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Longevity risk is the risk that people live longer than expected and it has a big impact on annuity providers and pension plans as well as on governments and individuals. Insurers have to estimate the future lifetimes of their policyholders in order to price their products and calculate the reserves. If mortality rates drop faster than expected, the insurer faces financial difficulties. The new Life Market introduces hedging techniques related to longevity risk, with one being the longevity bond. This thesis describes different aspects of the longevity bond and provides a theoretical analysis of the pricing method constructed in the article by Denuit et al. (2007), which uses the Wang transform to price a survivor bond.

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The focus of this master thesis is on mortality securitization, which is performed by the issuance of Catastrophe Mortality (CATM) bonds. However, the pricing of CATM can be challenging and can require the use of models. One can use the no-arbitrage pricing principle, which requires a stochastic mortality model, calibrated in the real-world probability measure. Then based on the prices of mortality-linked securities, the risk-neutral distribution can be estimated to find the no-arbitrage price. This is not always optimal as the risk-neutral measure is not always defined uniquely. Another approach is to use a distortion risk measure, namely the Wang transform and multivariate exponential tilting. However, the parameters of the model are hard to estimate and the Wang transform is not always suited as a risk measure for financial and insurance pricing. The no-arbitrage pricing principle can also be enhanced by using a utility function or by applying the extreme value theory, but limited tradeable mortality-linked securities and scarcity of data increase the difficulty of the pricing process. This paper extensively studies and compare the different pricing methods available in the literature.

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The securitization of the catastrophe risks is an alternative solution to traditional reinsurance in order to mitigate excessive losses due to natural disasters. The coupon payments and the principal of a catastrophe bond depend on the occurrence of a catastrophe event. If such an event occurs, the coupons and/or the principal will be reduced such that the insurer has enough money to reimburse the damage suffered. This important characteristic is introduced in the pricing formula via a payoff function. To calculate the price of CAT bonds, the risk-neutral probability must be used. The probability that an earthquake exceeds a certain magnitude is determined under the probability measure of the real world. Therefore, the Wang transform is used to change the probability measure. An illustration of an earthquake CAT bond shows that the fixed coupon rate is very sensitive to changes in some parameters of the model. The basis risk, i.e. the difference between the insurer’s actual loss and the composite index of losses, declines when the insurer has a larger market share and it increases when the quantile level of the index trigger increases. To determine the effectiveness of a loss index using call-spread hedging, the insurer must minimize a function of the hedged loss under a loss index subject to a cost constraint and finally, he must assess whether the hedge ratio is large enough.

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Pension products are becoming increasingly important due to an aging population. These long-term contracts contain a significant amount of longevity risk, which leads to high capital requirements. This dissertation investigates tontines, which are alternative products that transfers part of the longevity risk to a group of policyholders. It will be shown that tontines have lower capital requirements compared to annuities under the Solvency II standard formula. However, using the Lee-Carter model, the capital charges for a tontine are about the same as for an annuity. The capital charges and coupon structure of the Forman Sabin and Chen Hieber Klein tontine were also investigated. These are hybrid products that mix tontine and annuity elements. While they solve the problem of unattractive coupons of the tontine, only the Forman Sabin tontine considerably lowers capital requirements.