Exact Simulation of Quadratic Intensity Models

Abstract

We develop efficient algorithms of exact simulation for quadratic stochastic intensity models that have become increasingly popular for modeling events arrivals, especially in economics, finance, and insurance. They have huge potential to be applied to many other areas such as operations management, queueing science, biostatistics, and epidemiology. Our algorithms are developed by the principle of exact distributional decomposition, which lies in a fully analytical expression for the joint Laplace transform of quadratic process and its integral newly derived in this paper. They do not involve any numerical Laplace inversion, have been validated by extensive numerical experiments, and substantially outperform all existing alternatives in the literature. Moreover, our algorithms are extendable to multidimensional point processes and beyond Cox processes to additionally incorporate two-sided random jumps with arbitrarily distributed sizes in the intensity for capturing self-exciting and self-correcting effects in event arrivals. Applications to portfolio loss modeling are provided to demonstrate the applicability and flexibility of our algorithms. History: Accepted by Bruno Tuffin, Area Editor for Simulation. Funding: This work was supported by the Beijing University of Posts and Telecommunications [Grant 2022RC58], the Shanghai University of Finance and Economics [Grant 2020110930], the National Natural Science Foundation of China [Grant 71401147], and Graduate Innovation Fund of Shanghai University of Finance and Economics [CXJJ-2023-387]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0323 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0323 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .