Optimal Longevity Hedging Framework for Insurance Companies Considering Basis and Mispricing Risks

• Date: 01 September 2019
• Published date: 01 September 2019
• Author: Yu‐Yun Yeh,Hong‐Chih Huang,Sharon S. Yang
• DOI: http://doi.org/10.1111/jori.12238

OPTIMAL LONGEVITY HEDGING FRAMEWORK FOR

INSURANCE COMPANIES CONSIDERING BASIS AND

MISPRICING RISKS

Sharon S. Yang

Hong-Chih Huang

Yu-Yun Yeh

ABSTRACT

This article studies the optimal hedging strategy to deal with longevity risk

for the life insurer considering basis risk. We build up a longevity hedging

framework that incorporates not only the internal natural hedging but also

the external hedging by using the q-forwards. The optimal hedging strategy

is obtained by a minimizing-variance approach that can minimize the impact

of longevity risk on the insurer’s profit function. To investigate the basis risk,

instead of using population mortality, we adopt a unique mortality data set

of annuity and life insurance policies that enable us to calibrate the multi-

population mortality dynamics for different lines of insurance policies. We

consider three different hedging strategies: the natural hedging strategy, the

external hedging strategy, and combining both natural hedging, and

external hedging strategies. The hedge effectiveness for different hedging

strategies is evaluated. In addition, the mortality forecast model based on

VECM and ARIMA are used to examine the impact of basis risk on hedge

effectiveness. As a result, combining both internal and external hedging

strategies is the most effective way to manage longevity risk. Ignoring the

basis risk will decrease the hedge effectiveness.

INTRODUCTION

The recent increase in longevity has increased pressures on defined benefit (DB)

pension plan providers and annuity providers. Longevity risk has become non-

Sharon S. Yang is a Distinguished Professor at the Department of Finance and Associate Dean at

the School of Management, National Central University, Taiwan, and a Research Fellow at the

Risk and Insurance Research Center, College of Commerce, National Chengchi University,

Taiwan. Yang can be contacted via e-mail: syang@ncu.edu.tw. Hong-Chih Huang is a Professor

at the Department of Risk Management and Insurance, National Chengchi University, Taiwan,

and Director and Research Fellow at the Risk and Insurance Research Center, College of

Commerce, National Chengchi University, Taiwan. Huang can be contacted via e-mail:

jerryhch68@gmail.com. Yu-Yun Yeh is a Ph.D. Candidate at the Department of Finance,

National Central University, Taiwan. Yeh can be contacted via e-mail: yehun22@hotmail.com.

© 2018 The Journal of Risk and Insurance (2018).

DOI: 10.1111/jori.12238

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negligible and its influence is increasing gradually and globally. Hedging longevity

risks has taken on an increasingly important role for life insurance companies.

Finding a way to hedge longevity risk has received great attention in both academic

and practices.

In general, the hedging strategy can be categorized as an internal or external method.

Natural hedging is regarded as the internal hedging strategy that insurers can hedge

longevity risks with their own business products between life insurance and annuity

because these two types of products are sensitive in opposing ways to the changes in

mortality rates. Cox and Lin ( 2007) find empirical evidence that an nuity-writing insurers

who have more balanced business in life and annuity risks tend to charge lower

premiums than otherwise similar insurers. Wan ge t al. (2010) propose an immunization

model and Tsai, Wang, and Tzeng (2010) further use a conditional value at risk to

investigate the natural hedging strategy. Alternatively, the life insurer and pension

provider can seek to hedge longevity risk externally using capital market solutions.

Blake and Burrows (2001) first proposed that issuing survivor bonds could help a

pension fundinsure against longevityrisk. To utilize the capitalmarket for transferring

longevityrisk, more recent studies focuson the issue of securitization of longevityrisk,

and a variety of survivor securities and survivor derivatives have been developed in

bothacademic and practice(e.g., Lin and Cox,2005; Blake, Cairns,and Dowd, 2006; Cox,

Lin, and Wang, 2006; Dowd et al., 2006; Denuit, Devolder, and Goderniaux, 2007; Biffis

and Blake, 2009; Blake et al., 2010; Dawson et al., 2010). For example, the EIB/BNP

longevity bond aimed at transfering longevity risk, though it was never ultimately

issued. The world’s first capital market derivative transaction, a q-forward contract

between JPMorgan and the U.K. company Lucida, took place in January 2008;the first

capital marketlongevity swap, executed in July 2008, enabled Canada Lifeto hedge its

U.K.-based annuity policies. In December 2010, Swiss Re launched a series of 8-year

longevity-based insurance-linked securitynotes, which it calledKortis notes. Blakeet al.

(2013) note that the emergence of a traded market in longevity-linked capital market

instrumentswould act a catalyst to help facilitatethe development of annuity markets.

There are some discussions regarding external and internal hedging strategies for the

life insurer. Cox and Lin (2007) suggest that natural hedging is good but may be too

expensive to be effective in the context of internal life insurance and annuity products.

They show that insurers that exploit natural hedging by using a mortality swap can

charge a lower risk premium than others. In addition, the restriction of using the

natural hedging strategy for the insurers is that they must adjust the sales volume of

life insurance and annuity products to remain an optimal liability proportion, which

is sometime not feasible in practice. To overcome such a restriction, a natural hedging

strategy has been developed in some new forms in practice. For example, in

November 2012, in the United States, General Motors (GM) has offloaded a huge

amount of risk by transferring $25.1 billion of future pension obligations to Prudential

Financial. Since Prudential has a huge life assurance portfolio, its strategy is

motivated by a desire to exploit natural hedging that builds up its annuity exposure

by providing group annuities to GM. Regarding the external hedging strategy, Ngai

and Sherris (2011) investigate the effectiveness of static hedging strategies for

longevity risk management using longevity bonds and derivatives for annuity

products. Results show that static hedging using q-forwards or longevity bonds

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