High-Frequency Causality between Stochastic Volatility Time Series: Empirical Evidence

We study the role of linear causality between multivariate financial time series and their derivatives. Due to the shortcomings of statistical inferences for stochastic volatility models, the dynamics of the volatility expectation index VIX remain controversial. Leveraging intraday data using seemingly unrelated regression equations with a bivariate firstorder vector autoregression model, we discover novel empirical results describing their interaction. We find bidirectional causality between the VIX spot and the implied volatility of Standard & Poor’s 500 options, suggesting a volatility feedback effect. The spot index tends to be lagging its future derivatives, while our error correction mechanism reveals a significant mean-reverting equilibrium relationship. The evidence is consistent with recent theories indicating that volatility expectation has stronger feedback than realized volatility. The paper reveals a retroactive information flow and highlights novel insights behind this microstructure.