Estimation of Employee Stock Option Exercise Rates and Firm Cost: Methodology

Investors have become increasingly concerned about the cost of executive stock options to shareholders. Because executives face hedging constraints, standard option theory does not apply.The valuation problem reduces to accurately characterizing the option payoff. This paper develops a methodology for estimating option exercise and cancellation rates as a function of the stock price path, time to expiration, and firm and option holder characteristics. Our estimation accounts for correlation between exercises by the same executive. Valuation proceeds by using the estimated exercise rate function to describe the option’s expected payoff along each stock price path and then computing the present value of the payoff. The estimation of empirical exercise rates also allows us to test the predictions of theoretical models of option exercise behavior. The paper not only illustrates an ideal valuation method for a large dataset, but also shows how to evaluate the usefulness of some of the approximations proposed in the literature

Optimal Exercise of Executive Stock Options and Implications for Valuation

The cost of executive stock options to shareholders has become a focus of attention in finance and accounting. The difficulty is that the value of these options depends on the exercise policies of the executives. Because these options are nontransferable, the usual theory does not apply. We analyze the optimal exercise policy for a utility-maximizing executive and indicate when the policy is characterized by a critical stock price boundary. We provide a counterexample in which the executive exercises at low and high stock prices but not in between. We show how the policy varies with risk aversion, wealth, and volatility and explore implications for option value. For example, option value can decline as volatility rises

The Exercise and Valuation of Executive Stock Options

In theory, hedging restrictions faced by managers make executive stock options more difficult to value than ordinary options, because they imply that exercise policies of managers depend on their preferences and endowments. Using data on option exercises from 40 firms, this paper shows that a simple extension of the ordinary American option model which introduces random, exogenous exercise and forfeiture predicts actual exercise times and payoffs just as well as an elaborate utility-maximizing model that explicitly accounts for the nontransferability of options. The simpler model could therefore be more useful than the preference-based model for valuing executive options in practice

The Exercise and Valuation of Executive Stock Options

In theory, hedging restrictions faced by managers make executive stock options more difficult to value than ordinary options, because they imply that exercise policies of managers depend on their preferences and endowments. Using data on option exercises from 40 firms, this paper shows that a simple extension of the ordinary American option model which introduces random, exogenous exercise and forfeiture predicts actual exercise times and payoffs just as well as an elaborate utility-maximizing model that explicitly accounts for the nontransferability of options. The simpler model could therefore be more useful than the preference-based model for valuing executive options in practice

The Optimal Dynamic Investment Policy for A Fund Manager Compensated With An Incentive Fee

This paper solves the investment problem of a risk averse fund manager compensated with an incentive fee, a call option on the assets he controls. The optimal policy leads to all-or-nothing outcomes: the manager ends up either deep in or deep out of the money. The optimal trading strategy involves dynamically adjusting asset volatility as asset value changes. As assets grow large, the manager moderates portfolio risk. For example, if the manager has constant relative risk aversion, volatility converges to the Merton constant. On the other hand, as asset value goes to zero, portfolio volatility goes to infinity

The Optimal Dynamic Investment Policy for a Fund Manager Compensated with an Incentive Fee

We use martingale methods to solve the investment problem of a risk averse fund manager who charges an incentive fee which he cannot hedge in his personal account. An incentive fee is a share in the positive part of the returns on the client’s portfolio net of some benchmark return. The optimal policy is a long-shot; there is always some chance of bankrupting the client, but if the terminal fund value is nonzero, it is in the money by some strictly positive account. We provide explicit expressions for the optimal trading strategy with either the riskless asset or the market portfolio as benchmark and with either constant relative or absolute risk aversion. Rather than trying to maximize volatility, as earlier literature suggests, the manager dynamically adjusts volatility as the assets move in or out of the money. As the manager accumulates profits, he moderates portfolio risk. For example, if the manager has constant relative risk aversion, volatility converges to the Merton constant as fund value grows large. On the other hand, as bankruptcy approaches, portfolio volatility goes to infinity

The Valuation and Exercise of Executive Stock Options

Much has been made of the potential for hedging restrictions to reduce the value of executive stock options. We investigate this issue by comparing a rational utility-maximizing model that incorporates both hedging restrictions and an endogenous departure decision and a naïve value-maximizing model with an exogenous departure rate. While researchers mainly use these kinds of models to compute option values, we also use the models to generate forecasts of observable variables, the size and the timing of the payoffs of exercised options, and the annual rate at which options are canceled. We show that the naïve model provides just as good a description of actual exercise patterns of executives as the rational model in a sample of NYSE and AMEX firms. The more parsimonious naïve model may, there, be better for the purpose of valuation. The naïve incorporation of the exogenous departure rate in the standard America option model not only aligns predicted exercise and cancellation patterns with actual patterns, but also reduces option value by about a quarter

The Valuation and Exercise of Executive Stock Options

Much has been made of the potential for hedging restrictions to reduce the value of executive stock options. We investigate this issue by comparing a rational utility-maximizing model that incorporates both hedging restrictions and an endogenous departure decision and a naïve value-maximizing model with an exogenous departure rate. While researchers mainly use these kinds of models to compute option values, we also use the models to generate forecasts of observable variables, the size and the timing of the payoffs of exercised options, and the annual rate at which options are canceled. We show that the naïve model provides just as good a description of actual exercise patterns of executives as the rational model in a sample of NYSE and AMEX firms. The more parsimonious naïve model may, there, be better for the purpose of valuation. The naïve incorporation of the exogenous departure rate in the standard America option model not only aligns predicted exercise and cancellation patterns with actual patterns, but also reduces option value by about a quarter

Executive Stock Option Exercises and Inside Information

This paper examines whether corporate insiders use private information to time the exercises of their executive stock options. Prior to May 1991, insiders had to hold the stock they acquired through option exercise for six months. We find that exercises from this regulatory regime precede significantly positive abnormal stock returns. This suggests that insiders timed exercises so that the subsequent forced investment in the stock coincidedwith favorable price performance. By contrast, we find little evidence of the use of inside information to time exercises since the removal of the holding restriction in May 1991. When insiders can sell the acquired shares immediately, the use of private information should manifest itself as negative abnormal stock price performance following option exercise. However, only in the subsample of exercises by top managers at small firms, a tiny fraction of the full sample, do we find significantly negative post-exercise stock price performance after May 1991. We conclude that, in most cases, insiders' potential information advantage in timing exercises is not an important issue in valuing executive stock options