Efficient Simulation of Clustering Jumps with CIR Intensity

• 成果类型: Article
• 署名作者: Dassios, Angelos; Zhao, Hongbiao
• 署名单位: University of London; London School Economics & Political Science; Shanghai University of Finance & Economics
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2017.1640
• 发表日期: 2017
• 页码: 1494-1515
• 关键词: affine point-processes; stochastic volatility; SPECTRA; Poisson; default; MODEL; RISK

摘要

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.