Probabilities and Values of Early Exercise

Abstract

This article analyzes fundamental differences between American spot and futures options. These options differ in their early exercise probabilities and values, and in option buyers' exercise behavior. We find two key results: one theoretical and one empirical. First, unlike spot options, some futures options' early exercise probabilities and values do not correspond. Specifically, increased volatility raises the early exercise premium for in-the-money futures calls, but lowers the associated early exercise probability. Similarly, increasing the domestic interest rate raises the futures put early exercise premium, while lowering the associated early exercise probability. Second, observed early exercise experience of Philadelphia Stock Exchange spot options and Chicago Mercantile Exchange futures options is consistent with optimal early exercise behavior prescribed by a standard American option pricing model. Both types of option exercise events occur at or near the modeled early exercise boundaries.