Pricing executive stock options under employment shocks

Abstract

We obtain explicit expressions for the subjective, objective and market value of perpetual executive stock options (ESOs) under exogenous employment shocks driven by an independent Poisson process. Previously, we obtain the executive's optimal exercise policy from the subjective valuation that is necessary for the objective one, or fair value. The perpetual ESO is compared with the true finite maturity ESO finding that the approximation is reasonably good. To illustrate the usefulness of the objective valuation for accounting purposes, we analyze the statistical distribution of the fair value when there is uncertainty about the employment shock intensity. Finally, the role of ESOs in the design of executives’ incentives is also discussed.