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WHAT POLICY FEATURES DETERMINE LIFE INSURANCE

LAPSE? AN ANALYSIS OF THE GERMAN MARKET

MARTIN ELING

DIETER KIESENBAUER

WORKING PAPERS ON RISK MANAGEMENT AND INSURANCE NO. 95

EDITED BY HATO SCHMEISER

CHAIR FOR RISK MANAGEMENT AND INSURANCE

NOVEMBER 2011

WORKING PAPERS ON RISK MANAGEMENT AND INSURANCE, NO. 95 – NOVEMBER 2011

What Policy Features Determine Life Insurance Lapse?

An Analysis of the German Market

Martin Eling, Dieter Kiesenbauer*

Abstract

Considering the largest dataset ever used for this purpose (2.5 million contracts, 8.9 million

policy years), we analyze the impact of product and policyholder characteristics on lapse in the

German life insurance market. The sample period covers two periods of market turmoil that we

incorporate in our generalized linear models. The results show that product characteristics such as

product type or contract age and policyholder characteristics such as age or gender are important

drivers for lapse rates. Our findings improve the understanding of lapse drivers and might be used by

insurance managers and regulators for value and risk based management.

1 INTRODUCTION

In this work, we analyze the impact of product and policyholder characteristics on lapse and

surrender in the German life insurance industry using generalized linear models (GLMs).1 A proper

understanding of lapse drivers and the underlying dynamics is important for insurance managers and

regulators. Lapse influences an insurer’s liquidity and profitability (see Kuo et al., 2003; Prestele,

2006). Firstly, the insurer might suffer high losses from lapsed policies due to upfront investments for

acquiring new business (Pinquet et al., 2011). Secondly, the insurer faces the loss of future profits

from lapsed contracts. Thirdly, the insurer might face adverse selection with respect to mortality and

morbidity.2 Fourthly, the insurer might be exposed to a liquidity risk when forced to pay a surrender

* Martin Eling is professor of insurance management and director at the Institute of Insurance Economics at the

University of St. Gallen, Kirchlistrasse 2, 9010 St. Gallen, Switzerland ([email protected]). Dieter Kiesenbauer is with the Institute of Insurance Science at the University of Ulm, Germany (dieter.kiesenbauer@uni‐ulm.de).

1 Lapse and surrender both refer to the termination of an insurance contract before maturity, but there is a slight difference between these two terms (see, e.g., Kuo et al., 2003; Gatzert et al., 2009). While lapse refers to the termination of policies without payout to policyholders, surrender usually indicates that a surrender value is paid out to the policyholder. In accordance with Renshaw and Haberman (1986) and Kuo et al. (2003), the term ’lapse’ is used throughout to refer to both surrender and lapse. This is consistent with standard measures of lapse as they typically include lapsed policies as well as surrendered ones.

2 For example, customers in poor health condition might be less likely to lapse a contract including death cover as they will hardly find comparable insurance cover at the same premium level. Analyzing long‐term care insurance, Pinquet et al.


value for many lapsed policies at the same time; otherwise a more conservative investment strategy

might be used to ensure a sufficient liquidity at any time which reduces investment returns and

hence affects the profitability adversely.

The importance of lapse is especially discussed in the field of valuation and management of

embedded options in life insurance contracts. Historically, the right to lapse a life insurance contract

was not explicitly taken into account in the pricing process (Gatzert and Schmeiser, 2008). The

possibility to lapse a contract, however, constitutes an implicit option present in life insurance

contracts and its value can be quite substantial (see, e.g., Albizzati and Geman, 1994; Grosen and

Jørgensen, 2000; Bacinello, 2003; Gatzert and Schmeiser, 2008). The decline of Equitable Life in the

U.K. which was related to pension policies including guaranteed annuity options further intensified

this discussion (see O’Brien, 2006). In the 1990s, market annuity rates in the U.K. dropped

significantly and fell below the guaranteed level making that option particular valuable for the

customer. Therefore, insurers need to pay attention to all embedded options, including the

policyholder’s option to lapse a life insurance policy. Also regulators have identified lapse as one of

the major risk components of life insurance companies which needs proper monitoring and

management. For example, under the new European Union regulatory framework Solvency II lapse

risk constitutes the largest sub‐module in terms of solvency capital requirement within the life

underwriting risk module accounting for almost 40% of the capital requirement in this module (see

EIOPA, 2011, p. 77/78).3 The life underwriting risk itself accounts for almost 20% of the total capital

requirements constituting the second most material component in terms of capital requirements

behind market risk.

The existing empirical literature on lapse can be distinguished based on the explanatory variables

considered. The first set of literature uses environmental characteristics including macro‐economic

indicators and company data. Initially, only the impact of interest rates and unemployment on lapse

has been studied, referred to as interest rate and emergency fund hypotheses (see, e.g., Dar and

Dodds, 1989; Outreville, 1990; Kuo et al., 2003). This work has been extended by Kim (2005a,b), Cox

and Lin (2006), and Kiesenbauer (2011) considering additional economic indicators (such as gross

domestic product and capital markets development) and company characteristics (including

company size and legal form). The second set of literature uses single contract data to assess the

impact of product and policyholder characteristics on lapse. So far, only a limited number of such

analyses are available. Renshaw and Haberman (1986), Kagraoka (2005), Cerchiara et al. (2009), and

(2011) find that policyholders lapsing contracts have better health histories compared to their peers continuing the contracts.

3 Under Solvency II the capital requirement for the lapse risk sub‐module is calculated as maximum of three stress scenarios which are broadly defined as follows (see CEIOPS, 2010, p. 155‐159, for details): (1) a long‐term decrease of lapse rates by 50%; (2) a long‐term increase of lapse rates by 50%; and (3) a mass lapse event of 30% of all policyholders.


Milhaud et al. (2010) cover the Scottish, Japanese, Italian, and Spanish life insurance markets. Using

generalized linear models, these analyses indicate that factors such as policy duration, calendar year,

policyholder age, or method of payment significantly influence lapse.

