Consistent Dynamic Affine Mortality Models for Longevity Risk Applications

20 Pages Posted: 9 May 2011 Last revised: 14 Feb 2012

See all articles by Craig Blackburn

Craig Blackburn

University of New South Wales (UNSW) - School of Actuarial Studies; ARC Centre of Excellence in Population Ageing Research (CEPAR)

Michael Sherris

UNSW Business School

Date Written: February 8, 2012

Abstract

This paper proposes and calibrates a consistent multi-factor affine term structure mortality model for longevity risk applications. We show that this model is appropriate for fitting historical mortality rates. Without traded mortality instruments the choice of risk-neutral measure is not unique and we fit it to observed historical mortality rates in our framework. We show the risk-neutral parameters can be calibrated and are relatively insensitive of the historical period chosen. Importantly, the framework provides consistent future survival curves with the same parametric form as the initial curve in the risk-neutral measure. The multiple risk factors allow for applications in pricing and more general risk management problems. A state-space representation is used to estimate parameters for the model with the Kalman filter. A measurement error variance is included for each age to capture the effect of sample population size. Swedish mortality data is used to assess 2- and 3-factor implementations of the model. A 3-factor model specification is shown to provide a good fit to the observed survival curves, especially for older ages. Bootstrapping is used to derive parameter estimate distributions and residual analysis is used to confirm model fit. We use the Heath-Jarrow-Morton forward rate framework to verify consistency and to simulate cohort survivor curves under the risk-neutral measure.

Keywords: mortality model, longevity risk, multi-factor, affine, arbitrage-free, consistent, Kalman Filter, Swedish Mortality

JEL Classification: G12, G22, G23, C13, C51, C52, J11

Suggested Citation

Blackburn, Craig and Sherris, Michael, Consistent Dynamic Affine Mortality Models for Longevity Risk Applications (February 8, 2012). UNSW Australian School of Business Research Paper No. 2011ACTL08, Available at SSRN: https://ssrn.com/abstract=1832014

Craig Blackburn (Contact Author)

University of New South Wales (UNSW) - School of Actuarial Studies ( email )

Sydney, NSW 2052
Australia

ARC Centre of Excellence in Population Ageing Research (CEPAR) ( email )

Level 6, Central Lobby (enter via East Lobby)
Australian School of Business Building
Sydney, New South Wales NSW 2052
Australia

Michael Sherris

UNSW Business School ( email )

Sydney, NSW 2052
Australia

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