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Theses

Risques de taux et de longévité : Modélisation dynamique et Applications aux produits dérivés et à l'assurance-vie

Abstract : This thesis is divided into three parts. The first part is constituted by chapter 2 and chapter 3 in which we consider models that describe the evolution of a stock and the evolution of interest rates. Using Wishart processes, these models belong to affine class and extend multidimensional Heston model. We study the intrinsic properties and we consider the evaluation of vanilla options. After having recalled evaluation methods, we introduce approximation methods that provide closed formula for the asymptotic smile. These methods make easier the calibration procedure and allow an analysis of the parameters. The second part, from chapter 4 to chapter 6, studies mortality and longevity risks. First, we recall general concepts of longevity risk and the main challenges we have to tackle. Then, we study a model of mortality that takes into account age and other individual features that could explain mortality. This mortality model is calibrated on specific data what allows a study of the impact on mortality of different characteristics. Finally, we introduce a microscopic model for population dynamic in order to study the evolution in the future of an age-and-trait-structured population. Each person can be affected by different events: birth, death and evolution of his features. Moreover, this model takes into account of the stochastic evolution of the demographic rates in the time. We study a micro/macro link providing good macroscopic properties for this microscopic model. The last part, constituted by chapter 7 and chapter 8, deals with applications of the previous models. The first application concerns demography: the association of the microscopic model for population dynamic and the mortality model provide demographic projections of the French population. We consider the retirement issue by analyzing the solutions of an immigration policy and a reform about the start age of retirement. The second application refers to insurance life products associating longevity and interest rate risks that have been detailed in the previous parts of the thesis. We study the basis risk generated by the heterogeneity of portfolio. Moreover, we introduce the Life Nominal Chooser Swaption (LNCS), a derivative product in insurance life for the transfer of financial risks. The design of the Life Nominal Chooser Swaption is very interesting allowing an assurance owning a portfolio to transfer his interest rate risk to a bank.
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Harry Bensusan. Risques de taux et de longévité : Modélisation dynamique et Applications aux produits dérivés et à l'assurance-vie. Probabilités [math.PR]. Ecole Polytechnique X, 2010. Français. ⟨pastel-00563792⟩

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