Non Mean Reverting Affine Processes for Stochastic Mortality

ICER Applied Mathematics Working Paper No. 4 - 2005

32 Pages Posted: 20 May 2005

See all articles by Elisa Luciano

Elisa Luciano

Collegio Carlo Alberto; University of Turin - Department of Statistics and Applied Mathematics

Elena Vigna

University of Turin - Faculty of Economics; Collegio Carlo Alberto; CeRP

Date Written: May 2005

Abstract

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.

Keywords: Doubly stochastic processes (Cox processes), stochastic mortality, affine processes

JEL Classification: G22, J11

Suggested Citation

Luciano, Elisa and Vigna, Elena, Non Mean Reverting Affine Processes for Stochastic Mortality (May 2005). ICER Applied Mathematics Working Paper No. 4 - 2005, Available at SSRN: https://ssrn.com/abstract=724706 or http://dx.doi.org/10.2139/ssrn.724706

Elisa Luciano (Contact Author)

Collegio Carlo Alberto ( email )

via Real Collegio 30
Moncalieri, Torino 10024
Italy

HOME PAGE: http://www.carloalberto.org/people/faculty/fellows/luciano/

University of Turin - Department of Statistics and Applied Mathematics ( email )

Corso Unione Sovietica 218 bis
Turin, I-10122
Italy
+ 39 011 6705230 (Phone)

Elena Vigna

University of Turin - Faculty of Economics ( email )

Dipartimento di Statistica e Matematica Applicata
Corso Unione Sovietica 218 bis
Torino, 10134
Italy

Collegio Carlo Alberto ( email )

via Real Collegio 30
Moncalieri, Torino 10024
Italy

CeRP ( email )

Via Real Collegio, 30
Moncalieri, Turin 10024
Italy

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