Hawkes Graphs: The Analysis of Large Multitype Event Streams

Prof. Dr. Paul Embrechts

ETH Zurich

About the Speaker

Paul Embrechts is Professor of Mathematics at the ETH Zurich specialising in Actuarial Mathematics and Quantitative Risk Management.

Previous academic positions include the Universities of Leuven, Limburg and London (Imperial College). Dr. Embrechts has held visiting professorships at numerous universities and has an Honorary Doctorate from the University of Waterloo, the Heriot-Watt University, Edinburgh, and the Université Catholique de Louvain. He is an Elected Fellow of the Institute of Mathematical Statistics and the American Statistical Association, Honorary Fellow of the Institute and the Faculty of Actuaries, UK, and Institut des Actuaires, France and Member Honoris Causa of the Belgian Institute of Actuaries. He belongs to various national and international research and academic advisory committees.

He co-authored the influential books "Modelling of Extremal Events for Insurance and Finance", Springer, 1997, and "Quantitative Risk Management: Concepts, Techniques and Tools", Princeton University Press, 2005 and 2015.

Dr. Embrechts consults on issues in Quantitative Risk Management for financial institutions, insurance companies and international regulatory authorities.

Abstract

In this talk the Hawkes skeleton and the Hawkes graph are introduced. These objects summarize the branching structure of a multivariate Hawkes point process in a compact, yet meaningful way.

I demonstrate how graph-theoretic vocabulary is very convenient for the discussion of multivariate Hawkes processes. I also show how the graph view may be used for the specification and estimation of Hawkes models from large, multitype event streams. We pay special attention to computational issues in the implementation. This makes the results applicable to data with dozens of event streams and thousands of events per component.

A simulation study confirms that the presented procedure works as desired. The talk finishes with an application to the modeling of order book data in the context of high frequency finance. The results presented are based on joint work with Matthias Kirchner, RiskLab, ETH Zurich.