The Application of Affine Processes in Cohort Mortality Risk Models

28 Pages Posted: 7 Sep 2019

See all articles by Zhiping Huang

Zhiping Huang

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

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

Andres Villegas

University of New South Wales (UNSW)

Jonathan Ziveyi

UNSW Australia

Date Written: September 3, 2019

Abstract

This paper assesses and compares multi-factor continuous time affine mortality models applied to age-cohort mortality curves that are well suited for theoretical and practical application in finance and insurance. Models based on Gaussian distributed mortality rates, as well as the Cox-Ingersoll-Ross (CIR) process allowing for Gamma distributed mortality rates, are compared, also quantifying the probability of negative rates in the Gaussian models. In particular, we introduce the Gaussian Arbitrage-Free Nelson-Siegel (AFNS) mortality model incorporating level, slope and curvature factors. The models have appealing features including efficient estimation and computation. We estimate models using age-cohort data to capture cohort effects more effectively and in order to explain the variability in cohort mortality curves in the continuous time framework. The models allow for Poisson variation in the model estimation using the Kalman filter. The affine mortality models facilitate the derivation of closed-form survivor curves allowing for efficient valuation of mortality-linked claims. The models can also incorporate factor dependence allowing for age-dependence in the mortality curves. Importantly we show that the Gaussian independent factor AFNS model performs very well in explaining and forecasting cohort mortality.

Keywords: mortality models, continuous time, cohort curve, affine rates, Kalman filter

JEL Classification: G22, C13, C22, C52, J11

Suggested Citation

Huang, Zhiping and Sherris, Michael and Villegas, Andres and Ziveyi, Jonathan, The Application of Affine Processes in Cohort Mortality Risk Models (September 3, 2019). UNSW Business School Research Paper Forthcoming. Available at SSRN: https://ssrn.com/abstract=3446924 or http://dx.doi.org/10.2139/ssrn.3446924

Zhiping Huang

University of New South Wales (UNSW) - 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 (Contact Author)

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

Andres Villegas

University of New South Wales (UNSW)

Kensington
High St
Sydney, NSW 2052
Australia

Jonathan Ziveyi

UNSW Australia ( email )

School of Risk and Actuarial Studies
Level 6 East Wing, Business School
Sydney, NSW 2052
Australia
+61 2 9385 8006 (Phone)
+61 2 9385 1883 (Fax)

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