Executive Stock and Option Valuation in a Two State-Variable Framework: Allowing Optimal Investment of Outside Wealth in the Riskfree Asset and the Market Portfolio

Abstract

We provide a two state-variable discrete-time executive option valuation model that allows optimal investment of executive's outside wealth in the riskfree asset and the market portfolio. Our model adopts Rubinstein (1994) rainbow option pricing grid and leads to several improvements over the existing one state-variable models that allow outside investment only in the riskfree asset. First, our model is consistent with portfolio theory and the capital asset pricing model. Second, it produces executive option values that are always lower than risk-neutral values. Third, it implies less subjective values as it gives significantly lower sensitivities of option values to the unobservable expected market risk premium, executive's risk aversion, and the executive's diversification level. Fourth, we show that for common parameter values the executive values in our model are significantly lower than in the one state-variable model, but the company costs are not much lower. This suggests that options are an even more inefficient form of executive compensation than previously documented. Fifth, we show that our methodology can be easily applied to the valuation of American-style indexed strike price executive options.