Mathematical Models for the Longevity Risk in the Annuity Market

The markets for longevity derivatives are starting to develop. In last years, many companies have closed the defined benefit retirement plans that they used to offer to their employees. In addition, some governments increased the retirement age by 2 or 5 years to take into account longevity improvements, population ageing and the financing of pension. The insurance industry is also 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 develop the models of mortality rates and the pricing models of the longevity risk. We make some remarks regarding forecasting mortality rates using Lee-Carter model and own model. Also, we deal with the securitization of longevity risk through the longevity bonds (the straight bonds), the interest are split between the annuity provider and the investors depending on the realized mortality at each future time by a Special Purpose Company (SPC).