The dynamics of stochastic volatility: evidence from underlying and options markets

This paper proposes and estimates a more general parametric stochastic variance model of equity index returns than has been previously considered using data from both underlying and options markets. I conclude that the square root stochastic variance model of Heston (Rev. Financial Stud. 6 (1993) 327) is incapable of generating realistic returns behavior, and that the data are better represented by a stochastic variance model in the CEV class or a model with a time-varying leverage effect. As the level of market variance increases, the volatility of market variance increases rapidly and the leverage effect becomes substantially stronger. The heightened heteroskedasticity in market variance that results causes returns to display unconditional skewness and kurtosis much closer to their sample values, while the model falls short of explaining the implied volatility smile for short-dated options and conditional higher moments in returns.