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 do not exhibit this correlation. We extend the standard linear correlation to a nonlinear generalization in order to capture the complex nature of this effect using a newly developed Bayesian sequential computation method. Examining 615 stocks that comprise the S&P500 and Nikkei 225, we find nearly all of the stocks to exhibit leverage effects, of which most 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.
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