The Effect of Secondary Markets on Equity‐Linked Life Insurance With Surrender Guarantees

• Published date: 01 December 2014
• Date: 01 December 2014
• DOI: http://doi.org/10.1111/j.1539-6975.2013.12003.x

DOI: 10.1111/j.1539-6975.2013.12003.x

The Effect of Secondary Markets on Equity-Linked

Life Insurance With Surrender Guarantees

Christian Hilpert

Jing Li

Alexander Szimayer

Abstract

Many equity-linked life insurance products offer the possibility to surrender

policies prematurely. Secondary markets for policies with surrender guar-

antees influence both policyholders and insurers. We show that secondary

markets lead to a gap in policy value between insurer and policyholder. In-

surers increase premiums to adjust for higher surrender rates of customers

and optimized surrender behavior by investors acquiring the policies on sec-

ondary markets. Hence, the existence of secondary markets is not necessarily

profitable for the primary policyholders. The result depends on the demand

for and the supply of the contracts brought to the secondary markets.

Introduction

The world market for life insurance contracts is huge with a premium volume of 2,332

billion U.S. dollars in 2009 (SwissRe, 2010). Roughly 50 percent of these contracts in

most developed countries are terminated before the maturity date (Bundesverband

Verm¨

ogensanlagen im Zweitmarkt Lebensversicherung (BVZL) e.V., 2010; Gatzert,

2010). At the premature termination of contract, policyholders are offered predefined

lump-sum payments by the primal insurers called surrender guarantees. Usually,

these surrender guarantees are financially unattractive relative to the fair value of the

policy. In recent years, secondary markets for insurance contracts have developed.

They provide the policyholders with an alternative way to give up their contracts

Christian Hilpert is at the Bonn Graduate School of Economics, Adenauerallee 24-42, D-53113

Bonn, Germany.Jing Li is at the Department of Economics, Adenauerallee 24-42, D-53113 Bonn,

Germany. Alexander Szimayer is at the Department of Business Administration, University

of Hamburg, Von-Melle-Park 5, D-20146 Hamburg, Germany. The authors can be contacted

via e-mail: chilpert@uni-bonn.de, lijing@uni-bonn.de, and alexander.szimayer@wiso.uni-

hamburg.de. We thank Sven Balder, An Chen, Sebastian Ebert, two anonymous referees, par-

ticipants of the 7th World Congress of the Bachelier Finance Society, the 15th Conference of

the Swiss Society for Financial Market Research, and the Actuarial and Financial Mathematics

Conference 2012 as well as seminar participants in Bonn and Ulm for helpful comments and

discussions. C. Hilpert gratefully acknowledges financial support by the Deutsche Forschungs-

gemeinschaft (DFG) through the Bonn Graduate School of Economics.

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©The Journal of Risk and Insurance, 2013, Vol.81, No. 4, 943–968

944 The Journal of Risk and Insurance

prematurely by selling the contracts to thirdparties on these markets for higher prices.

In the United States and the United Kingdom, which are the world’s largest and third

largest life insurance markets, respectively, these secondary markets have a long his-

tory and have been growing in the last few decades. In other countries, like Japan and

Germany, secondary markets for life insurance contracts have been established

recently and a substantial increase in the trading volume on these markets can be

observed.1

In this article, we study the pricing of equity-linked life insurance contracts when a

secondary market exists. In our model, the secondary market increases the contract

value under the following two assumptions. First, primary policyholders surrender

contracts either for reasons exogenous to the conditions of the policy or because other

investment opportunities seem more advantageous. Second, contract buyers on the

secondary market are assumed to be financial experts being able to optimally exercise

the surrender option entitled by the insurers. The first assumption is in line with the

empirical study of Kuo, Tsai, and Chen (2003) who show in a cointegration analysis

that both endogenous (interest rate) and exogenous (unemployment) reasons affect

the lapse rate.2To model this behavior, we use the setup that can be found, for ex-

ample, in Albizzati and Geman (1994), Stanton (1995), deGiovanni (2010), and Li and

Szimayer (2010). Wecall this approach the bounded monetary rationality setup. In this

setting, the policyholders are not stopping the contingent claims optimally in mon-

etary terms, but make monetarily suboptimal surrender decisions. These surrenders

can still be rational, but due to reasons beyond the model. The second assumption

implies that the contracts become the pure American-style type once sold on the sec-

ondary market. Their prices can be derived within the American-style contingent

claim framework which is discussed, for example, in Grosen and Jørgensen (1997,

2000), Bacinello (2003, 2005), and Bacinello, Biffis, and Millossovich (2010). We show

that the added value created by the secondary market as a whole increases the sur-

render risk borne by the insurers, and hence, increases the contract value from the

insurers’ perspective. However, depending on the equilibrium out of the demand

for and the supply of the contracts brought to the secondary market, policyholders

may only receive part of the added value. The contract value from the policyhold-

ers’ perspective is thus lower than the value for the insurers. Overall, we find that

the policyholders may only profit partly from the secondary market. Although the

introduction of the secondary market may increase the payout to the policyholders,

it is not necessarily beneficial for them if the premium increases at the same time. We

1For the UK secondary markets for life insurance products can be traced back to 1844, for the

United States to 1911. The U.S. market has a volume of $US 2 million in 1990, $US 12 billion

in 2008, and BVZL estimates a traded volume of $30 billion for 2017. On the UK secondary

market, 20,000 contracts with a price volume of 200 million GBP were traded in 1996, which

increased to 200,000 contracts with a price volume of 500 million GBP in 2003. The price volume

of traded policies in Germany increased from D50 million in 2000 to D1.4 billion in 2007, while

the total volume of terminated contracts increased from D8.2 billion (2000) to D13.8 billion

(2009) (BVZL e.V.,2010; Gatzert, 2010)

2There are two ways of lapsing policies, either by surrendering the policy or by not paying

premiums. (see Kuo, Tsai, and Chen, 2003). In our article we only consider single-premium

contracts, and hence, the lapse rate is equivalent to the surrender rate.