We discuss generalizing the correlation between an asset's return and its volatility-- the leverage effect-- in the context of stochastic volatility. While it is a long standing consensus that leverage effects exist, empirical evidence paradoxically show that most individual stocks either do not exhibit this correlation or are very weak. This, at least partially, is due to an assumption that the correlationis linear, i. e., the effect of large shocks and small fluctuations changes linearly. We relax this standard assumption of linear correlation to a nonlinear generalization in order to capture the complex nature of this effect using a newly developed Bayesian sequential computation method that is fast, efficient, and on-line  . Examining 615 stocks that comprise the S  P500 and Nikkei 225, we find nearly all of the stocks to exhibit leverage effects, of which many would have been lost under the standard linear assumption. We further the analysis by exploring whether there are clear traits that characterize the complexity of the leverage effect and find that different countries and certain sectors to have tendencies for more complex leverage effects.\\%DIF > of all stocks exhibit general leverage effects. In contrast, under the linear assumption we find nearly half of the stocks to have no leverage effects. We further the analysis by exploring whether there are clear traits that characterize the complexity of the leverage effect. We find that there are country and some industry effects that help explain leverage complexity.
 While it is a long standing consensus that leverage effects exist, empirical evidence paradoxically show that most individual stocks do not exhibit this correlation . 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 . Examining 615 stocks that comprise the S \& P500 and Nikkei 225, we find that 89\\%DIF > of all stocks exhibit general leverage effects. In contrast, under the linear assumption we find nearly half of the stocks to have no leverage effects. We further the analysis by exploring whether there are clear traits that characterize the complexity of the leverage effect. We find that there are country and some industry effects that help explain leverage complexity.
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We discuss generalizing the correlation between an asset's return and its volatility-- the leverage effect-- in the context of stochastic volatility.
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nearly all of the stocks to exhibit leverage effects, of which many would have been lost under the standard linear assumption. We further the analysis by exploring whether there are clear traits that characterize the complexity of the leverage effect and find that different countries and certain sectors to have tendencies for more complex leverage effects.
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