Longevity risk and the implications for Norwegian annuity providers : a quantitative analysis of longevity risk in light of the solvency II standard formula and internal model
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- Master Thesis 
A signiﬁcant part of the liabilities of Norwegian insurance companies and annuity providers consists of lifetime pension products. These pension products are subject to what is referred to as longevity risk, i.e. the risk that individuals who receive pension annuities live longer than anticipated. Insurance companies and annuity providers are required to hold capital buﬀers today to cover for the uncertainty in future cash ﬂows. The calculation of the size of these buﬀers is regulated by a European-wide framework known as Solvency II. The Solvency II framework proposes two solutions for determining Solvency Capital Requirements (SCR); the Standard Formula and an Internal Model. For longevity risk, the Standard Formula assumes a 20% reduction in mortality rates, while the Internal Model is calculated based on the 99.5% Value-atRisk on a one-year time horizon. In this thesis, we compare the SCRs calculated by the Standard Formula with the SCRs calculated by an Internal Model, based on mortality projections from the Lee-Carter and the Cairns-Blake-Dowd mortality models. We use a simpliﬁed pension product to quantify the diﬀerence in capital requirements for Norwegian annuity providers. We ﬁnd that the 20% reduction of mortality rates following the Standard Formula leads to higher SCRs than those based on the 99.5% VaR-approach using Internal Models. Furthermore, we ﬁnd that the Lee-Carter model outperforms the CBD-model in terms of both describing historical Norwegian mortality rates, and in estimating lower SCRs. This implies that insurers and annuity providers should develop Internal Models based on a Lee-Carter model to minimize their SCRs. However, the implication is somewhat oﬀset by the costly process of developing Internal Models. This means that approximations by the Standard Formula may be more expedient for smaller insurers. Larger annuity providers, on the other hand, may beneﬁt from an Internal Model through both reduced capital requirements and a more detailed account of their risk exposure.