Content area
Full Text
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. (C) 2000 JohnWiley & Sons, Inc. Jrl Fut Mark 20:625-659, 2000
(ProQuest Information and Learning: ... denotes formulae omitted.)
INTRODUCTION
Option pricing is one of the most exciting areas in modern financial research. Ever since the famous Black and Scholes (1973) study, there are many extensions and modifications to the option-pricing model. One of the most important developments in this area is the assumption of stochastic volatility. Wiggins (1987), Hull and White (1987), Scott (1987), Johnson and Shanno (1987), and Stein and Stein (1991)use different techniques such as finite difference, series solution, Monte Carlo simulations, and Feynman-Kac function, and so on to model and test models with stochastic volatility. Heston (1993) introduces the first closed-form solution for stochastic-volatility models with applications to Europeanstyle options.
Stochastic-volatility models address some of the issues such as volatility smiles and skewness, as well as large kurtosis in the underlying distribution. Finucane and Tomas (1996) developed a lattice method to price American-call options. They used interpolations to find out the option prices on the lattice, so recombining nodes on the tree is not an issue in their model. Furthermore, the model is able to calculate several option prices with different underlying asset prices and volatilities from the same lattice as long as the time...