Semicoherent Multipopulation Mortality Modeling: The Impact on Longevity Risk Securitization

• DOI: http://doi.org/10.1111/jori.12135
• Author: Wai‐Sum Chan,Rui Zhou,Johnny Siu‐Hang Li
• Date: 01 September 2017
• Published date: 01 September 2017

©2015 The Journal of Risk and Insurance. Vol.84, No. 3, 1025–1065 (2017).

DOI: 10.1111/jori.12135

Semicoherent Multipopulation

Mortality Modeling: The Impact on

Longevity Risk Securitization

Johnny Siu-Hang Li

Wai-Sum Chan

Rui Zhou

Abstract

Multipopulation mortality models play an important role in longevity risk

transfers involving more than one population. Most of the existing multi-

population mortality models are built on the hypothesis of coherence, which

assumes that there always exists a force that brings the mortality differential

between any two populations back to a constant long-term equilibrium level.

This hypothesis prevents diverging long-term forecasts, which do not seem

to be biologically reasonable. However, the coherence assumption may be

perceived by market participants as too strong and is in fact not always

supported by empirical observations. In this article, we introduce a new

concept called “semicoherence,” which is less stringent in the sense that it

permits the mortality trajectories of two related populations to diverge, as

long as the divergence does not exceed a specific tolerance corridor, beyond

which mean reversion will come into effect. We further propose to produce

semicoherent mortality forecasts by using a vector threshold autoregression.

The proposed modeling approach is illustrated with mortality data fromU.S.

and English and Welsh male populations, and is applied to several pricing

and hedging scenarios.

Introduction

Longevity risk has become a high-profile risk in recent years, due partly to the changes

in insurance regulations after the global financial crisis. For instance, Solvency II,

which is presently scheduled to be implemented in January 2016, requires insurers

operating in the European Union to hold longevity risk solvency capital to cush-

ion against the adverse financial consequences arising from unexpected changes in

mortality rates. Another reason is the deep interest rate cuts followed by quantita-

tive easing. At the current low interest rates, life-contingent cash flows payable in

Johnny Siu-Hang Li is at the University of Waterloo, Department of Statistics and Actuarial

Science, Waterloo,Ontario, Canada, N2L 3G1. Li can be contacted via e-mail: shli@uwaterloo.ca.

Wai-Sum Chan is at the The Chinese University of Hong Kong, Department of Finance, Hong

Kong. Rui Zhou is at the University of Manitoba Warren Centre for Actuarial Studies and

Research, Winnipeg, Manitoba, Canada.

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1026 The Journal of Risk and Insurance

the distant future, which are subject to the greatest amount of longevity risk, are not

discounted that heavily.

Securitization is increasingly seen as a solution to the problem of longevity risk.

Through securitization, a financial institution can transfer its longevity risk expo-

sure to one or more counterparties who are interested in accepting the risk expo-

sure for a premium. The potential of the longevity risk transfer market is huge. It

is estimated that in the United Kingdom alone, there are approximately $1 trillion

of defined-benefit pension scheme liabilities managed by corporate pension schemes

and around $200 billion of insured annuity-in-payment liabilities managed by life

insurance companies (Bugg et al., 2010). The market has recently seen several large

transactions, exemplified by the $3 billion longevity swap that Rolls Royce transacted

with Deutsche Bank in 2011 to cover the longevity risk of the 37,000 pensioners in its

pension plan (Coughlan et al., 2013).

However,relative to its potential size, the longevity risk transfer market has developed

rather slowly (Coughlan et al., 2013). The market has to overcome many challenges

before it can become liquid, with substantial volumes on both the supply and demand

sides. As Cairns (2013a) pointed out, the key challenge on the modeling front is to

develop multipopulation stochastic mortality models, which are crucially important

for the following reasons.

Natural buyers of longevity risk are limited only to life (re)insurance companies with

a concentration on policies paying death benefits and perhaps companies in the health

care, long-term care, and pharmaceutical industries that would benefit fromincreased

longevity. To further expand in size, the longevity risk transfer market has to reach

out to other potential investors, such as hedge funds and asset managers, who may

be attracted to this new asset class due to its low correlation with other market risk

factors (Ribeiro and di Pietro, 2009). These investors prefer standardized index-based

securities to customized deals, because the former are more transparent and liquid.

