Before revision:  We examine this paradox by questioning the validity of the assumption of linearity in the correlation . Nonlinear generalizations of the leverage effect are proposed within the  stochastic volatility framework in order to capture flexible correlation structures . Efficient Bayesian sequential computation is  implemented to estimate this effect in a practical, on-line manner.
After revision:  We examine this paradox , with the goal to improve density forecasts, by relaxing the assumption of linearity in the correlation . Nonlinear generalizations of the leverage effect are proposed within the stochastic volatility framework in order to capture flexible correlation structures . Efficient Bayesian sequential computation is implemented to estimate this effect in a practical, on-line manner.