A Revisit to the Asymmetric Stochastic Volatility Models' Correlation Structures

Abstract

The asymmetric stochastic volatility (ASV) models extend the stochastic volatility model (SV) by modeling the correlation between the asset return and its volatility. We prove by simulation studies that fitting the ASV models may infer erroneous estimations of the correlation coefficients. Even if the true return-volatility correlation structure is different from the ASV models' specifications, the ASV models constantly provide significant correlation coefficients far from zero. The misidentification of the correlation parameter can be a significant issue considering that in-conclusive empirical evidence regarding the asymmetry has been documented, and the ASV model can only represent the general asymmetry according to its return-volatility correlation specification. The incorporation of ex-post volatility helps the ASV model to identify the true return-volatility correlation. Empirical evidence on major U.S. equity market indexes verifies that ASV models with ex-post volatility obtain significantly different estimations of the correlation parameters compared to the benchmark ASV models. Moreover, the inclusion of the ex-post volatility also significantly improves the ASV models in return density forecasting. It is necessary to include the ex-post volatility when estimating the ASV model.