Incentives from stock option grants: a behavioral approach
Résumé
This paper examines the incentives from stock options for loss-averse employees subject to probability weighting. Employing the certainty equivalence principle, I built on insights from Cumulative Prospect Theory (CPT) to derive a continuous time model to value options from the perspective of a representative employee. Consistent with a growing body of empirical and experimental studies (Lambert and Larcker, 2001; Hodge et al., 2006), the model predicts that the employee may overestimate the value of his options in-excess of their risk-neutral value. This is nevertheless in stark contrast with a common finding of standard models based on the Expected Utility Theory (EUT) framework that options value to a risk-averse undiversified employee is strictly lower than the value to risk-neutral outside investors. In particular, I proved that loss aversion and probability weighting have countervailing effects on the option subjective value. In addition, for typical setting of preferences parameters around the experimental estimates (Tversky and Kahneman, 1992; Abdellaoui, 2000), 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 that standard EUT-based models have difficulties accommodating their existence. The paper also examines the relationship between risk taking incentives and stock options and finds 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.
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