Valuation Techniques: Discounted Cash Flow, Earnings Quality, Measures of Value Added, and Real Options

CONCLUSION

Empirical evidence and financial theory suggest that employees considering exercise of an ESO make a trade-off between option value captured and time value forgone. We have proposed a new ESO-pricing lattice model that explicitly recognizes and accounts for this reality. We demonstrated the properties of our μ model and showed why it is less prone to bias than an L or M model when parameter inputs are calculated from historical observations of voluntary exercise behaviors.

Using a well-known power utility model of employee exercise behavior (Carpenter 1998) as a benchmark confirmed our intuitions. Depending on the stock price path, L, M, and μ estimated from a single voluntary exercise can lead to any of the three heuristic models yielding the lowest or highest ESO price estimate. On average, however, across all possible price paths, the μ model most accurately approximates the objective ESO values generated by the Carpenter model. Because the μ values determined from past exercise observations are less sensitive to the particular historical stock price path traveled than are L and M values, estimates from the μ model have much smaller mean squared deviations from objective ESO values for reasonable parameters of risk aversion and option specifications. The L model (or modified Black–Scholes model) is particularly prone to significantly underestimating option values. The M model may be adequate for practical purposes in some circumstances, but it is potentially vulnerable ...