Longevity risk

N. El Karoui, C. Hillairet, S.Loisel

February-March 2022

Longevity risk is a long-term risk, which is the financial risk associated with the fact that individuals live significantly longer on average than expected. This risk is an important issue, whether from a social, political or economic point of view … For the time being, it is mainly insurers who manage this risk for their clients, by developing products called variable annuities. As insurers have to provide more and more capital to face this long-term risk, it becomes crucial for them to find an adequate and efficient way to transfer part of this risk to reinsurers and financial markets. The transfer of longevity risk is very delicate because it is a complex and long-term risk. Some banks, having bought positions from insurers, find themselves exposed to this risk even though they have little expertise in this area.

To model future longevity, most players in the insurance and reinsurance market use prospective mortality tables which aim to project current longevity trends into the future. The basic model in this area is that of Lee-Carter (1992). The parameters of the model are estimated from past data and backtesting is done on the most recent years to check the predictive power of the model. Most of the longevity risk is a trend risk, i.e. a change in the average rate of improvement in longevity. In addition to this trend risk, there is a risk of oscillations around the average trend, with catch-up phenomena. Moreover, the evolution of the mortality level is relatively different from one portfolio of insureds to another. This is what is known as the base risk, which is also found in credit due to the heterogeneity of borrowers. This basis risk is important from the point of view of transferring longevity risk: even if a systemic part is very clear, it is nevertheless difficult to refer to a national index to manage the longevity risk of a given portfolio. The alternative proposed in this course is to use a microscopic approach via population dynamics methods, close to biology models, and based on the theory of point processes (cf. Thomas Duquesne’s course “Introduction to jump models”). This approach takes into account the characteristics of individuals (social-economic levels, marital status, etc.) and uses tools that have applications in various settings.

In addition to this “pure longevity” risk, insurers and organisations involved in paying pensions are also exposed to financial risks (long-term interest rate risk, counterparty risk…) that should not be underestimated. The aim of this course is to define the general concepts of longevity risk and the underlying issues related to this risk. The latest developments in longevity risk modelling will be discussed, as well as the challenges of longevity risk management for the insurance and financial industry.

  1. Introduction to longevity risk and life insurance opportunities
  2. Classical mortality data and models
  3. Introduction to the valuation methods of longevity derivatives and long-term interest rates
  4. Introduction to the Poisson Process and birth and death processes
  5. Population dynamics and applications.


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