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**Longevity bond premiums: the extreme value approach and risk cubic pricing.**
*(English)*
Zbl 1231.91427

Summary: The purpose of this study is to analyze the securitization of longevity risk with an emphasis on longevity risk modeling and longevity bond premium pricing. Various longevity derivatives have been proposed, and the capital market has experienced one unsuccessful attempt by the European Investment Bank (EIB) in 2004. After carefully analyzing the pros and cons of previous securitizations, we present our proposed longevity bonds, whose payoffs are structured as a series of put option spreads. We utilize a random walk model with drift to fit small variations of mortality improvements and employ extreme value theory to model rare longevity events. Our method is a new approach in longevity risk securitization, which has the advantage of both capturing mortality improvements within sample and extrapolating rare, out-of- sample longevity events. We demonstrate that the risk cubic model developed for pricing catastrophe bonds can be applied to mortality and longevity bond pricing and use the model to calculate risk premiums for longevity bonds.

### MSC:

91G20 | Derivative securities (option pricing, hedging, etc.) |

60G70 | Extreme value theory; extremal stochastic processes |

91G70 | Statistical methods; risk measures |

91G80 | Financial applications of other theories |

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\textit{H. Chen} and \textit{J. D. Cummins}, Insur. Math. Econ. 46, No. 1, 150--161 (2010; Zbl 1231.91427)

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