By contrast, hedgers may prefer customized hedging solutions, due to their concerns

about the population basis risk that arises from the difference in mortality experi-

ence between the populations associated with their portfolios and the populations to

which the standardized hedging instruments are linked. Multipopulation stochastic

mortality models permit hedgers to better measure the potential population basis risk,

giving them more confidence in hedging with standardized securities.

The European Union’s rules on gender-neutralpricing have recently become effective.

The rules require insurers in Europe to chargethe same prices to women and men for

the same insurance products without distinction on the grounds of sex. Life insurers

in Europe therefore have a pressing need for multipopulation stochastic mortality

models, which they can use to simultaneously forecast the mortality of both genders.

Multipopulation models can also assist them with the calculation of solvency risk

capital and the amount of risk exposurethat should be transferred through reinsurance

or capital markets.

In the market, there exist mortality-linked securities that areassociated with more than

one population. For instance, in 2010, Swiss Re issued a series of 8-year longevity

Semicoherent Multipopulation Mortality Modeling 1027

bonds (known as the Kortis deal) valued at $50 million to hedge its life insurance

exposure in the United States and pension exposure in the United Kingdom (Blake

et al., 2014). The principal repayment of this bond depends on the divergence in

realized mortality improvements between males aged 55–65 in the United States and

males aged 75–85 in England and Wales.To value securities similar to the Kortis deal,

a multipopulation stochastic mortality model is indispensable.

In the past few years, there has been a significant volume of research work on the

problem of multipopulation mortality modeling. Several multipopulation stochastic

mortality models have been proposed by researchers, including Li and Lee (2005),

Cairns et al. (2011), Dowd et al. (2011), Jarner and Kryger (2011), Chen et al. (2013),

Hatzopoulos and Haberman (2013), Hunt and Blake (2013), Li and Hardy (2011), Lin

et al. (2013), Yangand Wang (2013), Zhou et al. (2013), Zhou et al. (2014), and Ahmadi

and Li (2014). The majority of the recent developments in multipopulation mortal-

ity modeling have been built on an important concept called coherence, originally

proposed by Li and Lee (2005).

In coherent mortality forecasting, the future mortality rates of two or more related

populations are modeled jointly in such a way that there is always a force that brings

the spread between the mortality rates of any two populations being modeled back

to a constant level. Hence, coherent mortality forecasts do not diverge indefinitely

over time. For example, in Li and Lee’s (2005) augmented common factor model, co-

herence is achieved by modeling each population-specific time trend by a first-order

autoregressive process. The coherence hypothesis is supported in part by the argu-

ment that differences in mortality between related populations should not increase

over time indefinitely if their similar socioeconomic conditions and close connections

continue. It is also supported by certain empirical observations. For instance, Wilson

(2001) finds a global convergence in mortality levels by comparing the distributions of

the global population by life expectancy over three different time periods, 1950–1955,

1975–1980, and 2000. The same conclusion is drawn by White (2002) who considers

mortality data from 21 high-income countries over the period of 1955–1996.

Nevertheless, whether a mortality convergence can be observed depends very much

on the observation window and the populations involved. Oeppen and Vaupel(2002),

who introduced the notion of best-practice life expectancy, note that although a num-

ber of countries including Japan and Chile are converging to the best-practice level,

some countries such as the United States have been moving away from it in recent

decades. Hatzopoulos and Haberman (2013) compute the probabilities of noncoher-

ence (nonconvergence) for the residual age-period model structures for a group of

35 national populations. Their estimation results indicate that for some populations,

for example, England and Wales, the probabilities of noncoherence were large. The

conclusions of several other studies have contradicted the hypothesis of coherence.

Based on data from the U.S. National Longitudinal Mortality Study, Waldron (2007)

finds that for individuals who died in 1972–2001 at ages 60–89, the top half of the aver-

age relative earnings distribution experienced faster mortality improvement than the

bottom half. This pattern, according to Mackenbach et al. (2003), also exists in some

other developed countries, including Finland, Sweden, Norway, Denmark, England

and Wales, and Italy. Therefore, the hypothesis of coherence may be too strong and