Electronic Communications in Probability

Exact simulation of Hawkes process with exponentially decaying intensity

Angelos Dassios and Hongbiao Zhao

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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.

Article information

Electron. Commun. Probab., Volume 18 (2013), paper no. 62, 13 pp.

Accepted: 15 July 2013
First available in Project Euclid: 7 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G55: Point processes
Secondary: 60H35: Computational methods for stochastic equations [See also 65C30] 65C05: Monte Carlo methods 60G17: Sample path properties

Contagion risk Stochastic intensity model Self-exciting point process Hawkes process Hawkes process with exponentially decaying intensity Exact simulation Monte Carlo simulation

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Dassios, Angelos; Zhao, Hongbiao. Exact simulation of Hawkes process with exponentially decaying intensity. Electron. Commun. Probab. 18 (2013), paper no. 62, 13 pp. doi:10.1214/ECP.v18-2717. https://projecteuclid.org/euclid.ecp/1465315601

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