The VIX, VXO and realised volatility: a test of lagged and contemporaneous relationships

The VIX has traditionally been considered a forward indicator of realised volatility. This follows from its original formulation as the implied volatility of an option on the S%P 100 index and its later incarnation based on the fair price of a realised volatility swap. We focus on the related issue of Granger causality. Our results suggest that realised volatility Granger causes the VIX. In fact, it appears that the VIX lags realised volatility by about one month. Overall, our results are consistent with the notion that participants rely more on objective probabilities derived from past observations and less on future subjective probabilities. We also use threshold analysis to investigate asymmetric relationships between realised and implied volatility.