Executive Stock Option Valuation Under Multiple Severance Risks

Executive stock option (ESO) grants have a number of important features that do not conform with the Black-Scholes model. This paper presents a risk-neutral model for valuing such options where the holder is exposed to multiple severance risks (e.g. termination with cause, without cause, mortality) with varying cause-contingent ex-severance payoffs and stock holding restrictions. We find that Black-Scholes significantly overestimates the cost of ESOs to the firm (e.g. 28-39% for a severance rate of 5%) and the bias is inversely related to volatility. For valuation, we construct a multi-severance binomial ESO (MSB-ESO) model and identify the corresponding multi-severance partial differential equation. The severance event is modeled using a flexible doubly stochastic Poisson process which permits rich information structures between state variables and the severance event to be endogenously captured in the valuation