Reducing Model Risk and Improving Mortality Forecasts for Life Insurance Product Pricing

31 Pages Posted: 31 Jan 2019

See all articles by Hongxuan Yan

Hongxuan Yan

The University of Sydney - School of Mathematics and Statistics

Gareth Peters

Department of Actuarial Mathematics and Statistics, Heriot-Watt University; University College London - Department of Statistical Science; University of Oxford - Oxford-Man Institute of Quantitative Finance; London School of Economics & Political Science (LSE) - Systemic Risk Centre; University of New South Wales (UNSW) - Faculty of Science

Jennifer Chan

The University of Sydney - School of Mathematics and Statistics

Date Written: January 20, 2019

Abstract

The pricing of life insurance products depends critically on the ability to model and forecast three core stochastic drivers. Firstly, the ability to accurately forecast expected mortality rates by age group for a given population in order to construct estimates of the life expectancy required for survival linked insurance products. Secondly, the ability to model interest rate dynamics accurately over multi-decade time horizons, and thirdly the ability to model the causal relationship between mortality events and interest rate fluctuations.

In this work we tackle all three aspects of these challenging problems faced by actuaries seeking to robustly price life products. We demonstrate with real data for three major populations, U.K., U.S.A. and Australia that we are able to reduce the model risk and associated forecast errors of classical Lee-Carter models in constructing forecasts for mortality and subsequent life expectancy by age and gender. This is achieved by developing new classes of multivariate long-memory models for mortality which we compare to extensions of classical Lee-Carter models. Secondly, we develop standard short rate one factor models for interest rates, in which we incorporate dependence links with our stochastic mortality models. We develop a Bayesian calibration and forecasting framework which is estimated with a Hamiltonian Markov Chain Monte Carlo sampling procedure.

We then utilise these frameworks to study the influence of model risk for life products including annuity portfolios and the valuation of a guaranteed annuity option (GAO). We demonstrate that classical Lee-Carter type models can produce less accurate model forecasts than our proposed multivariate long memory models and we quantify the mispricing cost of this model risk.

Keywords: Life Table, Gengenbauer Polynomial, Lee Carter Model, Long Memory, Bayesian Inference, Annuity Pricing, Guaranteed Annuity Option

Suggested Citation

Yan, Hongxuan and Peters, Gareth and Chan, Jennifer, Reducing Model Risk and Improving Mortality Forecasts for Life Insurance Product Pricing (January 20, 2019). Available at SSRN: https://ssrn.com/abstract=3319355 or http://dx.doi.org/10.2139/ssrn.3319355

Hongxuan Yan

The University of Sydney - School of Mathematics and Statistics ( email )

Sydney, New South Wales 2006
Australia

Gareth Peters (Contact Author)

Department of Actuarial Mathematics and Statistics, Heriot-Watt University ( email )

Edinburgh Campus
Edinburgh, EH14 4AS
United Kingdom

HOME PAGE: http://garethpeters78.wixsite.com/garethwpeters

University College London - Department of Statistical Science ( email )

1-19 Torrington Place
London, WC1 7HB
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

University of Oxford Eagle House
Walton Well Road
Oxford, OX2 6ED
United Kingdom

London School of Economics & Political Science (LSE) - Systemic Risk Centre ( email )

Houghton St
London
United Kingdom

University of New South Wales (UNSW) - Faculty of Science ( email )

Australia

Jennifer Chan

The University of Sydney - School of Mathematics and Statistics ( email )

Sydney, New South Wales 2006
Australia

Register to save articles to
your library

Register

Paper statistics

Downloads
24
Abstract Views
153
PlumX Metrics