Efficient Simulation of Clustering Jumps with CIR Intensity

Angelos Dassios () and Hongbiao Zhao ()
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Angelos Dassios: Department of Statistics, London School of Economics, London WC2A 2AE, United Kingdom
Hongbiao Zhao: School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, China

Operations Research, 2017, vol. 65, issue 6, 1494-1515

Abstract: We introduce a broad family of generalised self-exciting point processes with CIR-type intensities, and we develop associated algorithms for their exact simulation. The underlying models are extensions of the classical Hawkes process, which already has numerous applications in modelling the arrival of events with clustering or contagion effect in finance, economics, and many other fields. Interestingly, we find that the CIR-type intensity, together with its point process, can be sequentially decomposed into simple random variables, which immediately leads to a very efficient simulation scheme. Our algorithms are also pretty accurate and flexible. They can be easily extended to further incorporate externally excited jumps, or, to a multidimensional framework. Some typical numerical examples and comparisons with other well-known schemes are reported in detail. In addition, a simple application for modelling a portfolio loss process is presented.

Keywords: contagion risk; jump clustering; stochastic intensity model; self-exciting point process; self-exciting point process with CIR intensity; Hawkes process; CIR process; square-root process; exact simulation; Monte Carlo simulation; portfolio risk (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (16)

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