Before revision: We show that, for a class of mean-reverting models , the correlation function of stochastic variance (squared volatility) contains only one -- relaxation -- parameter. We generalize and simplify the expression for leverage for this class of models. We apply our results to specific examples of such models -- multiplicative, Heston , and combined multiplicative-Heston -- and use historic stock market data to obtain parameters of their steady-state distributions and cross-correlations between Weiner processes in the models for stock returns and stochastic variance .
After revision: We show that, for a class of mean-reverting models for stochastic variances. We derive closed-form expressions for the correlation functions and leverage for a general form of the stochastic term. We also discuss correlation functions and leverage for three specific models -- multiplicative, Heston , and combined multiplicative-Heston -- and use historic stock market data to obtain parameters of their steady-state distributions and cross-correlations between Weiner processes in the models for stock returns and stochastic variance .