Executive Stock Options with Effort Disutility and Choice of Volatility∗

We consider the problem of an executive that receives call options as compensation in a dynamic setting. She can influence the stock price return with her effort. In addition, she determines the level of volatility of the stock through the choice of projects. The executive is risk-averse and experiences disutility from the effort. In this framework, we introduce the problem of the company that wants to maximize the final expected value of the price of the stock minus the cost of the compensation package. The company has to design a compensation package such that the executive reaches the minimum level of utility or opportunity cost (individual rationality constraint). We characterize the optimal strike price the company should choose, and compute it numerically for the logarithmic case. When the executive can affect the mean return of the stock, we find that in the vast majority of cases options should be granted outof-the-money. A key parameter in the model is the parameter that measures the quality of the projects. When this parameter is very high, it is optimal to grant stock rather than options. We distinguish between “large” companies, that emphasize the expected value of the stock, and “small” companies, that are more interested in keeping the cost of the compensation low. We find that stock is more likely to be the optimal contract for small companies.