Mortality Risk and Its Effect on Shortfall and Risk Management in Life Insurance

• Author: Hannah Wesker,Nadine Gatzert
• Date: 01 March 2014
• DOI: http://doi.org/10.1111/j.1539-6975.2012.01496.x
• Published date: 01 March 2014

© The Journal of Risk and Insurance, 2014, Vol. 81, No. 1, 57–90

DOI: 10.1111/j.1539-6975.2012.01496.x

57

MORTALITY RISK AND ITS EFFECT ON SHORTFALL AND

RISK MANAGEMENT IN LIFE INSURANCE

Nadine Gatzert

Hannah Wesker

ABSTRACT

Mortality risk is a key risk factor for life insurance companies and can have a

crucial impact on its risk situation. In general, mortality risk can be divided

into different subcategories, among them unsystematic risk, adverse selec-

tion, and systematic risk. In addition, basis risk may arise in case of hedging,

for example, longevity risk. The aim of this article is to holistically analyze

the impact of these different types of mortality risk on the risk situation and

the risk management of a life insurer. Toward this end, we extend previous

models of adverse selection, empirically calibrate mortality rates, and study

the interaction among the mortality risk components in the case of an insurer

holding a portfolio of annuities and term life insurance contracts. For risk

management, we examine natural hedging and mortality contingent bonds.

Our results show that particularly adverse selection and basis risk can have

crucial impact not only on the effectiveness of mortality contingent bonds,

but also on the insurer’s risk level, especially when a portfolio consists of

several types of products.

INTRODUCTION

Recently, there has been a growing interest in mortality risk and its management in

the scientific literature as well as in practice, especially due to the demographic devel-

opment in most industrialized countries. The increasing life expectancy poses serious

problems to life insurance companies selling annuities and to pension funds. These

problems are especially severe because of a scarcity of possibilities to hedge against

this risk. Due to the limited capacity of reinsurance, several alternative instruments

for managing demographic risk, for example, by transferring mortality risk to the

capital market or the use of natural hedging, have been discussed in the scientific

literature and by practitioners. However, mortality heterogeneity as well as infor-

mation asymmetries between the insurance company and the insured about these

The authors are with the Friedrich-Alexander-University (FAU)of Erlangen-Nuremberg, Ger-

many. The authors can be contacted via e-mail: nadine.gatzert@wiso.uni-erlangen.de and

hannah.wesker@wiso.uni-erlangen.de. The authors would like to thank the anonymous refer-

ees for valuable comments and suggestions on an earlier version of this article, and gratefully

acknowledge financial support by the German Research Foundation.

58 THE JOURNAL OF RISK AND INSURANCE

different mortality experiences of individuals can lead to adverse selection. In partic-

ular, annuitants generally have a systematically lower mortality than the population

as a whole.1Mortality heterogeneity and information asymmetries can thus severely

limit the usefulness of these risk management tools. Therefore, the aim of this article

is to study the interaction among different types of mortality risk—unsystematic mor-

tality risk, basis risk, adverse selection, and systematic mortality risk—with respect

to the risk situation of an insurance company.Furthermore, we analyze the impact of

mortality risk components on the effectiveness of two risk management tools: (1) a

natural hedging strategy, using the opposed reaction toward changes in mortality of

term life insurance and annuities for eliminating the impact of systematic mortality

risk, and (2) a mortality contingent bond (MCB) for transferring mortality risk to the

capital market.

In the literature, mortality risk is generally divided into different subcategories: (1)

unsystematic mortality risk that the individual time of death is a random variable

with a certain probability distribution (see Biffis, Denuit, and Devolder, 2010); (2)

systematic mortality risk, which is the risk of unexpected changes in the underlying

population mortality, for example due to common factors impacting the mortality

of the population as a whole, which causes dependencies between lives and is thus

not diversifiable through enlarging the portfolio (see Wills and Sherris, 2010); and (3)

adverse selection, which refers to the fact that the probability distribution differs in

the level and trend over age for different populations of insured, for example, for life

insurance holders and annuitants2(see, e.g., Brouhns, Denuit, and Vermunt [BDV],

2002a). Furthermore, adverse selection, which is due to the mortality heterogeneity

of individuals and information asymmetries between the insurance company and the

insured, is one important source of basis risk when hedging longevity risk through

MCBs or other capital market instruments (see Sweeting, 2007). Basis risk arises if the

population mortality underlying the hedge and the hedged portfolio mortality do not

coincide. Thus, the differences in the mortality of the population and the mortality

of the insured annuitants caused by adverse selection imply basis risk in longevity

hedges. In this analysis, we solely consider the basis risk in longevity hedges3and

model all types of mortality risk explicitly in order to analyze their impact on a life

insurer’s risk situation.

