Economics Insights @ CBS

Abstract: In many of the numerical methods for pricing American options based on the dynamic programming approach, the most computationally intensive part can be formulated as the summation of Gaussians. Though this operation usually requires O(NN') work when there are N' summations to compute and the number of terms appearing in each summation is N, we can reduce the amount of work to O(N+N') by using a technique called the fast Gauss transform.

We estimate the relation between stock option (ESO) grants to the top five executives and future earnings to examine whether incentive alignment or rent extraction by top managers explains option granting behavior. The future operating income associated with a dollar of Black-Scholes value of an ESO grant is $3.71. To understand the source of these positive payoffs, we parse out ESO grant values into components predicted by economic determinants of option grants, governance quality, and a residual grant value.

The push for increased transparency in financial reporting and corporate governance serves shareholders only up to a point. The problem of assessing the value of transparency to shareholders is subtle because both the level and pattern of earnings can convey information. Even when earnings management conceals information, it can be beneficial to shareholders. Distinguishing between ex ante and ex post efficiency underscores the advantages of achieving a balance between transparency and privacy in corporations.