Related papers: Semiparametric estimation for multivariate Hawkes …

We introduce a Cox-type model for relative intensities of orders flows in a limit order book. The model assumes that all intensities share a common baseline intensity, which may for example represent the global market activity. Parameters…

Multivariate Hawkes Processes (MHPs) are a class of point processes that can account for complex temporal dynamics among event sequences. In this work, we study the accuracy and computational efficiency of three classes of algorithms which,…

The Hawkes process has garnered attention in recent years for its suitability to describe the behavior of online information cascades. Here, we present a fully tractable approach to analytically describe the distribution of the number of…

Numerous studies grounded on Hawkes processes have been carried out in many fields including finance, biology and social network. Hawkes processes form a class of selfexciting simple point processes. In this article, we consider a general…

Hawkes processes have recently gained increasing attention from the machine learning community for their versatility in modeling event sequence data. While they have a rich history going back decades, some of their properties, such as…

We consider a 1-dimensional diffusion process X with jumps. The particularity of this model relies in the jumps which are driven by a multidimensional Hawkes process denoted N. This article is dedicated to the study of a nonparametric…

We consider the problem of estimating the parameters of a non-stationary Hawkes process with time-dependent reproduction rate and baseline intensity. Our approach relies on the standard maximum likelihood estimator (MLE), coinciding with…

Point processes are widely used statistical models for continuous-time discrete event data, such as medical records, crime reports, and social network interactions, to capture the influence of historical events on future occurrences. In…

We derive a semi-analytical pricing formula for European VIX call options under the Heston-Hawkes stochastic volatility model introduced in arXiv:2210.15343. This arbitrage-free model incorporates the volatility clustering feature by adding…

Classic estimation methods for Hawkes processes rely on the assumption that observed event times are indeed a realisation of a Hawkes process, without considering any potential perturbation of the model. However, in practice, observations…

We study a linear price impact model including other liquidity takers, whose flow of orders either follows a Poisson or a Hawkes process. The optimal execution problem is solved explicitly in this context, and the closed-formula optimal…

The self-exciting Hawkes process is widely used to model events which occur in bursts. However, many real world data sets contain missing events and/or noisily observed event times, which we refer to as data distortion. The presence of such…

This research attempts to model the stochastic process of trades in a limit order book market as a marked point process. We propose a semi-parametric model for the conditional distribution given the past, attempting to capture the effect of…

Multivariate Hawkes processes are past-dependant point processes originally introduced to model excitation effects, later extended to a nonlinear framework to account for the opposite effect, known as inhibition. Motivated by applications…

We adopt the interpretability offered by a parametric, Hawkes-process-inspired conditional probability mass function for the marks and apply variational inference techniques to derive a general and scalable inferential framework for marked…

The rise of "big data" has led to the frequent need to process and store datasets containing large numbers of high dimensional observations. Due to storage restrictions, these observations might be recorded in a lossy-but-sparse manner,…

We introduce a nonlinear modification of the classical Hawkes process, which allows inhibitory couplings between units without restrictions. The resulting system of interacting point processes provides a useful mathematical model for…

We introduce a Hawkes-like process and study its scaling limit as the system becomes increasingly endogenous. We derive functional limit theorems for intensity and fluctuations. Then, we introduce a high-frequency model for a price of a…

We investigate applications of deep neural networks to a point process having an intensity with mixing covariates processes as input. Our generic model includes Cox-type models and marked point processes as well as multivariate point…

We develop a Malliavin calculus for nonlinear Hawkes processes in the sense of Carlen and Pardoux. This approach, based on perturbations of the jump times of the process, enables the construction of a local Dirichlet form. As an…