Although exercise prices for executive stock options can be set either below or above the grant-date market price, in practice virtually all options are granted at the money. We offer an economic rationale for this apparent puzzle, by showing that pay-to-performance incentives for risk-averse...

A new options-pricing formula applies to far-out-of-the money put options on the overall stock market when disaster risk is the dominant force, the size distribution of disasters follows a power law, and the economy has a representative agent with Epstein-Zin utility. In the applicable region,...

We investigate the importance of ambiguity, or Knightian uncertainty, in executives' decisions about when to exercise stock options. We develop an empirical estimate of ambiguity and include it in regression models alongside the more traditional measure of risk, equity volatility. We show that...

We examine how an increase in stock option grants affects CEO risk-taking. The overall net effect of option grants is theoretically ambiguous for risk-averse CEOs. To overcome the endogeneity of option grants, we exploit institutional features of multi-year compensation plans, which generate two...

The dramatic rise in CEO compensation during the 1990s and early 2000s is a longstanding puzzle. In this paper, we show that much of the rise can be explained by a tendency of firms to grant the same number of options each year. Number-rigidity implies that the grant-date value of option awards...

We analyze the long-run trends in executive compensation using a new panel dataset of top executives in large publicly-held firms from 1936 to 2005, collected from corporate reports. This historic perspective reveals several surprising new facts that conflict with inferences based only on data...

This paper develops an account of the role and significance of rent extraction in executive compensation. Under the optimal contracting view of executive compensation, which has dominated academic research on the subject, pay arrangements are set by a board of directors that aims to maximize...

Detailed data about stock option contracts are used to measure and analyze the pay to performance incentives of executive stock options. Two main issues are addressed. The first is the pay to performance incentives created by the revaluation of stock option holdings. The findings suggest that if...