This paper aims to analyze the valuation of stock options from the perspective of an employee exhibiting preferences as described by cumulative prospect theory (CPT). In addition, it elaborates on their incentives effect and some implications in terms of design aspects.
The paper draws on the CPT framework to derive a continuous time model of the stock option subjective value using the certainty equivalence principle. Numerical simulations are used in order to analyze the subjective value sensitivity with respect to preferences‐related parameters and to investigate the incentives effect.
Consistent with a growing body of empirical and experimental studies, the model predicts that the employee may overestimate the value of his options in‐excess of their risk‐neutral value. Moreover, for typical setting of preferences parameters around the experimental estimates, and assuming the company is allowed to adjust existing compensation when making new stock option grants, the model predicts that incentives are maximized for strike prices set around the stock price at inception. This finding is consistent with companies’ actual compensation practices. Finally, the model predicts that an executive who is subject to probability weighting may be more prompted than a risk‐neutral executive to act in order to increase the firm's assets volatility.
This research proposes an alternative theoretical framework for the analysis of pay‐to‐performance sensitivity of equity‐based compensation that takes into account a number of prominent patterns of employee behavior that expected utility theory cannot explain. It contributes to recent empirical and theoretical researches that have advanced CPT framework as a promising candidate for the analysis of equity‐based compensation contracts.
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