 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.abstract %DIF > of all stocks compared to the conventional model assumption.
The leverage effect-- the correlation between an asset's return and its volatility-- has played a key role in forecasting and understanding volatility and risk. While it is a long standing consensus that leverage effects exist and improve forecasts , empirical evidence paradoxically do not show that most individual stocks exhibit this phenomena, mischaracterizing risk and therefore leading to poor predictive performance . We examine this paradox , with the goal to improve density forecasts, by relaxing the assumption of linearity in the leverage effect . Nonlinear generalizations of the leverage effect are proposed within the Bayesian stochastic volatility framework in order to capture flexible leverage structures, where small fluctuations in prices have a different effect from large shocks . Efficient Bayesian sequential computation is developed and 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 relaxing the linear assumption to our proposed nonlinear leverage effect function improves predictive performances for 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.abstract %DIF > of all stocks compared to the conventional model assumption.
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The leverage effect-- the correlation between an asset's return and its volatility-- has played a key role in forecasting and understanding volatility and risk.
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and improve forecasts
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do not
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do not exhibit this correlation
exhibit this phenomena, mischaracterizing risk and therefore leading to poor predictive performance
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by questioning the validity of the
, with the goal to improve density forecasts, by relaxing the
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correlation
leverage effect
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Bayesian
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correlation structures
leverage structures, where small fluctuations in prices have a different effect from large shocks
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developed and
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relaxing the linear assumption to our proposed nonlinear leverage effect function improves predictive performances for