A comment of `Valuation of Executive Stock Options and the FASB Proposal'

Abstract

J N a recent FASB proposal, Swieringa (1987) tentatively concluded that executive stock options (ESOs) should be valued at fair values, with a lower bound constraint. In a recent article in this journal, Foster et al. (1991) argue that a candidate model to establish the fair value of an ESO is the Black-Scholes (B-S) call option pricing model with a constant, continuous dividend yield. The B-S model, however, misses one aspect of ESOs that is different from ordinary call options: ESOs have stochastic lives. That is, an ESO is personal and remains valid only for as long as the executive in question remains in the employ of the company that originally granted the ESO. The possibility that an ESO will not be exercised leads to a reduction in value, in comparison with an ordinary call option. Foster et al. (1991, 597) point out that this is a potentially severe departure from the assumptions of received option theory, and other authors have also noted this feature of ESOs (Noreen and Wolfson 1981, 385-86; Weygandt 1977, 48-49). The purpose of this comment is to show that ESOs can actually be valued in a fashion that explicitly incorporates their stochastic life feature if one can quantify the rate at which executives leave their current jobs. Our proposed valuation model reduces to the B-S model multiplied by the probability that the ESO will not be cancelled prior to expiration for the particular case of the ESO that can be exercised only upon termination. More complex cases must be handled through numerical methods. Section I of this comment outlines our valuation model. In section II, we consider the special case of an ESO that may not be exercised before expiration, and in section III, a more complex case that permits exercise before expiration. Section IV contains concluding remarks. Formally, our valution model is a partial differential equation subject to various initial and side conditions (just like the ordinary B-S model). A separate appendix contains the derivation of that partial differential equation. This comment is concerned with ESO valuation from the company's point of view. However, section IV includes a brief remark on valuation from the point of view of an individual executive.