Our study contributes to existing literature in four ways: Firstly, we consider the largest data set ever

used for such purposes (2.5 million contracts, 8.9 million policy years). The data is obtained from a

large German life insurer and includes seven different product categories including traditional and

unit‐linked products. We are thus able to investigate whether different products exhibit different

lapse behavior, in particular comparing traditional and unit‐linked products. The existence of such

differences has not been studied empirically so far. Secondly, this is to our knowledge the first

empirical study for the German life insurance market analyzing the impact of product and

policyholder characteristics on lapse.4 So far, only the relationship between surplus participation

rates and lapse rates has been discussed by Cottin et al. (2007), Eling and Kiesenbauer (2011), and

Kiesenbauer (2011) using market data. Thirdly, the analyzed time period from 2000 to 2010 is of

particular interest since it incorporates two phases of crisis (the stock market plunge from 2001 to

2003 and the 2008 financial crisis) which can be integrated in the analysis. Finally, the available data

address some of the shortcomings mentioned in previous studies. Having detailed information on the

date of policy inception, exact policy durations can be calculated, i.e., not only in terms of calendar

years (see Renshaw and Haberman, 1986). Furthermore, the data are already split into disjoint and

homogeneous product categories such that grouping is not necessary (see Cerchiara et al., 2009).

Moreover, we extend the existing literature by considering remaining policy duration, distribution

channel and supplementary cover, which are all significant lapse drivers as we will show throughout

our analysis.5

Regarding the main results, we find that all considered product and policyholder characteristics have

a statistically significant impact on the lapse rate development, but the magnitude of the effects

varies. The largest variations are observed for calendar year, contract age, remaining policy duration,

and premium payment (single vs. regular). The direction of impact is consistent with the existing

literature (Renshaw and Haberman, 1986; Kagraoka, 2005; Cerchiara et al., 2009; Milhaud et al.,

2010), except for product type which has only a limited effect on lapse rates. We extend the existing

4 Lapse is usually measured in terms of sum insured in the German market. Additionally, we consider lapse rates in terms of number of contracts and regular premiums as robustness measures (see Eling and Kiesenbauer, 2011). The modeling approach is the same as for the existing studies in this field, i.e., generalized linear models, which allows comparing our results with the existing ones.

5 The existing studies indicate further possibly relevant characteristics identifying different client segments based on socio‐economic information (e.g., policyholder income, area of residence, or tenant vs. homeowner). Due to strict regulation of data protection, insurers are only allowed to ask for information relevant for the risk assessment and pricing. Therefore, just like in all other existing studies such information is also not available in the German market. Also due to confidentiality reasons, actual lapse rates are not presented in this paper. Instead, similar to Cerchiara et al. (2009), we restrict to relative effects when presenting the results.


knowledge in that we show that the remaining policy duration, distribution channel, and

supplementary cover are significant lapse drivers. Finally, we consider interactions between one

fixed variable and all other characteristics in order to assess whether there exist differences for the

different levels of product categories, distribution channels, supplementary cover, or premium

payment. Again we find that the impact on lapse rates for all policy(holder) characteristics is very

consistent across product categories. All these results are helpful for insurance managers and

regulators, especially in the context of risk and value based management.

The remainder of this paper is structured as follows: Section 2 provides an overview of the empirical

literature regarding life insurance lapse. Section 3 describes the methodology and data. Section 4

presents and discusses the results of our analyses. We conclude with Section 5.

2 EMPIRICAL LITERATURE ON LIFE INSURANCE LAPSE

The existing empirical literature studying lapse drivers can be subdivided into two classes depending

on the characteristics considered as explanatory variables (see Figure 1). While the first set of

literature focuses on environmental specifics (i.e., macro‐economic indicators or company

characteristics), the second part focuses on product and policyholder features. Regarding the first

stream much more research has been published since publicly available data can be used. The

number of papers in the second stream is smaller and more recent since individual data on policies

are needed, which are typically treated highly confidential.

Considering the first stream of literature, the research on environmental root causes of life insurance

lapse focused on the so‐called interest rate and emergency fund hypotheses for a long time. The

interest rate hypothesis assumes that lapse rates are negatively related to internal rates of return,

e.g., surplus participation, and positively related to external rates of return, e.g., market interest

rates or stock returns (for details see Dar and Dodds, 1989; Kuo et al., 2003). The emergency fund

hypothesis conjectures that personal financial distress forces policyholders to lapse their contracts in

order to access the surrender value (see, e.g., Outreville, 1990). These two hypotheses have been

studied empirically, e.g., by Dar and Dodds (1989), Outreville (1990), and Kuo et al. (2003) with focus

on different life insurance markets and product types. It is hence not surprising that the results are

not consistent, in particular as the variable specifications vary widely (see Kiesenbauer, 2011, for a

more detailed discussion). These studies focus on information on interest rates or unemployment (as

indicator for adverse economic conditions), but do not take into account other economic factors

(e.g., stock returns, gross domestic product), company characteristics, or product and policyholder

information.


Kim (2005a) provides the first empirical study considering a broader set of economic explanatory

variables including, e.g., economic growth rates and seasonal effects. Moreover, the contract age

since policy inception is considered as product characteristic. Kim (2005a) models aggregate lapse

rates of a South Korean life insurer for four different product categories (endowment, annuity,

protection plan, and education) using the logit and complementary log‐log model, respectively. The

results indicate that policyholder lapse behavior indeed depends on additional exogenous factors

beyond interest rates and unemployment rates. Using a similar set of explanatory variables to

analyze single premium deferred annuities in the U.S., Kim (2005b) and Cox and Lin (2006) arrive at

similar conclusions deploying a logit and tobit model, respectively. Additionally, Cox and Lin (2006)

indicate that the Poisson and the negative binomial regression model are more appropriate to model

lapse behavior, but these models require individual (i.e., single contract) data rather than aggregate

lapse rate data. All these models, i.e., logit, complementary log‐log, tobit, Poisson, and negative

binomial, belong to the same broad class of models, the so‐called generalized linear models.

