A simulation-based algorithm for American executive stock option valuation

Abstract

We present an algorithm that merges a certainty-equivalence framework with the least-squares Monte Carlo algorithm to obtain the executive stock option (ESO) value for a risk-averse and undiversified agent. We account for the difference between executive’s value and firm cost of the ESO. We show how early-exercise decisions depend on executive’s preferences and its diversification degree. Because of the algorithm flexibility, it allows for multiple state-variables. As an example, we consider the case of indexed ESOs revealing a significant improvement in terms of executive’s discount respect to fixed strike ESOs.