The simultaneous occurrence of jumps in several stocks can be associated with major financial news, triggers short-term predictability in stock returns, is correlated with sudden spikes of the variance risk premium, and determines a persistent increase (decrease) of stock variances and...

Having observed a cluster of jumps produced by an exponential Hawkes process, we study and quantify the residual length of the cluster. We then formalize the stochastic increasingness property of the durations between two consecutive jumps, which strengthens their positive correlation. Finally...

Having observed a cluster of jumps in the discrete prices of a financial asset, and modeling the jump arrival times with an exponential Hawkes process, we study and quantify the probability that the cluster is going to produce further jumps. We also provide bounds for the probability of...

Having observed a cluster of jumps in the discrete prices of a financial asset, we study and quantify the probability that the cluster is going to produce further jumps.Modeling the jump arrival times with an exponential Hawkes process, we provide some bounds for the future stochastic jump...

Equi-spaced sampling is the norm in applied work using high-frequency data. Due to trade intermittency, however, this traditional sampling scheme amounts to implicit random sampling. Under implicit random sampling and on continuous trajectories, we quantify the asymptotic biases of even realized...