Kiesenbauer (2011) analyzes lapse rates in the German life insurance market using the same

modeling approach as Kim (2005a). The author employs market data to study lapse behavior with

respect to economic indicators and additional company characteristics such as company age,

company size, or legal form. The analysis is based on publicly available market data and does not take

into account any product or policyholder characteristics, except for the product split distinguishing

endowment, annuity, term life, group, and unit‐linked business. The results support the above

conclusion that other factors beyond interest rates and unemployment influence lapse behavior,

including company characteristics.6

Empirical literature analyzing life insurance lapse with respect to product and policyholder

characteristics is rather limited. This is probably due to the fact that lapse data are treated highly

confidential by most life insurers. Therefore, only aggregated lapse rate information is usually

publicly available in most life insurance markets. An analysis of product and policyholder

characteristics requires a more detailed data split which can only be provided by life insurers. The

first empirical study of Renshaw and Haberman (1986) dates back to the mid‐1980s, but only recently

the topic attracts more attention. This is driven by accounting and regulatory changes which require

an appropriate assessment of lapse. Table 1 provides an overview of the empirical literature

comparing time period covered, sample size, products and policyholder characteristics considered,

and modeling approaches.

6 Additionally, Kiesenbauer (2011) examines to which extent the interest rate and emergency fund hypotheses do hold for the German life insurance market. Both hypotheses do not hold for traditional, i.e., not unit‐linked, life insurance products, while they are supported when unit‐linked business is considered.


Renshaw and Haberman (1986) is the only work analyzing multiple companies based on a data set

provided by the former Scottish Faculty of Actuaries. It is also the only work considering different

product categories. All other existing studies focus on data of a single life insurer and consider only

one product category. All existing empirical studies, which analyze the impact of product and

policyholder characteristics on lapse behavior, use generalized linear models to assess the relevant

contract features and policyholder characteristics.7 Generalized linear models have been applied to a

wide range of problems in actuarial science. Using these models in non‐life insurance pricing, in

particular for motor insurance (see, e.g., Brockman and Wright, 1992; Ohlsson and Johansson, 2010),

might be the most prominent example. Other fields include, e.g., survival modeling, multiple‐state

models, and reserving (see, e.g., Renshaw and Haberman, 1996; Mosley, 2004). An exhaustive

overview of the applications of generalized linear models in actuarial science can be found in

Renshaw and Haberman (1996) or de Jong and Heller (2008). Generalized linear models are an

extension of the widely used linear regression models and provide a particular rich class of models

which are neither restricted to linear relationships nor to the usual normality assumption. The

pioneering work in applying generalized linear models to life insurance lapse is Renshaw and

Haberman (1986). According to Cerchiara et al. (2009), generalized linear models are especially

powerful in investigating the relationship between the available explanatory variables and the

observed response variable, i.e., lapse behavior in this case. GLMs allow assessing the direction and

magnitude of the impact on the lapse behavior caused by the variability of single parameters, which

is the main topic of this paper.

Due to the different data samples and, in particular, the different explanatory variables, the results of

the existing empirical studies analyzing product and policyholder characteristics are not directly

comparable. The results are, however, consistent to the extent that all existing studies identify

several significant explanatory variables and indicate their importance for lapse behavior. Renshaw

and Haberman (1986) find an additional significant interaction between policy type and duration of

policy meaning that the lapse rate not only depends on single factors but also on the combination of

factors. All characteristics considered in Kagraoka (2005) are identified as significant including the

change in unemployment rate being an economic indicator. Latter result supports the above

mentioned emergency fund hypothesis. Such effects are captured only indirectly in the other studies

using calendar year information. The study of Cerchiara et al. (2009) shows the importance of policy

duration, calendar year, and product class. Milhaud et al. (2010) find the biggest surrender risks for

policies including a fiscality constraint, i.e., surrender charges only apply for a certain part of the

7 Milhaud et al. (2010) consider additionally the CART model which does not belong to the class of generalized linear models.


contract duration.8 As soon as the contract has reached the point when the policyholder can

surrender without penalty, the lapse risk increases significantly. Other relevant risk factors include

policyholder age or method of payment (i.e., regular vs. single premiums where regular premiums

are further divided into monthly, bi‐monthly, quarterly, half‐yearly, and annual installments).9

3 DATA AND METHODOLOGY

3.1 Data

The German supervisor BaFin distinguishes three types of lapse rates: (1) early lapse representing the

counseling and product quality; (2) late lapse assessing the insurer’s service quality during the policy

term; and (3) total lapse measuring portfolio growth, i.e., to which extent is lapsed business offset by

new business written. The corresponding lapse rates are calculated in terms of sum insured. The

early lapse rate is defined as ratio of all lapses without surrender value over new business written.

The surrender value and thus this ratio strongly depend on the product design, e.g., term life

insurance has a very limited surrender value for the entire contract duration. The late lapse rate is

defined as ratio of all lapses with surrender value plus all policies made paid‐up (i.e., the customer

stops or reduces premium payments but does not lapse the contract) over sum insured of the entire

portfolio at the beginning of the calendar year.10 Again this ratio depends on the product design. The

total lapse rate is given by the aggregated sum insured of early and late lapses divided by the average

volume of business in force during the calendar year (i.e., half of the portfolio sum insured at the

beginning and at the end of the calendar year).

Early, late, and total lapse rates in the German life insurance industry are displayed in Figure 2. These

rates represent the entire market, as no further breakdown by product categories is available. The

higher volatility of the early lapse rate fluctuating between 7 and 17% can be explained by the

different denominator compared to late and total lapses. Sum insured is far less for new business

compared to total business in force. The exceptional fluctuations for the early lapse rate in

8 This is a specific contract feature which does not exist in all insurance markets. In particular, surrender fees always apply in case of lapsing before maturity in the German life insurance market.

