The Leverage Effect Puzzle under Semi-nonparametric Stochastic Volatility Models

This article extends the solution proposed by Aït-Sahalia, Fan, and Li for the leverage effect puzzle, which refers to a fact that empirical correlation between daily asset returns and the changes of daily volatility estimated from high frequency data is nearly zero. Complementing the analysis in Aït-Sahalia, Fan, and Li via the Heston model, we work with a generic semi-nonparametric stochastic volatility model via an operator-based expansion method. Under such a general setup, we identify a new source of bias due to the flexibility of variance dynamics, distinguishing the leverage effect parameter from the instantaneous correlation parameter. For estimating the leverage effect parameter, we show that the main results on analyzing the various sources of biases as well as the resulting statistical procedures for biases correction in Aït-Sahalia, Fan, and Li hold true and are thus indeed theoretically robust. For estimating the instantaneous correlation parameter, we developed a new nonparametric estimation method.