Self-exciting spatio-temporal point process models predict the rate of events as a function of
space, time, and the previous history of events. These models naturally capture triggering …

In this paper we propose an overview of the recent academic literature devoted to the
applications of Hawkes processes in finance. Hawkes processes constitute a particular class …

Long-memory, or more generally fractal, processes are known to play an important role in
many scientific disciplines and applied fields such as physics, geophysics, hydrology …

Oil markets are subject to extreme shocks (eg Iraq's invasion of Kuwait), causing the oil
market price exhibits extreme movements, called jumps (or spikes). These jumps pose …

Limit order books (LOBs) match buyers and sellers in more than half of the world's financial
markets. This survey highlights the insights that have emerged from the wealth of empirical …

We introduce a new stochastic model for the variations of asset prices at the tick-by-tick level
in dimension 1 (for a single asset) and 2 (for a pair of assets). The construction is based on …

We introduce a measure of activity of financial markets that provides a direct access to their
level of endogeneity. This measure quantifies how much of price changes is due to …

In the context of statistics for random processes, we prove a law of large numbers and a
functional central limit theorem for multivariate Hawkes processes observed over a time …

We define a numerical method that provides a non-parametric estimation of the kernel
shape in symmetric multivariate Hawkes processes. This method relies on second order …

We introduce a multivariate Hawkes process that accounts for the dynamics of market prices
through the impact of market order arrivals at microstructural level. Our model is a point …