9 When discussing lapse, the existence of the secondary market for life insurance might affect customer behavior in certain product categories. Policies are purchased by life settlement providers, market makers, or auctioneers. Those contracts are placed in closed funds or trusts for life settlement securitization or kept in the buyer’s own books (see Gatzert, 2010). Certain life insurance policies, which would be lapsed otherwise, are continued through the existence of a secondary market. Thus, lapse rates and surrender profits will decrease in markets with increasing relevance of the secondary market (see Gatzert et al., 2009). The importance the secondary market is still limited for the German life insurance market as it enters a state of stagnation (see Gatzert, 2010). Therefore, neglecting the secondary market for our analysis should have limited influence on the results.

10 This consideration is in contrast to Renshaw and Haberman (1986). Their definition of lapse only includes the premature termination of contracts (with or without paying a surrender value), but explicitly excludes conversion to a paid‐up amount or premium reduction.


1999/2000 and 2004/05 were driven by announcements of the German federal government to

enforce the tax treatment for certain life insurance policies from the beginning of 2000 and 2005,

respectively. This led to a kind of ‘closing sale’ significantly increasing the sales volumes in 1999 and

2004 and decreasing sales volumes in the following years.

For the life insurance industry, premium volume and number of contracts belong to the key

performance indicators and, hence, are in general more relevant than sum insured. Thus, it is not

uncommon to calculate lapse rates in terms of lapsed regular premiums or lapsed number of

contracts. Regular premiums, however, do not take into account single premium business. Number

of contracts lacks completely any volume information, i.e., contracts with small and high premium

are treated identically. The sum insured instead takes into account both single premium business and

reflects contract size.11 This explains the use of sum insured by the German supervisor. In this work,

we measure lapse rates using sum insured according to the BaFin definitions (differentiating between

early12, late, and total lapse), but also consider regular premiums and number of contracts. This

allows investigating whether significant differences exist.

The data analyzed in this paper have been provided by a German life insurer13 and cover the time

period 2000 to 2010 including only contracts which have been newly issued during this time. The

data set comprises seven different product types: term life insurance, endowment, (traditional)

annuity, unit‐linked annuity, Riester pensions, (traditional) Rürup pensions, and unit‐linked Rürup

pensions. While the first four products are common for many insurance markets, the latter three are

specific to the German market. Riester and Rürup products constitute state‐aided private pension

schemes.14 Furthermore, as the unit‐linked business accounts for one third of all policies, we are able

to assess whether there exist significant differences between these products and traditional business

11 The sum insured, however, varies widely for different life insurance products. For instance, the sum insured of term life insurance is usually much higher than for, e.g., disability insurance.

12 Contrary to the BaFin definition, we model the early lapse rate in terms of total business in force instead of using only new business. This changes the absolute lapse rate level, but should have only a limited impact on the relative effects. Using generalized linear models for the analyses (see Section 3.2) and focusing on new business neglects completely all early lapse events which do not occur within in the first year after policy inception which might bias the results heavily.

13 Lapse rate information is treated highly confidential by life insurance companies. Therefore, confidentiality needs to be maintained throughout the paper. We are thus not able to show absolute lapse rates. Instead we present effects relative to a reference level, i.e., how much smaller or higher is the lapse rate for a certain level (e.g., endowment) compared to a reference level (e.g., traditional annuity). This still allows to draw conclusions on the importance of the considered product and policy(holder) characteristics and the magnitude of the corresponding effects. Additionally, we cannot indicate the distribution mix of the company as it potentially allows identifying the company.

14 As the population in Germany and most developed countries is aging, the benefits of the social pension insurance are cut. Riester and Rürup pensions have been introduced in 2002 and 2005, respectively. Eligible beneficiaries for the Riester pension include employees being mandatory enrolled in the German statutory pension insurance, recipients of wage compensation benefits, and tenured civil servants. The detailed eligibility criteria, however, are complex (see, e.g., Börsch‐Supan et al., 2008). The Riester subsidization consists either of tax funded contributions (basis allowance plus children allowance) or an income tax refund. These subsidies depend on certain criteria and additional restrictions apply for such contracts (for details see Börsch‐Supan et al., 2008). Rürup pensions are subsidized private pensions especially targeting people that are not mandatory insured in the German statutory pension insurance (e.g., self‐employed people) and hence are not eligible for the Riester subsidies. Contributions are tax‐deductible and the accumulated capital needs to be repaid as a monthly, life‐long annuity (see, e.g., Corneo et al., 2010).


(endowment, annuity). Beyond the above outlined product split the following policy and policyholder

information is available:

Calendar year Strictly speaking, the calendar year constitutes an exogenous variable not being

directly related to an insurance contract. The lapse behavior of customers, however, usually also

depends on exogenous factors (see the above discussion on the emergency fund and interest rate

hypotheses). The consideration of calendar year effects allows, for instance, to assess the existence

of systematic deviations in lapse rates for certain years, e.g., in the stock market plunge from 2001 to

2003, driven by the enforced tax treatment starting in 2005, or during and following the 2008

financial crisis.

Contract age Having the inception date of the policy, the contract age since inception is calculated

in years. A contract age of t means that a policy is in its t‐th contract year. As the data set only

includes polices written from 2000 onwards, the maximum observed contract age is eleven. This

variable allows drawing conclusions on the counseling and service quality of the insurer, but also

might reflect changes in customer needs.

Remaining policy duration The termination date of the main insurance contract allows to calculate

the remaining contract duration. It is measured in remaining years, i.e., a duration of t means that

the contract will expire within the t‐th year from today. The customer can modify the contract term

and, hence, the remaining contract duration changes accordingly.

Policyholder age / sex The data include only information on age and sex of the person insured but

not the policyholder. In all cases where the person insured is older than 18 years at policy inception,

it seems likely that the person insured is actually the policyholder. Therefore, we restrict our analysis

to those policies which only slightly reduces the extent of the data set.

