While not a focus of our analysis, we also examine how option values from the
utility-based model compare to those calculated from a simple extended American
option pricing model with an exogenous stopping state. We examine the stopping
state model because Carpenter (1998) concludes that it calibrates well to the data and
produces objective values for ESOs that are similar to those produced by the more
elaborate utility model. See Carpenter for more details about the stopping state
model. In our sample, we find that the random stopping state model produces model forecasts of exercise behavior that are further away from the sample values when
compared to the utility-based model. Moreover, the objective option values from the
stopping state model are significantly different from those produced by the utility
model calibrations.