The Application of Affine Processes in Multi-Cohort Mortality Model

36 Pages Posted: 7 May 2015

See all articles by Yajing Xu

Yajing Xu

UNSW Australia Business School, School of Risk & Actuarial Studies

Michael Sherris

University of New South Wales - ARC Centre of Excellence in Population Ageing Research and School of Risk and Actuarial Studies; UNSW Australia Business School

Jonathan Ziveyi

UNSW Australia Business School, School of Risk & Actuarial Studies

Date Written: May 4, 2015

Abstract

Cohort effects have been identified in many countries. However, some mortality models only consider the modelling and projection of age-period effects. Others, that incorporate cohort effects, do not consider cohort specific survival curves that are important for pricing and hedging purposes. In this paper, we consider modelling mortality development on a cohort basis, propose and assess a multi-cohort mortality model in an affine framework. We model the mortality intensity with common factors that affect all the cohorts as well as cohort specific factors that only affect specific cohorts, so that the correlations among cohorts are not perfect.

In particular, we consider a three-factor case. The three-factor multi-cohort model is established using Danish male mortality data. The two common factors are extracted using a Kalman Filter algorithm and cohort specific factors are estimated by minimizing the residual calibration error. The calibration results demonstrate the need for cohort effects. The out-of-sample forecast performance of the proposed model, the RH model (age-period-cohort model developed of Renshaw and Haberman (2006)) and the CBD model (age-period model developed of Cairns et al. (2006)) are compared to actual mortality data. The results show that the proposed model produces more consistent estimates of cohort survival curves.

Keywords: Multi-cohort mortality model, Affne framework, Common factors, Cohort specific factors, Mortality projections

JEL Classification: C13, C15, C51, C52, G22, G23, J11

Suggested Citation

Xu, Yajing and Sherris, Michael and Ziveyi, Jonathan, The Application of Affine Processes in Multi-Cohort Mortality Model (May 4, 2015). UNSW Business School Research Paper No. 2015ACTL13. Available at SSRN: https://ssrn.com/abstract=2603524 or http://dx.doi.org/10.2139/ssrn.2603524

Yajing Xu (Contact Author)

UNSW Australia Business School, School of Risk & Actuarial Studies ( email )

Room 2058 South Wing 2nd Floor
Quadrangle building, Kensington Campus
Sydney, NSW 2052
Australia

Michael Sherris

University of New South Wales - ARC Centre of Excellence in Population Ageing Research and School of Risk and Actuarial Studies ( email )

UNSW Business School
Risk and Actuarial Studies
Sydney, NSW 2052
Australia
+61 2 9385 2333 (Phone)
+61 2 9385 1883 (Fax)

HOME PAGE: http://www.asb.unsw.edu.au/schools/Pages/MichaelSherris.aspx

UNSW Australia Business School ( email )

Sydney, NSW 2052
Australia

Jonathan Ziveyi

UNSW Australia Business School, School of Risk & Actuarial Studies ( email )

Room 2058 South Wing 2nd Floor
Quadrangle building, Kensington Campus
Sydney, NSW 2052
Australia

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