Distribution channel The data allow to identify both the distribution channel when the policy is

issued as well as the currently responsible distribution channel. The considered life insurer uses a

multi‐line distribution strategy as most German life insurers do. Due to confidentiality reasons, we

only distinguish four distribution channels which are used by most life insurers in the German

market, i.e., tied agents, brokers, banks, and other. For our analysis we focus on the current

distribution channel since it might be more relevant than the original one for the lapse decision.15

Supplementary insurance It is possible to combine a main insurance contract with additional

covers. In the present data set supplementary covers include term life insurance, disability insurance,

15 All analyses have also been performed using the original distribution channel. As changes of the responsible distribution do not occur very often, the results do not change much. In particular, the observed effects and conclusions still hold when the original distribution channel is considered. Detailed results are available upon request.


accident insurance, and surviving dependents insurance. As these supplementary covers can be

arbitrarily combined, the number of possible combinations is high. In order to reduce complexity, we

only model whether a policy includes any supplementary cover or not, but do not distinguish

between the number and/or type of supplementary cover(s).16 It is possible that some of the other

policy(holder) characteristics vary for main cover and supplementary cover (e.g., policyholder

age/sex or policy duration). We always focus on the main insurance contract to determine the value

of the corresponding characteristic. A contract with supplementary cover is counted as single

contract since usually only the entire contract can be lapsed. For premiums and sum insured, we

always consider the total amount including all additional covers.

Premium payment We distinguish between single premium business and contracts with regular

premium payments. The data do not distinguish between different regular premium installments,

e.g., monthly, quarterly, or semi‐annually (see Milhaud et al., 2010). Most customers pay their

premiums monthly or annually in the German life insurance market.

Changes in the underlying policy(holder) characteristics for a single contract as well as premium

exemptions or reductions are identified comparing year end values for the entire portfolio from one

year to the next. For simplicity reasons, we assume that contract modifications always take place at

the ‘anniversary’ of the contract. It might be interesting to investigate seasonal effects (see Kagraoka,

2005). This requires, however, monthly or quarterly data which tremendously increases the cost of

data provision.

Some characteristics change during the life time of an insurance contract, e.g., policyholder age,

contract age, or remaining policyholder duration. Therefore, the data need to be prepared for the

analysis as follows. Each contract is split into all possible combinations of considered product and

policy(holder) characteristics. We denote such a combination of characteristics as model point. A

sample model point is: endowment (product type), 2005 (calendar year), 5 (contract age), 35

(remaining policy duration), 25 (policyholder age), broker (distribution channel), no (supplementary

cover), male (policyholder sex), and regular (premium payment). For each model point, the exposure

of all contracts in the portfolio needs to be determined, i.e., the time (measured in years on a daily

basis) all contracts belong to the corresponding model point. Finally, we determine the number of

early and late lapse events for each model point. Each lapsed contract is counted as lapse in the

model point which represents the product and policy(holder) characteristics at the lapse date.

16 Some combinations of main insurance and supplementary cover are only available in a limited number of cases. Having a

reasonable number of observations for each characteristic is a prerequisite to run the generalized linear model; otherwise the results might be strongly biased.


The data set considered covers 2.5 million contracts and almost 8.9 million contract years. It, hence,

represents the broadest study in terms of sample size compared to all existing analyses (see Table 1).

Number of contracts, contract years, and early/late lapse events are displayed for all product

categories in Table 2. The contract years and early/late lapse events are further broken down by

calender years. As only new business written from 2000 onwards is considered, the number of

contract years is strongly increasing during the first years and stabilizing at later years. Riester and

Rürup pensions have been introduced in 2002 and 2005, respectively. Therefore, these products did

not exist in previous years. Term life insurance accounts only for about 5% of the entire portfolio. The

split between early and late lapse is different for term life. As this product does not accumulate

major savings, most lapse events are classified as early lapse even if the lapsed contract has been in

force for several years.

3.2 Methodology

We use generalized linear models (GLMs) to analyze lapse rates depending on the considered

product and policy(holder) characteristics. This class of models has been introduced by Nelder and

Wedderburn (1972) as extension to linear regression models weakening the restrictive assumptions

of those models (i.e., normally distributed errors, constant variance, and additivity of explanatory

variables). As GLMs have been widely applied in actuarial science (see, e.g., Renshaw and Haberman,

1996), we only provide a short summary of relevant aspects for our analysis. McCullagh and Nelder

(1989) discuss theory and application of GLMs in detail.

The generalized linear model is defined as X) (g = E(Y) -1 , where Y represents the vector of

dependent variables, E(.) refers to the expected value, and X denotes the matrix of observed values

of the considered characteristics. Y is called the random component of the GLM. Its elements Yu are

assumed to be independent having a distribution which belongs to the exponential family (e.g.,

Normal, Binomial, or Poisson). The linear predictor X is called systematic component where

denotes the regression coefficients. The relationship between random and systematic component is

given through the monotonic and differentiable link function g.

In our case, the random component Yu models the number of lapses for the model point u of the

considered product and policy(holder) characteristics. The possible values for each product and

policy(holder) characteristic are referred to as 1,,0 VarniVariv and are displayed in Table 3. Var

determines the considered characteristic and nVar represents the total number of values for each

characteristic.