Adverse selection (and basis risk) is modeled differently in the literature. Plat (2009)

proposes to model the difference in mortality rates for annuitants and the popula-

tion through an age- and time-dependent portfolio-specific mortality factor, which

reflects the relative difference between annuitant mortality and population mortality.

1See Finkelstein and Poterba (2002) and Cohen and Siegelmann (2010).

2In general, adverse selection refers to information asymmetry and hidden characteristics. In

this paper,we follow BDV (2002a) and refer to adverse selection as the observation that due to

mortality heterogeneity and asymmetric information, annuitants experience a lower mortality

than the average population and therefore have a higher life expectancy. Other papers (e.g.,

Coughlan et al., 2007) refer to this as basis risk. In the following analysis, we consider two cases

in order to highlight the importance of mortality information in underwriting, one where the

insurer is not fully informed about the mortality of its annuitants, and one case where adverse

selection can be fully addressed.

3Other potential sources of basis risk in longevity hedges are stated, for example, by Sweeting

(2007) or Coughlan et al. (2007) and include age mismatch or geographic differences.

MORTALITY RISK AND ITS EFFECT IN LIFE INSURANCE 59

Ngai and Sherris (2011) also use a portfolio-specific mortality factor and, following

Stevenson and Wilson (2008), assume a linear and constant effect of age as the only

impact factor. BDV (2002a) choose a different approachand model annuitant mortal-

ity through a Brass-type relational model for the central death rates. Concerning the

effectiveness of MCBs (or other instruments for transferring mortality risk to capital

markets) under basis risk resulting from adverse selection, other certain aspects have

already been discussed in the literature. Sweeting (2007) discusses the influence of

basis risk when using a survivor swap qualitatively in a utility-maximizing frame-

work and concludes that basis risk is comparatively small, and thus will not hinder

the occurrence of hedging transactions. In terms of the effectiveness of q-forwards4

based on the population mortality for hedging insured lives, Coughlan et al. (2007)

use historical data and conclude that the loss in efficiency is small from a long-term

perspective. Ngai and Sherris (2011) quantify the impact of basis risk in longevity

bonds and q-forwards in a static framework and find that basis risk does not signif-

icantly affect the hedging effectiveness. Coughlan et al. (2010) introduce a general

framework for assessing basis risk in longevity hedges and conclude that it can be

reduced considerably by applying their framework for calibrating the hedge. A more

general concept in this context, the so-called population basis risk, describes the risk

of basing the payout of the risk management instrument on a different population5

and is discussed by Li and Hardy (2009) and Coughlan et al. (2007). Thus, to date,

results in the literature suggest that basis risk in longevity hedges overall has a minor

impact on the effectiveness of the hedge.

The second risk management instrument, natural hedging, has also been studied in

the literature. Cox and Lin (2007) as well as Bayraktar and Young (2007) examine the

impact of natural hedging on pricing. Gr ¨

undl, Post, and Schulze (2006) and Hanewald,

Post, and Gr ¨

undl (2011) compare the effects of differentrisk management strategies on

shareholder value, concluding that natural hedging is the preferred risk management

tool, but only under certain circumstances. Wang et al. (2010) apply the concept of

duration to mortality and derive an optimal liability mix, which is characterized

by a portfolio mortality duration of zero, while Wetzel and Zwiesler (2008) show

that the mortality variance, i.e., the variance due to fluctuations in mortality, can be

reduced by more than 99 percent through portfolio composition. Gatzert and Wesker

(Forthcoming) consider the insurer as a whole and show how to immunize a given

risk level by simultaneously considering the investment and insurance portfolio.

Despite a fair amount of research on mortality risk, the impact of all three mortality

risk components (separately and combined) and basis risk resulting from adverse

selection on the risk level of a life insurance company and on the effectiveness of

different risk management strategies with respect to reaching a desired risk level as

well as hedging against unexpected changes in mortality has not been systematically

4Aq-forward is a standardized mortality contingent swap, based on the LifeMetrics index

by JP Morgan. The LifeMetrics index is distinguished by gender and age for the popula-

tion of United States, England, Wales, the Netherlands, and Germany (for more informa-

tion and current index data, see http://www.jpmorgan.com/pages/jpmorgan/investbk/

solutions/lifemetrics).

5Potential sources of population mismatch include differences in geographic location, age,

social status, etc.