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

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 f or the volatility risk and correlation with the underlying process. A gener al solution of risk-neutral probabilities and price movements is derived, w hich avoids the common negative-probability problem in numerical-option pri cing with stochastic volatility. The empirical test shows clear evidence su pporting 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-vol atility model, but also has better prediction power. In addition, both mode ls perform well in the dynamic intraday hedging test. However, the constant -volatility model seems to have a slightly better hedging effectiveness. Th e profitability test shows that the stochastic volatility is able to captur e statistically significant profits while the constant volatility model pro duces losses. (C) 2000 John Wiley & Sons, Inc.