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

TY - JOUR

T1 - Transitory mortality jump modeling with renewal process and its impact on pricing of catastrophic bonds

AU - Özen, Selin

AU - Şahin, Şule

PY - 2020/10/1

Y1 - 2020/10/1

N2 - 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.

AB - 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.

KW - Catastrophic bonds

KW - Jump–diffusion process

KW - Merton model

KW - Mortality risks

KW - Renewal process

KW - Stochastic mortality

UR - http://www.scopus.com/inward/record.url?scp=85081140293&partnerID=8YFLogxK

U2 - 10.1016/j.cam.2020.112829

DO - 10.1016/j.cam.2020.112829

M3 - Article

AN - SCOPUS:85081140293

SN - 0377-0427

VL - 376

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

M1 - 112829

ER -