An improved of Hull–White model for valuing Employee Stock Options (ESOs)

Employee stock options (ESOs) are call options granted by a company to its employees as a means to retain and to motivate them for working towards improvement of the company’s earning and management. ESOs have unique characteristics, such as: they have long maturity time, they are not tradable, and they can be exercised only after the vesting period. All these characteristics have significant implication on the valuation of ESOs. In this paper, we improve Hull–White ESO model using Bino-Trinomial tree method. We also modify a single psychological barrier on Hull–White model with moving psychological barriers based on empirical study that the ESO’s holders require the stock price to be at relatively high to induce voluntary exercise, yet later they will exercise at relatively low stock price near the time to maturity. Numerical experiments are given to verify the robustness of the proposed model and to analyze the sensitivity with respect to the model parameters. The ESO prices become cheaper if the holders degrade their psychological barriers.