Exact simulation of Hawkes process with exponentially decaying intensity

By Angelos Dassios, Hongbiao Zhao. 2013

134 citations recorded by the source corpus.

We introduce a numerically efficient simulation algorithm for Hawkes process with exponentially decaying intensity, a special case of general Hawkes process that is most widely implemented in practice. This computational method is able to exactly generate the point process and intensity process, by sampling interarrival-times directly via the underlying analytic distribution functions without numerical inverse, and hence avoids simulating intensity paths and introducing discretisation bias. Moreover, it is flexible to generate points with either stationary or non-stationary intensity, starting from any arbitrary time with any arbitrary initial intensity. It is also straightforward to implement, and can easily extend to multi-dimensional versions, for further applications in modelling contagion risk or clustering arrival of events in finance, insurance, economics and many other fields. Simulation algorithms for one dimension and multi-dimension are represented, with numerical examples of univariate and bivariate processes provided as illustrations.

Subfields: Applied Mathematics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/fed5e22c2c5cfbacb89c2c6c60e96e37ffb9b28f

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In Applied Mathematics

In Molecular Biology

Citations in the corpus

Hawkes Processes in Finance (2015, methodology): “A short survey and a more comprehensive list of references can be found in the recent work [24].”
Reliability for systems with self-healing effect under shock models (2018, background): “Hawkes process: the reader can refer to Møller and Rasmussen (2005), Dassios and Zhao (2013). Case 4.”