A Study on Longevity Risk Hedging in the Presence of Population Basis Risk

Abstract

Longevity risk refers to uncertainty surrounding the trend in human life expectancy. Standardized hedging instruments that are linked to broad-based mortality indexes can be used to offload longevity risk from pension plans and annuities. However, hedges that are based on such instruments are subject to population basis risk, which arises from the difference in mortality improvements between the hedger's population and the reference population to which the hedging instruments are linked. This thesis attempts to address some issues that are related to longevity risk hedging in the presence of population basis risk.

In the first chapter, a graphical risk metric is proposed to intuitively measure population basis risk, which is believed to be a major obstacle to market development. It allows market participants to not only visually evaluate the extent of population basis risk, but also determine the most appropriate reference population. Compared to existing population basis risk metrics which are mostly numerical, the proposed graphical risk metric is more informative in that it captures more aspects of population basis risk. Along with the existing numerical risk metrics, the proposed graphical risk metric may help hedgers better understand population basis risk and hence make their risk management decisions.

In the second chapter, the feasibility of dynamic longevity hedging with standardized hedging instruments is studied. To this end, the dynamic hedging strategy developed by Cairns (2011) is generalized to incorporate the situation when the hedger's population and the reference population are different. The empirical results indicate that dynamic hedging can effectively reduce the longevity risk exposures of a typical pension plan, even if population basis risk is taken into account. Further, by considering data from a large group of national populations, it is found that population basis risk and small sample risk can possibly be diversified across different hedgers. Hedgers may therefore be able to completely eliminate their longevity risk exposures by removing the underlying trend risk with a dynamic index-based hedge and transferring the residual risks through a reinsurance mechanism.