Transitory mortality jump modeling with renewal process and its impact on pricing of catastrophic bonds

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:376

Article

Ozen, Selin^1,2,3  Sahin, Sule^1,2,3,4 

[1] Karabuk Univ, Dept Actuarial Sci & Risk Management, Karabuk, Turkey

[2] Univ Liverpool, Inst Financial & Actuarial Math, Dept Math Sci, Liverpool, Merseyside, England

[3] Hacettepe Univ, Dept Actuarial Sci, Ankara, Turkey

[4] Math Sci Bldg, Liverpool L69 7ZL, Merseyside, England

关键词: Renewal process;    Mortality risks;    Jump-diffusion process;    Stochastic mortality;    Merton model;    Catastrophic bonds;   

DOI  :  10.1016/j.cam.2020.112829

来源: Elsevier

【 摘 要 】

A number of stochastic mortality models with transitory jump effects have been proposed for the securitization of catastrophic mortality risks. Most of the studies on catastrophic mortality risk modeling assumed that the mortality jumps occur once a year or used a Poisson process for their jump frequencies. Although the timing and the frequency of catastrophic events are unknown, the history of the events might provide information about their future occurrences. In this paper, we propose a specification of the Lee-Carter model by using the renewal process and we assume that the mean time between jump arrivals is no longer constant. Our aim is to find a more realistic mortality model by incorporating the history of catastrophic events. We illustrate the proposed model with mortality data from the US, the UK, Switzerland, France, and Italy. Our proposed model fits the historical data better than the other jump models for all countries. Furthermore, we price hypothetical mortality bonds and show that the renewal process has a significant impact on the estimated prices. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free