American GARCH Employee Stock Option Valuation

Abstract

We implement a new and flexible simulation based approach for the fair value of Employee Stock Option (ESO) plans to value American options in order to consider the common ESO characteristics of vesting period, departure risk and voluntary suboptimal early exercise. We introduce GARCH effects on the underlying asset and we analyze the price bias with respect to the constant volatility case. We also find a significant bias if we value the ESO using a short-memory GARCH model instead of a long-memory one. We also develop a sensitivity analysis with respect to changes in several ESO characteristics. We compare this valuation with FAS 123 method using the implicit expected life of the ESO revealing a FAS overvaluation. Finally, we value a real ESO plan providing the confidence intervals for the estimated ESO prices.