Estimating extreme cancellation rates in life insurance

• Published date: 01 December 2021
• Author: Francesca Biagini,Tobias Huber,Johannes G. Jaspersen,Andrea Mazzon
• Date: 01 December 2021
• DOI: http://doi.org/10.1111/jori.12336

Received: 14 May 2019

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Revised: 26 October 2020

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Accepted: 22 November 2020

DOI: 10.1111/jori.12336

ORIGINAL ARTICLE

Estimating extreme cancellation rates in

life insurance

Francesca Biagini

1

|Tobias Huber

2

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Johannes G. Jaspersen

3

|Andrea Mazzon

1

1

Workgroup Financial and

Insurance Mathematics,

Munich Risk and Insurance Center,

Ludwig‐Maximilians‐Universität

München, Munich, Germany

2

Institute for Risk Management and

Insurance, Munich Risk and Insurance

Center, Ludwig‐Maximilians‐Universität

München, Munich, Germany

3

Institut für Versicherungsbetriebslehre,

Gottfried Wilhelm Leibniz Universität

Hannover, Hanover, Germany

Correspondence

Tobias Huber, Institute for Risk

Management and Insurance,

Munich Risk and Insurance Center,

Ludwig‐Maximilians‐Universität

München, Geschwister‐Scholl‐Platz 1,

80539 Munich, Germany.

Email: tobias.huber@lmu.de

Abstract

This paper assesses the risk of a mass lapse event in life

insurance. The rarity of the event and the complexity of

policyholder behavior make the risk assessment of

such a scenario difficult. Using a simulation study, we

evaluate how different estimation methods can assess

the risk of this scenario, using panel data at the com-

pany level. We then use the best‐performing method to

estimate the probability distribution function of a mass

cancellation event in the United States and Germany.

We identify dependencies of the event on company and

country characteristics, which have not been taken into

account by regulating agencies. We also find that the

current mass lapse scenario in Solvency II has no

empirical foundation for the German market. We show

that an empirically valid scenario leads to a sig-

nificantly lower solvency capital requirement for the

average German life insurer.

KEYWORDS

dynamic peaks over threshold, extreme value theory,

life insurance, mass cancellation

JEL CLASSIFICATION

C14; G18; G22; G32

J Risk Insur. 2021;88:971–1000. wileyonlinelibrary.com/journal/JORI

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This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and

reproduction in any medium, provided the original work is properly cited.

© 2021 The Authors. Journal of Risk and Insurance published by Wiley Periodicals LLC on behalf of American Risk and Insurance

Association.

1|INTRODUCTION

Rare events with extreme consequences often have a profound influence on economies and

their economic agents. The 9/11 terrorist attacks led to considerable changes in many economic

sectors, such as the airline industry. Hurricanes, such as Katrina and Sandy, have shaped how

we see flood protection and insurance. Financial crises, such as the Great Depression and that

of 2009, influence our considerations of financial regulation and economic risks, in general. For

organizations, extreme events can similarly shape existence. One such extreme event for life

insurance companies is the occurrence of a mass cancellation event, that is, a large portion or

even a majority of the policyholders who cancel their life insurance policy abruptly. Even

though policyholder‐cancellation behavior has received considerable attention in the academic

literature (e.g., Eling & Kiesenbauer, 2013; Kuo et al., 2003), the question of how to model mass

cancellation scenarios has received scant attention. This is surprising because the possibility of

mass cancellations has a large effect on insurance companies' asset liability management and

leads to one of the largest financial reserves in the European risk management framework

Solvency II (EIOPA, 2011).

This omission in the literature can be explained, in part, by the data requirements associated

with estimating extreme cancellation events. Extreme cancellation, and its associated rates, is a rare

event; thus, data sourced from only one insurer are not sufficient to estimate this tail risk. In this

paper, we address this challenge by employing the estimation approach of Chavez‐Demoulin et al.

(2016), which is based on extreme value theory and can be applied to panel data. We consider

cancellation rates as realizations of random variables but do not make any assumptions about their

distribution functions, except that they are continuous.

1

This method enables us to estimate the

unknown probability distribution functions and associated risk measures for extreme cancellation

events from readily available panel data at the company level.

Dependent on contract characteristics, cancellations can either negatively or positively af-

fect an insurer's profits. Unexpected changes in the level of cancellation rates can lead to

liquidity problems, the loss of expected future profits, and unbalanced initial expenses (Eling &

Kiesenbauer, 2013; Kuo et al., 2003). Life insurers are, thus, interested in assessing their

exposure to this risk as accurately as possible. U.S. life insurers can potentially face very high

cancellation rates, particularly after premium guarantee periods expire (SOA & LIMRA, 2018,

p. 29). The possibility of such an extreme event needs to be taken into consideration for a

company's asset liability management. In other situations, however, cancellations can increase

an insurer's profits, as policies are usually front‐loaded, and a cancellation allows insurers to

reap the early profits without having to incur expected losses in the later part of the policy's life

cycle (Gottlieb & Smetters, 2020). In each case, understanding cancellation behavior is crucial

for life insurers to ensure adequate asset liability management.

For the European market, the importance of understanding the cancellation behavior of

policyholders has become critical with the introduction of the new regulatory framework

Solvency II. The framework's solvency capital requirement (SCR) has a great sensitivity to lapse

risk (EIOPA, 2011, p. 67). In the standard model of the regulation framework, the mass lapse

1

The continuity assumption enables us to obtain results on the far end tail of the cancellation rates' distribution functions under technically mild assumptions.

The literature shows that the conditions for the existence of a limit distribution for discrete distribution functions are strong (Davison & Huser, 2015;

Hitz et al., 2017; Nadarajah & Mitov, 2002). Our continuity assumption allows us to consider a more flexible framework. The following reasons justify our

continuity assumption: (1) We observe no evidence for a discontinuous distribution function in the histograms of cancellation rates stemming from two

different countries (United States and Germany) between 1996 and 2018 (see Figures 1and 4). (2) The commonly assumed sources (e.g., unemployment rate or

interest rate) of cancellation rates are modeled as continuous random variables.

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