Co-jumps, co-jump tests, and volatility forecasting: Monte Carlo and empirical evidence

This study classifies jumps into idiosyncratic jumps and co-jumps to quantitatively identify systematic risk and idiosyncratic risk by utilizing high-frequency data. We found that systematic risk occurs more frequently and has larger magnitudes than the idiosyncratic risk in an individual asset, which indicates that volatilities from one sector are largely derived from the contagious effect of other sectors. We further investigated the importance of idiosyncratic jumps and co-jumps to predict the sector-level S&P500 exchange-traded fund (ETF) volatility. It was found that the predictive content of co-jumps is higher than that of idiosyncratic jumps, suggesting that systematic risk is more informative than idiosyncratic risk in volatility forecasting. Additionally, we carried out Monte Carlo experiments designed to examine the relative performances of the four co-jump tests. The findings indicate that the BLT test and the co-exceedance rule of the LM test outperform other tests, while the co-exceedance rule of the LM test has larger power and a smaller empirical size than that of the BLT test.