Non Mean Reverting Affine Processes for Stochastic Mortality
University of Turin - Department of Statistics and Applied Mathematics; International Centre for Economic Research (ICER); Collegio Carlo Alberto
University of Turin - Faculty of Economics; Collegio Carlo Alberto; CeRP
ICER Applied Mathematics Working Paper No. 4 - 2005
In this paper we use doubly stochastic processes (or Cox processes) in order to model the random evolution of mortality of an individual. These processes have been widely used in the credit risk literature in modelling default arrival, and in this context have proved to be quite flexible, especially when the intensity process is of the affine class. We investigate the applicability of affine processes in describing the individual's intensity of mortality, and provide a calibration to the Italian and UK populations. Results from the calibration seem to suggest that, in spite of their popularity in the financial context, mean reverting processes are not suitable for describing the death intensity of individuals. On the contrary, affine processes whose deterministic part increases exponentially seem to be appropriate. As for the stochastic part, negative jumps seem to do a better job than diffusive components. Stress analysis and analytical results indicate that increasing the randomness of the intensity process results in improvements in survivorship.
Number of Pages in PDF File: 32
Keywords: Doubly stochastic processes (Cox processes), stochastic mortality, affine processes
JEL Classification: G22, J11working papers series
Date posted: May 20, 2005
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