Let TPPPTu xxx ˆ,,ˆˆ represent the vector of observed values for model point u. Modeling all

characteristics categorically, we consider the vector 1,,0 VarniVarix which is defined as

else0

ˆif1 VarVariVar

i

xvx

The value Varv0 is referred to as reference level of the corresponding characteristic. In order to have a

common reference level for all analyses, we use the value that has the largest exposure and

represents at least one early and one late lapse event.17 For instance, no Riester pension has been

terminated early in calendar year 2009 or 2010. As those ’empty’ cells bias the results, they are not

taken into account.18 In order to reduce the number of regression coefficients to be estimated, the

reference levels of all characteristics are combined with the intercept of the linear predictor. The

linear predictor can thus be written as follows:

PPPPPSPSSCSCDCDCDCDC

PSPAPAPAPDPDPDPDCACACACA

CYCYCYCYPTPTPTPT

xxxxx

xxxxxx

xxxxX

1111113311

484811464611101011

10101166110

According to Cerchiara et al. (2009), the logit link g(x) = log(x/(1−x)) along with binomial error terms

is the typical approach for modeling lapse (or retention or new business conversion) rates. The

resulting modeling results are, however, not easily interpretable. The Poisson model with g(x) =

log(x) which is favored by Kagraoka (2005) provides a reasonable approximation, if (1) the response

variable is close to zero (being usually the case for lapse rates) and (2) the model output is used

qualitatively rather than quantitatively, i.e., the focus is rather on the identification of relevant lapse

drivers and not on predicting future lapse rates accurately (which fits our research focus as outlined

in Section 2).19 As each model point defines a specific combination of the product and policy(holder)

characteristics considered, each contract has a unique path through a certain subset of all possible

model points. The time each contract belongs to a certain model point u is used to define the

exposure (time) eu. Latter is the sum of the time that each contract belongs to the model point u (in

years, possibly zero) taking into account all contracts in the portfolio. Introducing additionally the

lapse rate lru, we can rewrite the GLM as E(Yu) = eu · lru = exp(X). This yields 17 The reference level for the distribution channel is chosen arbitrarily in order to maintain confidentiality. 18 Removing data might also bias the results. As the considered data set is very large and only a negligible amount of data is removed, we assume this effect to be very limited.

19 The binomial model (mentioned by Cerchiara et al., 2009) and the negative binomial model (mentioned by Kagraoka, 2005) have also been analyzed. These modeling approaches require count data instead of exposure data. Compared with the Poisson model on count data, the parameter estimates of the Binomial model are almost identical, while those of the negative binomial model are different to a certain extent but still yield qualitatively identical conclusions. Detailed results are available upon request.


payment premiumfor factor Adj.

11

peproduct tyfor factor Adj.

6611

levelBase

0 expexp)exp( PPPPPTPTPTPT

uu xxx

elr

i.e., the lapse rate depends on a multiplicative structure. The base level, which corresponds to the

lapse rate of the joint reference level for all considered characteristics, is adjusted for each product

and policy(holder) characteristic if it differs from the reference level. Note that for each model point

and each characteristic 0Varix for at most one 1,,1 Varni .

The above discussion focuses – strictly speaking – on the consideration of number of contracts. The

same line of argument can, however, be applied for lapsed regular premiums and lapsed sum insured

assuming that each single Euro can be lapsed or not. Thus, the same modeling approach is used,

except that the exposure is measured in Euros instead of years. The exposure of regular premiums

and sum insured for the model point of a single contract is determined as product of timely exposure

(in years) multiplied by yearly premium and total sum insured, respectively.

So far, only single effects of the explanatory variables have been considered (e.g., product category

or calendar year), but not the combination of different variables, e.g., effects of calendar year 2008

for Riester pensions. These so‐called interactions allow to take into account not only changes within

one explanatory characteristic, but also combinations of two or more characteristics (see, e.g.,

Renshaw and Haberman, 1986; Cerchiara et al., 2009). We focus on interactions between only two

factors as interactions increase the model complexity and, hence, increase the run time of the

corresponding GLM analyses tremendously.20 The same reference levels are considered for the

generalized linear model including interactions as for the model without interactions.

4 RESULTS

We present the results of two model specifications in the following. The results of the generalized

linear model (GLM) without interactions are discussed in Section 4.1. The results including

interactions between product category, supplementary cover, premium payment, and distribution

channel, respectively, with all other characteristics (as described in Section 3.2) can be found in

Section 4.2.

4.1 GLM without interactions

20 For each interaction of two factors, the number of additional variables is calculated as product of the number of levels for each considered characteristic less one. For instance, the consideration of interactions between product category and

distribution channel introduces 18=(7−1)∗(4−1) additional regression coefficients to be estimated.


Table 4 displays the results of the GLM estimations without interactions for total lapse considering

three different measures for lapse rates, i.e., number of contracts, regular premium volume, and sum

insured. The resulting lapse rate levels differ for the different measures. The effects of the

considered product and policy(holder) characteristics relative to the reference level are, however,

very consistent as shown in Table 4. Most of the considered variables are consistently significant at

the 1% level and the coefficient estimates are close to each other. The parameter estimates

represent the natural logarithm of the multiplicative effect relative to the reference level. For

instance, a value of 0.15 for endowment (using number of contracts to measure exposure) means

that the lapse rate for endowment policies is exp(0.15) = 1.16 times the lapse rate of annuities

representing the reference level; in other words, the lapse rate for endowments is 16% higher than

the lapse rate of traditional annuities. In Table 4 we focus on total lapse, but similar results do hold

for early and late lapse. These results are available upon request.

In the following, we discuss the results of each characteristic in detail. Due to the above observation,

we focus on the consideration of number of contracts. The results are visualized using a similar

format compared to Cerchiara et al. (2009). The solid, dashed, and dotted line represent the

estimated regression coefficients for total (as displayed in Table 4), late, and early lapse, respectively

(left axis). The estimate for the reference level is set to zero as it is included in the intercept term

(see Section 3.2). The columns represent the exposure in million years as volume measure for the

different levels of the characteristic (right axis). The GLM does only provide results for such classes

for which at least one lapse event is present. Classes which do not contain any lapse event need to

be removed from the analysis. The exposure for the analysis of early lapse (light gray boxes) is hence

usually less than the exposure for late and total lapse (additional dark gray boxes). We use the same

scale for both axes in all figures to facilitate the comparability of the magnitude of the effects across

different characteristics. Whenever possible, our results are compared to the results of the existing

studies.

