On the Longevity Risk in the Annuity Market: Some Mathematical Models

Abstract

AbstractThe insurance industry is facing some specific challenges related to longevity risk. More and more capital has to be constituted to face this long-term risk, and new regulations in Europe, together with the recent financial crisis only amplify this phenomenon. Hence, it has become more important for insurance companies and pension funds to find a suitable and efficient way to cross-hedge or to transfer part of the longevity risk to reinsurers or to financial markets.In this study, we analyze some models of mortality rates and pricing the longevity risk. We make some remarks regarding forecasting mortality rates using the Lee-Carter model and our own developed model. Also, we deal with the securitization of longevity risk through the longevity bonds (the straight bonds), the interest being split between the annuity provider and the investors depending on the realized mortality at each future time, by a Special Purpose Company (SPC).Keywordsstochastic mortality modelLee-Carter modellongevity risklongevity bonds (straight bonds)