A Multivariate Forward-Rate Mortality Framework

24 Pages Posted: 18 Dec 2014 Last revised: 2 Jan 2015

See all articles by Daniel H. Alai

Daniel H. Alai

University of Kent

Katja Ignatieva

University of New South Wales - Australian School of Business

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

Date Written: December 16, 2014

Abstract

Stochastic mortality models have been developed for a range of applications from demographic projections to financial management. Financial risk based models build on methods used for interest rates and apply these to mortality rates. They have the advantage of being applied to financial pricing and the management of longevity risk. Olivier and Jeffery (2004) and Smith (2005) proposed a model based on a forward-rate mortality framework with stochastic factors driven by univariate gamma random variables irrespective of age or duration. We assess and further develop this model. We generalize random shocks from a univariate gamma to a univariate Tweedie distribution and allow for the distributions to vary by age. Furthermore, since dependence between ages is an observed characteristic of mortality rate improvements, we formulate a multivariate framework using copulas. We find that dependence increases with age and introduce a suitable covariance structure, one that is related to the notion of a minimum. The resulting model provides a more realistic basis for capturing the risk of mortality improvements and serves to enhance longevity risk management for pension and insurance funds.

Keywords: longevity risk, Olivier-Smith model, forward-rate mortality framework, minimum covariance pattern, copulas

JEL Classification: G23, G22, C58, C13

Suggested Citation

Alai, Daniel H. and Ignatieva, Katja and Sherris, Michael, A Multivariate Forward-Rate Mortality Framework (December 16, 2014). UNSW Business School Research Paper No. 2014ACTL08. Available at SSRN: https://ssrn.com/abstract=2539434 or http://dx.doi.org/10.2139/ssrn.2539434

Daniel H. Alai (Contact Author)

University of Kent ( email )

Cornwallis Building
Canterbury, CT2 7NF
United Kingdom

Katja Ignatieva

University of New South Wales - Australian School of Business ( email )

UNSW Business School
High St
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

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