Product type The total lapse rate does not vary much across product categories (see Figure 3).

Compared to the lapse rate of traditional annuities, which constitutes the reference level, the lapse

rates of the other products are between exp(−0.37) = 0.69 for traditional Rürup pensions and

exp(0.15) = 1.16 for endowments, i.e., from 31% less to 16% higher. Endowments experience the

highest lapse rate followed by Riester pensions. While this result might be expected for Riester

pensions (due to the complicated product introduction and the recent discussion regarding high

acquisition and administration cost of those products), it is rather surprising for endowments. Latter

effect might be explained by the restriction to new business written since 2000 (neglecting the large

portfolio of policies in force for a long time and hence less prone to lapse). This indicates, however,


that customer lapse behavior for endowments might be changing in the future. The results regarding

traditional and unit‐linked products are mixed. While unit‐linked annuities have a lower lapse rate,

unit‐linked Rürup pensions experience higher lapse rates compared to their traditional counterparts.

Compared to annuities, Rürup pensions experienced so far reduced lapse rates. Rürup pensions are

designed for self‐employed people and are state‐aided. As those customers might be better

financially educated and the federal subsidies might be lost in case of lapse, this might explain the

lower lapse rates. The potential loss of federal subsidies, however, has no observable impact on

Riester policies. The significantly lower early lapse rate for Riester policies is due to the different

treatment of acquisition costs in these policies. They have to be equally distributed over the first five

years of the contract term. Therefore, a surrender value is built up much earlier such that a lapse in

the first contract years is counted as late lapse instead of early lapse, i.e., it is a reclassification of

lapse which has only a minor impact on the overall lapse rate level. This effect is reversed for term

life insurance. These products provide almost pure risk cover and have only a very limited savings

component. Therefore, most of these policies do not possess a surrender value when they are

lapsed. Most lapses are, hence, classified as early lapse.

Product types or groups are also considered by Renshaw and Haberman (1986), Cerchiara et al.

(2009), and Milhaud et al. (2010). The results of Renshaw and Haberman (1986) indicate that term

life insurance has higher lapse rates than endowment policies and unit‐linked products suffer the

most lapses. These results are different to our results, which might be credited to the differences in

the underlying products, i.e., life insurance in the U.K. and Germany might not be directly

comparable. In particular, the guarantee levels of unit‐linked products might have changed. While

these policies possessed initially almost no guarantee (Renshaw and Haberman (1986) use data from

1976), today these products usually include a variety of guarantees, e.g., investment guarantees at

contract maturity (see, e.g., Gatzert et al., 2011). Cerchiara et al. (2009) categorize the analyzed

portfolio consisting exclusively of savings policies into reasonably homogeneous product groups, but

not providing further details on the exact methodology. They find that the product group has a

strong effect varying from ‐56% to +421% relative to the reference product group. Four product

groups of endowment policies are distinguished by Milhaud et al. (2010) based on profit participation

(with vs. without) and premium payment (single vs. regular). As there are no and only two lapse

events for non‐profit policies with regular and single premiums, respectively, the regression result

seem not to be representative and reliable for these groups. When comparing with‐profit policies,

single premium business is lapsed less often than regular premium business.

Calendar year The development of lapse rates with respect to calendar year is displayed in Figure

5(a). The total lapse rate was 66% lower in 2000 compared to 2008. Lapse rates have been steadily


increasing from 2000 to 2004 in the years of and following the stock market plunge. They remained

stable from 2004 to 2007, but increased strongly in 2008 and 2009 (+22% and +20% compared to the

previous year), the year of and following the 2008 financial crisis. Lapse rates begin to deteriorate

again in 2010 reaching almost the 2008 level. Therefore, increasing lapse rates might be a

consequence of economic crises which is in line with the emergency fund hypothesis and which is

argued by German life insurers (see, e.g., Lier, 2010). While the development of the late lapse rate is

almost identical compared to total lapse, the development of the early lapse rate is different.

Developing similar until 2007, the early lapse rate constantly falls from 2007 to 2010. This might also

be related to the different treatment of acquisition cost as discussed above. Due to court rulings, this

cost has to be distributed over the first contract years instead of deducting it completely from the

first premium(s). This yields (higher) surrender values from the contract beginning such that lapsed

policies are classified more often as late lapse which is also in line with the fact that the late lapse

rate increases more strongly than the total lapse rate. Additionally, new business volume (of regular

premium business) has decreased following the 2008 financial crisis and thus early lapse volume

might have been further reduced.

Cerchiara et al. (2009) is the only study also considering calendar year effects from 1991 to 2007. In

general, lapse rates have been constantly falling until the end of the 1990s. In the following years,

the lapse rate has been increasing reaching the maximum in 2007. This result is consistent with our

findings. The lapse rate increase in the Italian data, however, is not constant since it is disrupted with

two peaks in 2000 and 2004. The authors, however, do not provide any explanation for these

exceptional developments.

Contract age The differentiation of early and late lapse might seem odd when contract age is

considered. The difference between both lapse rates is the (non‐)existence of a surrender value. As

discussed in Section 3.1, this is not necessarily related to the contract age and depends on product

design and regulation. Therefore, it still makes sense to consider these lapse types separately for

contract age. Total and late lapse rates are highest for young policies and are afterwards steadily

decreasing with contract age (see Figure 5(b)). Most policyholders realize quickly whether they really

need a purchased policy and have been advised appropriately by the salesperson. If the customer,

for instance, cannot afford the regular premium payments, the customer might lapse the contract

within the first years after policy inception. If a product really fits the policyholder’s need, it is less

likely that the policy will be lapsed. Life insurance savings might then only be used in case of personal

financial distress according to the emergency fund hypothesis (see, e.g., Dar and Dodds, 1989; Kuo et

al., 2003). The development of the early lapse rate is slightly different, as it first decreases and


increases again. This is driven by term life insurance policies.21 As those products are almost pure risk

insurance, no surrender value is built up. Any lapse – independent of contract age – is, hence,

classified as early lapse. Moreover, term life insurance is often used to backup mortgages. As soon as

the mortgage is repaid, the insurance coverage might not be required anymore explaining the lapse

rate increase with increasing contract age.

