Constructing dynamic life tables with a single-factor model
- PDF / 3,700,682 Bytes
- 39 Pages / 439.37 x 666.142 pts Page_size
- 17 Downloads / 213 Views
Constructing dynamic life tables with a single-factor model David Atance1
· Alejandro Balbás2
· Eliseo Navarro1
Received: 25 November 2019 / Accepted: 26 September 2020 © Associazione per la Matematica Applicata alle Scienze Economiche e Sociali (AMASES) 2020
Abstract The paper deals with the mortality risk evolution and presents a one-factor model explaining the dynamics of all mortality rates. The selected factor will be the mortality rate at the key age, and an empirical study involving males and females in France and Spain reveals that the present approach is not outperformed by more complex factor models. The key age seems to reflect several advantages with respect to other factors available in the literature. Actually, it is totally observable, and the methodology may be easily extended so as to incorporate more factors (more key ages), a cohort effect, specific mortality causes or specific ages. Furthermore, the choice of a key age as an explanatory factor is inspired by former studies about the dynamics of interest rates which allows us to draw on the model in order to address some longevity risklinked problems. Indeed, one only has to slightly modify some interest rate-linked methodologies. Illustrative examples will be given. Keywords Dynamic life table · Key mortality rate · Mortality · Forecasting Jel Classification G52 · G53 · J11
1 Introduction Longevity risk is becoming more and more important in insurance industry. The evolution of the mortality table may provoke significant capital losses in the portfolio of long-term contracts, and consequently, the study of this evolution has became a major issue in life insurance. Actuarial literature has focused on the dynamics of the mortality table by means of several complementary approaches. On the one hand, the seminal paper by Lee and Carter (1992) proposed to deal with a risk-factor model. They introduced their
B
David Atance [email protected]
1
Departamento de Economía y Dirección de Empresas, Universidad de Alcalá, Madrid, Spain
2
Departamento de Economía de la Empresa, Universidad Carlos III de Madrid, Madrid, Spain
123
D. Atance et al.
famous one-factor model and, since then, many authors have extended the discussion by dealing with more factors (Booth et al. 2002; Brouhns et al. 2002; Cairns et al. 2006, 2009) or cohort effects (Holford 1983; Renshaw and Haberman 2006; Haberman and Renshaw 2009). On the other hand, the stochastic mortality modeling (Biffis 2005; Di Lorenzo et al. 2006; Schrager 2006; Plat 2009) has become a second line of research providing us with suitable models which can be calibrated to market prices (Russo et al. 2011). This paper attempts to capture the strengths of both approaches. Indeed, a one-factor model in the line of Lee and Carter (1992) is presented, but the significant difference with respect to former analyses is the chosen factor, which is equal to the mortality rate at the “key age.” Actually, every age might be selected as an explanatory factor, but the key age will equal to that minimizing the i
Data Loading...
