Pricing American options with stochastic volatility: Evidence from S&P 500 futures options

Abstract

This article is the first attempt to test empirically a numerical solution to price American options under stochastic volatility. The model allows for a mean-reverting stochastic-volatility process with non-zero risk premium for the volatility risk and correlation with the underlying process. A general solution of risk-neutral probabilities and price movements is derived, which avoids the common negative-probability problem in numerical-option pricing with stochastic volatility. The empirical test shows clear evidence supporting the occurrence of stochastic volatility. The stochastic-volatility model outperforms the constant-volatility model by producing smaller bias and better goodness of fit in both the in-sample and out-of-sample test. It not only eliminates systematic moneyness bias produced by the constant-volatility model, but also has better prediction power. In addition, both models perform well in the dynamic intraday hedging test. However, the constant-volatility model seems to have a slightly better hedging effectiveness. The profitability test shows that the stochastic volatility is able to capture statistically significant profits while the constant volatility model produces losses. © 2000 John Wiley & Sons, Inc.