standard errors in the finance panel data. Using executive stock options and compensation data paid between 1992 and 2004 for firms covered by the Compustat Executive Compensation Database, we find that subjective value is positively related to sentiment and negatively related to illiquidity in all specifications, consistent with the offsetting roles of sentiment and risk aversion. Moreover, executives value ESOs at a 48 % premium to the Black-Scholes value and ESO premiums are explained by a sentiment level of 12 % in risk-adjusted, annualized excess return, suggesting a high level of executive overconfidence.