Is a co-jump in prices a sparse jump?

Systematic co-jumps in asset prices are generally thought to account for only a small proportion of overall jumps. In actual observations, however, jumps in asset prices are often persistent, and the time of persistence varies. In this context, we develop a new rule to identify co-jumps and improve traditional tests by considering different sampling frequencies and different sampling starting points to re-evaluate the occurrence rate of systematic co-jumps in financial assets. We conduct a simulation experiment to show that the current test procedures generally underestimate the number of co-jumps when considering persistence, but that the proposed procedure can identify co-jumps more accurately. We also perform an empirical analysis using price data from the Shanghai 50 Index and its 25 constituent stocks in China’s stock market. The average proportion of systematic co-jumps detected by the improved s-BNS is approximately 30%, which shows that the co-jump and even the systematic co-jump are not sparse jumps. The results also reveal the shortcomings of traditional jump tests in estimating persistent jumps and demonstrate that the proposed method can better detect the possible nondiversifiable risks between market indices and their constituent stocks, thereby contributing to financial risk management.