acknowledged. We also wish to thank the two reviewers for useful comments. All correspon-

This paper is the first attempt to empirically test a numerical solu-tion to price American options under stochastic volatility. The model allows for mean reverting stochastic volatility process with non-zero risk premium for the volatility risk and correlation with the underlying pro-cess. A general solution of risk-neutral probabilities and price movements is derived, which avoids the common negative probability problem in nu-merical option pricing with stochastic volatility. The empirical test shows clear evidences 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 test and the out-of-sample test. It not only eliminates systematic money-ness 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. ∗Both authors are from the National University of Singapore, Centre for Financial Engi-neering. Financial support from the Institute of High Performance Computing is gratefull