Every option-valuation approach makes assumptions about the behavior employees will follow when exercising their options. Consider the binomial tree in Figure 20.1. In a large number of cases, the option is in the money and exercisable, and it is up to the employee to decide when to exercise. But to make the valuing of options manageable, some assumptions must be made about the circumstances under which exercise occurs.

Assumptions about Exercise

One of the major insights underpinning the traditional Black–Scholes model for traded options is that one can infer optimal exercise. In particular, for options that are tradable on non-dividend-paying stocks, early exercise is generally not optimal.7 As a result, for most traded options, exercise can be assumed to occur whenever the option is in the money at the end of its life, and no earlier. Therefore, option valuations can be developed based on forecasting stock price paths through to option expiration, attaching probabilities, and discounting back to the present. In terms of Figure 20.1, that assumption would imply exercise in all cases in the 10th year (conditional on the option being in the money).

In part, the optimality of exercise only at maturity reflects the fact that, besides being exercised, publicly traded options can be sold or hedged, so an individual’s risk profile and liquidity needs do not enter into the calculation. Conversely, employee stock options generally cannot be sold, and employees ...

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