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Affine stochastic mortality. (English) Zbl 1103.60063

The author proposes a new model for mortality intensity. The approach is based on the observation that if the mortality intensity is an affine function of a number of latent factors, the survival and death probabilities are known in closed form. Most of the results are based on the literature on affine term structure models and the credit risk literature based on the subfiltration approach. The contribution consists of the application of these ideas to model the evolution of mortality rates over time. The author provides in the need for a model of mortality forces which can be combined consistently with continuous time models known from the derivative pricing literature. For some well known functional dependencies between age and mortality intensity (i.e. the Thiele and Makeham mortality laws) a new setup is introduced. The three main advantages of the model are a rich analytical structure (inherited from the affine setup), clear interpretation of the latent factors and the aforementioned consistency with derivative pricing models. In contrast to previous work, the mortality intensity is simultaneously considered for all ages. The author does not explicitly focus on the time series properties of mortality (although the model is extremely well suited for estimation to empirical data), rather he has a pricing and risk management application in mind. Four types of mortality risk are usually distinguished: trend (i.e. longevity), level (portfolio versus population), volatility (discrepancies between trend/level and observed mortality) and catastrophe. The model captures three of these types and the risks are directly quantified by parameter estimates. The author shows, using historical Dutch mortality rates, that the proposed Thiele and Makeham functional forms fit the data sufficiently well. Assuming independence of financial and mortality risk one can easily combine the proposed model with, for instance, a term structure model. One could then easily price several well studied options embedded in insurance contracts under stochastic mortality. To illustrate the effect of stochastic mortality on the pricing of a guaranteed annuity option the author calculates the value of an option on a life long annuity in a combined single factor Hull-White Makeham model.

MSC:

60H30 Applications of stochastic analysis (to PDEs, etc.)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
91G20 Derivative securities (option pricing, hedging, etc.)
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