Efficient Simulation of Clustering Jumps with CIR Intensity

Operations Research, 65(6), 1494-1515, 2017

40 Pages Posted: 30 Jan 2018

See all articles by Angelos Dassios

Angelos Dassios

London School of Economics & Political Science (LSE) - Department of Statistics

Hongbiao Zhao

Shanghai University of Finance and Economics; London School of Economics & Political Science (LSE)

Date Written: November 8, 2017

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

JEL Classification: C15, C53, C63

Suggested Citation

Dassios, Angelos and Zhao, Hongbiao, Efficient Simulation of Clustering Jumps with CIR Intensity (November 8, 2017). Operations Research, 65(6), 1494-1515, 2017, Available at SSRN: https://ssrn.com/abstract=3070860

Angelos Dassios

London School of Economics & Political Science (LSE) - Department of Statistics ( email )

Houghton Street
London, England WC2A 2AE
United Kingdom

Hongbiao Zhao (Contact Author)

Shanghai University of Finance and Economics ( email )

No. 777 Guoding Road
Yangpu District
Shanghai, Shanghai 200433
China

HOME PAGE: http://hongbiaozhao.weebly.com/

London School of Economics & Political Science (LSE)

Houghton Street
London, WC2A 2AE
United Kingdom

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
103
Abstract Views
372
Rank
534,631
PlumX Metrics