Dynamic Longevity Hedging in the Presence of Population Basis Risk: A Feasibility Analysis From Technical and Economic Perspectives

• DOI: http://doi.org/10.1111/jori.12158
• Date: 01 April 2017
• Author: Kenneth Q. Zhou,Johnny Siu‐Hang Li
• Published date: 01 April 2017

©2016 The Journal of Risk and Insurance. Vol.84, No. S1, 417–437 (2017).

DOI: 10.1111/jori.12158

Dynamic Longevity Hedging in the Presence of

Population Basis Risk: A Feasibility Analysis From

Technical and Economic Perspectives

Kenneth Q. Zhou

Johnny Siu-Hang Li

Abstract

In this article, we study the feasibility of dynamic longevity hedging with

standardized securities that are linked to broad-based mortality indexes. On

the technical front, we generalize the dynamic “delta” hedging strategy de-

veloped by Cairns (2011) to incorporate the situation when population basis

risk exists. On the economic front, we discuss the potential financial benefits

of an index-based hedge over a bespoke risk transfer. By considering data

from a large group of national populations, we find evidence supporting the

diversifiability of population basis risk. We further propose a customized

surplus swap—executed between a hedger and reinsurer—to utilize the di-

versifiability.As standardized instruments demand less illiquidity premium,

a combination of a dynamic index-based hedge and the proposed customized

surplus swap may possibly be a more economical (and equally effective) al-

ternative to a bespoke risk transfer.

Introduction

The market for longevity risk transfers started about 10 years ago. Since then, the

market has seen some significant developments, most notably in terms of the num-

ber and size of deals (Blake et al., 2014). However, relative to the size of the global

longevity risk exposure, the present longevity risk transfer market is still very small.

A small market not only impedes longevity risk management, but also poses sys-

temic concerns, because when longevity risk is shifted from the corporate sector to a

limited number of (re)insurers, with global interconnections, there may be systemic

Kenneth Q. Zhou is a PhD Candidate in the Department of Statistics and Actuarial Science at the

University of Waterloo, Canada. Johnny Siu-Hang Li holds the Fairfax Chair in Risk Manage-

ment in the Department of Statistics and Actuarial Science at the University of Waterloo,Canada.

Zhou and Li can be contacted via e-mail: kenneth.zhou@uwaterloo.ca and shli@uwaterloo.ca,

respectively. The authors are grateful to the anonymous reviewers for their very constructive

comments and suggestions. The authors would also like to thank participants at the Tenth

International Longevity Risk and Capital Markets Solutions Conference for their stimulating

discussions on an earlier version of this article. This work is supported by the Global Risk

Institute, the Society of Actuaries Center of Actuarial Excellence Programme, and the Natural

Sciences and Engineering Research Council of Canada (Discovery Grant RGPIN-356050-2013).

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consequences in the case of a failure of a key player (Basel Committee of Banking

Supervision, 2013).

The underdevelopment of the longevity risk transfer market may be attributed to

the marked imbalance between demand and supply. To date, most of the longevity

risk transfers executed are insurance based, typically in the form of pension buy-ins,

pension buy-outs, or bespoke longevity swaps. While the insurance industry has the

scope and financial stability to assume longevity risk, it does not generate sufficient

supply for acceptance of the risk because of its capacity constraints. Using the assets

for pension plans, in excess of 31 trillion USD, as a proxy for demand and the assets of

2.6 trillion USD held by the global insurance industry to cover nonlife risks as a proxy

for supply, Graziani (2014) concludes that the demand for acceptance of longevity

risk exceeds supply by a multiple of 10. Michaelson and Mulholland (2014) reach a

similar conclusion by comparing the potential increase in pension liabilities due to

unforeseen longevity improvement with the aggregate capital of the global insurance

industry.

The growth of the longevity risk transfer market, therefore, depends highly on the

creation of supply, most likely by inviting participation from capital markets, which

are capable of assuming a larger portion of the longevity risk exposures from pension

plans around the world.1The longevity asset class offers capital market investors a

risk premium, plus potential diversification benefits due to its very low correlation

with other asset classes. However, drawing interest from such investors requires the

longevity risk transfer market to package the risk as standardized products that are

structured like typical capital market derivatives and linked to broad-based mortality

indexes. The act of standardization is important in part because it fosters the develop-

ment of liquidity, and in part because it removes the information asymmetry arising

from the fact that hedgers (pension plans) have better knowledge about the mortality

experience of their own portfolios.

Toward the goal of standardization, the market for longevity risk transfers has to

overcome two technical challenges that discourage hedgers from using standardized

hedging instruments. The first challenge is to find out how standardized instruments

can be used to form a hedge that can eliminate a meaningful portion of the hedger’s

longevity risk exposure. Hedging strategies have to be developed so that hedgers

know the type and notional amounts of hedging instruments they need to acquire.

The second challenge is to understand and, more importantly, mitigate the residual

risks that are left behind by a standardized, index-based longevity hedge. Of the resid-

ual risks the most significant constituent is population basis risk, which arises from the

difference in future mortality improvements between the population associated with

the hedger’s own portfolio and the population(s) to which the standardized instru-

ments are linked. However, as explained below, the research questions on longevity

hedging strategies and population basis risk are still open.

1According to Roxburgh (2011),the total value of the world’s financial stock, comprising equity

market capitalization and outstanding bonds and loans, is 212 trillion USD at the end of 2010.