A Generalised CIR Process with Externally-Exciting and Self-Exciting Jumps and Its Applications in Insurance and Finance

Angelos Dassios, Jiwook Jang and Hongbiao Zhao
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Angelos Dassios: Department of Statistics, London School of Economics, Houghton Street, London WC2A 2AE, UK
Jiwook Jang: Department of Actuarial Studies & Business Analytics, Macquarie Business School, Macquarie University, Sydney NSW 2109, Australia
Hongbiao Zhao: School of Statistics and Management, Shanghai University of Finance and Economics, No. 777 Guoding Road, Shanghai 200433, China

Risks, 2019, vol. 7, issue 4, 1-18

Abstract: In this paper, we study a generalised CIR process with externally-exciting and self-exciting jumps, and focus on the distributional properties and applications of this process and its aggregated process. The aim of the paper is to introduce a more general process that includes many models in the literature with self-exciting and external-exciting jumps. The first and second moments of this jump-diffusion process are used to calculate the insurance premium based on mean-variance principle. The Laplace transform of aggregated process is derived, and this leads to an application for pricing default-free bonds which could capture the impacts of both exogenous and endogenous shocks. Illustrative numerical examples and comparisons with other models are also provided.

Keywords: contagion risk; insurance premium; aggregate claims; default-free bond pricing; self-exciting process; hawkes process; CIR process (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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