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Clustering Effects via Hawkes Processes

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From Probability to Finance

Part of the book series: Mathematical Lectures from Peking University ((MLPKU))

Abstract

Hawkes processes are a class of self-exciting point processes. They are characterized by the presence of clusters of jumps, which can be found in many natural phenomena (from biology to seismology) as well as in finance. First, we study the general properties of point processes. Then, we propose a constructive approach to Hawkes processes. Main properties as well as extensions are also studied. Special attention has been paid to the application of Hawkes processes in finance. We also propose to illustrate theses processes as a special case of branching processes with immigration.

Bernis—The analysis and views expressed in this chapter are those of the authors and do not necessarily reflect those of Natixis Assurances.

Scotti—This research is supported by Institute Europlace de Finance, research program “Clusters and Information Flow: Modelling, Analysis and Implications”.

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Author information

Authors and Affiliations

  1. Natixis Assurances, Paris, France

    Guillaume Bernis

  2. LPSM - Université Paris Diderot, 8 place Aurélie Nemours, 75013, Paris, France

    Simone Scotti

Authors
  1. Guillaume Bernis
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  2. Simone Scotti
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Correspondence to Simone Scotti .

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Editors and Affiliations

  1. Institut de Science Financière et d’Assurances, Université Claude Bernard Lyon 1, Lyon, France

    Ying Jiao

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Bernis, G., Scotti, S. (2020). Clustering Effects via Hawkes Processes. In: Jiao, Y. (eds) From Probability to Finance. Mathematical Lectures from Peking University. Springer, Singapore. https://doi.org/10.1007/978-981-15-1576-7_3

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