On the modeling of employee voluntary early exercise for the valuation of employee stock options

Abstract

Employee Stock Options (ESOs) are call options granted by a company to its employees on the stock of the company. ESOs are an important part of company compensation and the valuation of these options has become a focus attention in finance and accounting. ESOs have special characteristics, such as: they are not tradable; they can be exercised only after the vesting period; if employees leave the company during the vesting period then the ESOs are forfeited. So valuing these options using Black-Scholes framework is less appropriate. This paper extends the model proposed by Brisley and Anderson to account for the restricted set of possible exercise dates (Bermudan style) and the state-dependent employee exit rate. We analyze the optimal early exercise decision by risk neutral valuation model. Then the price of ESOs is computed using Monte Carlo method. The Monte Carlo method is flexible and easy to implement and modify. We also analyze ESOs properties and sensitivity with respect to the model parameters.