[We introduce a model that captures the main properties that characterize employee stock options (ESO). We discuss the likelihood of early voluntary ESO exercise, and the obligation to exercise immediately if the employee leaves the firm, except if this happens before options are vested, in which case the options are forfeited. We derive an analytic formula for the price of the ESO and in a case study compare it to alternative methods.]
[We determine the minimum cost of superreplicating a nonnegative contingent claim when there are convex constraints on portfolio weights. We show that the optimal cost with constraints is equal to the price of a related claim without constraints. The related claim is a dominating claim, that is, a claim whose payoffs are increased in an appropriate way relative to the original claim. The results hold for a variety of options, including some path-dependent options. Constraints on the gamma of the replicating portfolio, constraints on portfolio amounts, and constraints on the number of shares are also considered.]
We derive a closed-form solution for the optimal portfolio of a nonmyopic utility maximizer who has incomplete information about the alphas or abnormal returns of risky securities. We show that the hedging component induced by learning about the expected return can be a substantial part of the demand. Using our methodology, we perform an "ex ante" empirical exercise, which shows that the utility gains resulting from optimal allocation are substantial in general, especially for long horizons, and an "ex post" empirical exercise, which shows that analysts' recommendations are not very useful.
We introduce a model that captures the main properties that characterize employee stock options (ESO). We discuss the likelihood of early voluntary ESO exercise, and the obligation to exercise immediately if the employee leaves the firm, except if this happens before options are vested, in which case the options are forfeited. We derive an analytic formula for the price of the ESO and in a case study compare it to alternative methods. Since the mid-1980s, stock options have been a substantial component of com-pensation packages for employees. For example, in 1999, 94 % of companies in the S&P 500 offered stock options to their top employees (see Murphy, 1999; Hall and Murphy, 2002). In 1995, the Financial Accounting Standards Board (FASB) (with FAS 123) set a standard that required firms to expend stock-based compensation at the moment the compensation was granted (see FASB, 1995). Firms were encour-aged to use the “fair value ” of the stock option to compute the value of the compensation, but were allowed to use the “intrinsic value”—market price of the stock minus strike price. Since employee stock options (ESOs) are typically granted at the money, the intrinsic value is zero, which results in no expense recorded at the time of the grant, and this is probably one of the reasons that helped their popularity.
We derive a closed-form solution for the optimal portfolio of a nonmyopic utility maximizer who has incomplete information about the alphas or abnormal returns of risky securities. We show that the hedging component induced by learning about the expected return can be a substantial part of the demand. Using our methodology, we perform an “ex ante” empirical exercise, which shows that the utility gains resulting from optimal allocation are substantial in general, especially for long horizons, and an “ex post” empirical exercise, which shows that analysts’ recommendations are not very useful.