The Dynamics of Price Jumps in the Stock Market : An Empirical Study on Europe and U.S

We study the bivariate jump process involving the S&P 500 and the Euro Stoxx 50 with jumps extracted from high frequency data using non-parametric methods. Our analysis, based on a generalized Hawkes process, reveals the presence of self-excitation in the jump activity which is responsible for jump clustering but has a very small persistence in time. Concerning cross-market effects, we find statistically significant co-jumps occurring when both markets are simultaneously operating but no evidence of contagion in the jump activity, suggesting that the role of jumps in volatility transmission is negligible. Moreover, we find a negative relationship between the jump activity and the continuous volatility indicating that jumps are mostly detected during tranquil market conditions rather than in periods of stress. Importantly, our empirical results are robust under different jump detection methods