Hawkes Processes

Neural Hawkes: Non-Parametric Estimation in High Dimension and Causality Analysis in Cryptocurrency Markets ArXiv ID: 2401.09361 “View on arXiv” Authors: Unknown Abstract We propose a novel approach to marked Hawkes kernel inference which we name the moment-based neural Hawkes estimation method. Hawkes processes are fully characterized by their first and second order statistics through a Fredholm integral equation of the second kind. Using recent advances in solving partial differential equations with physics-informed neural networks, we provide a numerical procedure to solve this integral equation in high dimension. Together with an adapted training pipeline, we give a generic set of hyperparameters that produces robust results across a wide range of kernel shapes. We conduct an extensive numerical validation on simulated data. We finally propose two applications of the method to the analysis of the microstructure of cryptocurrency markets. In a first application we extract the influence of volume on the arrival rate of BTC-USD trades and in a second application we analyze the causality relationships and their directions amongst a universe of 15 cryptocurrency pairs in a centralized exchange. ...

Uncovering Market Disorder and Liquidity Trends Detection ArXiv ID: 2310.09273 “View on arXiv” Authors: Unknown Abstract The primary objective of this paper is to conceive and develop a new methodology to detect notable changes in liquidity within an order-driven market. We study a market liquidity model which allows us to dynamically quantify the level of liquidity of a traded asset using its limit order book data. The proposed metric holds potential for enhancing the aggressiveness of optimal execution algorithms, minimizing market impact and transaction costs, and serving as a reliable indicator of market liquidity for market makers. As part of our approach, we employ Marked Hawkes processes to model trades-through which constitute our liquidity proxy. Subsequently, our focus lies in accurately identifying the moment when a significant increase or decrease in its intensity takes place. We consider the minimax quickest detection problem of unobservable changes in the intensity of a doubly-stochastic Poisson process. The goal is to develop a stopping rule that minimizes the robust Lorden criterion, measured in terms of the number of events until detection, for both worst-case delay and false alarm constraint. We prove our procedure’s optimality in the case of a Cox process with simultaneous jumps, while considering a finite time horizon. Finally, this novel approach is empirically validated by means of real market data analyses. ...

Investigating Short-Term Dynamics in Green Bond Markets ArXiv ID: 2308.12179 “View on arXiv” Authors: Unknown Abstract The paper investigates the effect of the label green in bond markets from the lens of the trading activity. The idea is that jumps in the dynamics of returns have a specific memory nature that can be well represented through a self-exciting process. Specifically, using Hawkes processes where the intensity is described through a continuous time moving average model, we study the high-frequency dynamics of bond prices. We also introduce a bivariate extension of the model that deals with the cross-effect of upward and downward price movements. Empirical results suggest that differences emerge if we consider periods with relevant interest rate announcements, especially in the case of an issuer operating in the energy market. ...