Unveiling Bidirectional Forecasting Between Volatility of VIX and Stock Market: Insights From Asymmetric Jumps and Cojumps

This study explores the bidirectional forecasting between the realized volatility of VIX and S&P 500 index, especially the impact of asymmetric jumps and cojumps. Empirical results show that stock market jumps contain positive content for predicting the realized volatility of VIX while jumps contained in VIX can also improve predictive power for the realized volatility of the stock market. The positive and negative jumps of stock market and VIX have different asymmetric effects on realized volatility forecasts. Specifically, the negative jumps of stock index performs better whereas the positive jumps of VIX have stronger forecasting power, and each contains incremental information about the volatility prediction of the other party. Moreover, the cojumps enhance the forecasting ability, especially for the realized volatility prediction of VIX.