Executive Stock Options: Value to the Executive and Cost to the Firm

Abstract

We develop a continuous time utility-based model for valuing executive stock options (ESOs). We solve for the optimal exercise policy and the value of ESOs from an executive's perspective. Assuming ESOs to be perpetual and the executive to have Constant Absolute Risk Aversion, we derive explicit formulas for the optimal exercise price and the executive's value of a vested ESO. We also prove the verification theorem for the optimal stopping problem related to this valuation. Using the optimal exercise policy that emerges, we derive a simple formula for the cost of ESOs to the firm at the grant date. From an accounting perspective, this cost formula has the advantage of being transparent and straightforward to implement using data on previous ESO exercises. Using numerical analysis, we find that our model may provide cost estimates significantly lower than cost estimates found using the Black-Scholes-Merton model, especially for firms with low expected returns and high volatilities.