Pricing executive stock options under employment shocks

Resumen

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. Within this setup,we obtain the executive's optimal exercise policy which allows us to analyze the determinants of both, the subjective valuation by executives and the objective valuation by firms. The perpetual ESO is compared with the more realistic finite maturity ESO finding that the approximation is reasonably good. We also use the objective valuation's results for accounting purposes. Further,we analyze the objective valuation distribution when there is uncertainty about the employment shock parameter. Finally, the role of ESOs in the design of executive's incentives is also discussed.