Are There Critical Levels of Stochastic Volatility for Early Option Exercise?

Abstract

An appealing feature of Heston's stochastic volatility model is that it captures empirical characteristics such as fat return tails, leverage and volatility clustering. Another is the resulting analytic European option pricing formula, which can be computed efficiently. However, the corresponding, and more common, American option pricing problem is significantly more complex. In this paper we propose an American option pricing technique that is not only computationally efficient but also highlights the role played by the equilibrium volatility associated with Heston's model for early exercise. Our approach combines an early exercise boundary approximation involving this (constant) equilibrium volatility, for which fast and accurate algorithms abound, with the price decomposition formula for American options in Heston's model. Numerical comparisons against recent alternative techniques show our approach to be far more efficient. We also conduct an empirical out-of-sample validation based on S&P 100 data that shows that our mixed approach does result in a model that generates prices close to actuals.