Contract age is considered as explanatory variable in all existing empirical studies (see Renshaw and

Haberman, 1986; Kagraoka, 2005; Cerchiara et al., 2009; Milhaud et al., 2010). The results are very

consistent with our findings as the general development is similar. The lapse rate is highest for the

first contract years and then gradually decreases.

Remaining policy duration The relationship between remaining policy duration and lapse rates is

displayed in Figure 5(c). Apart from policies with a very short remaining duration, lapse rates increase

with increasing remaining duration. This effect is in line with the above observation regarding

contract age. Policies having a long remaining duration have usually been issued in the last year(s),

while policies with shorter remaining durations are already in force for a longer time period. The

different behavior of policies with a remaining duration of less than five years is driven by early lapse

events which are related to term life insurance. As mentioned above, these policies do not build any

material surrender value and, hence, might be terminated premature when the insurance coverage is

not needed anymore.

Remaining policy duration has not been considered as explanatory factor in existing studies.

Policyholder age When considering the relationship between age of the policyholder and lapse

rates in Figure 5(d), the magnitude of the age effect is limited as the corresponding curves are

relatively flat. Three age groups can be distinguished: policyholders until age 25, policyholders

between 26 and 40, and policyholders older than 40. Policyholders in the middle group have an

almost constant lapse rate at the level of the reference age 39.22 The lapse rate for the youngest

policyholders is significantly below, but steadily increasing. Such policies might be initially

’sponsored’ by the policyholder’s parents. When the family circumstances change (e.g., marriage or

birth of children) the needs might change and the insurance premiums are not affordable any longer.

Lapse rates for the oldest age group are steadily increasing until age 60, before decreasing again. For

products with a savings component, a possible explanation for this effect is that especially people

older than 50 might have difficulties to find a new job in case of unemployment. According to the

21 When the same analysis is performed excluding term life insurance, the early lapse rate decreases quickly to zero within

the first four contract years. Results are available upon request. 22 As the estimates of the corresponding regression coefficients are close to zero, the corresponding variables are not

statistically significant different from zero.


emergency fund hypothesis (see Outreville, 1990), those persons might access their life insurance

savings as emergency funds. Other customers in the late 50’s might choose to retire early and use

their life insurance savings to bridge the gap until the payments from the social pension scheme

start. The following decline might be driven by two effects. First, the likelihood of immediate access

to life insurance savings (due to unemployment or early retirement) decreases with age. Second,

single premium business might increase in this age group (i.e., paying a lump sum into a deferred

annuity to receive later a life‐long annuity). As this business experiences less lapse (see below), it

might yield reduced lapse rates.

The policyholder age is also considered as explanatory factor in all existing empirical studies (see

Renshaw and Haberman, 1986; Kagraoka, 2005; Cerchiara et al., 2009; Milhaud et al., 2010).

However, the modeling approach differs. Cerchiara et al. (2009) is the only work considering the

current policyholder age as we do, while all other studies focus on the underwriting age of the

policyholder, i.e., age of the policyholder at policy inception. We decided to use the current

policyholder age as it reflects the current policyholder status and, hence, seems to be more relevant

for the lapse decisions. All other studies use age buckets combining up to 40 years instead of

considering effects for each age. Moreover, the considered range of age values differs across studies.

Therefore, our results are not directly comparable to the existing findings. The results of the existing

studies are consistent as all find decreasing lapse rates with increasing policyholder age (group).

Distribution channel Most German life insurance companies use different distribution channels

including tied agents, brokers, and banks, among others, but have one main distribution channel. The

insurer providing the data follows a similar strategy.23 As displayed in Figure 6(a), early, late, and

total lapse rate are close to each other for the different distribution channels considered. Compared

to the tied agent channel, the lapse rate in the bank channel is 25% higher, while it is 6% less for

brokers. Existing literature on the coexistence of different distribution channels discusses two main

hypothesis: the product quality hypothesis and the market imperfection hypothesis (Trigo‐Gamarra,

2008). The product quality hypothesis conjectures that the service quality, among others, differs

between distribution channels. Trigo‐Gamarra (2008) and Eckardt and Räthke‐Döppner (2010) find

evidence of an increased service level among independent agents (i.e., brokers) for the German

market. Our results thus support the existing literature studying the product quality hypothesis in

Germany. Although the product quality hypothesis has only been studied for dependent and

independent agents, it might also apply to the bank channel. Bank agents might focus on the

fulfillment of short‐term sales targets, while tied agents should focus to maintain a long‐term

customer relationship. This increases the risk of miscounseling and, hence, lowers service quality in

23 Due to confidentiality reasons, we cannot unveil the concrete distribution mix, in particular the weight of the different channels. This information might allow reconciling the underlying company.


the bank channel providing a possible explanation for the higher lapse rate. Other distribution

channels include, e.g., branches or direct.

Distribution channels have not been considered as explanatory factor in existing studies.

Supplementary cover Contracts including supplementary cover(s), e.g., disability insurance, exhibit

higher lapse rates than contracts without those additional covers. The effect is displayed in Figure

6(b) and amounts to +16% for total lapse, +18% for late lapse, and +7% for early lapse. On the one

hand, this result might be surprising since one might expect that policies with additional covers

experience less lapse, as it gets more expensive (if possible at all) to obtain identical insurance

coverage for the additional covers, e.g., by purchasing stand‐alone disability insurance at a higher

entry age. On the other hand, the premium for policies including additional cover is higher than for

stand‐alone policies. In case of financial distress, it is more likely that a policyholder is forced to lapse

such a product bundle. Additionally, Pinquet et al. (2011) believe that customers’ insufficient

knowledge of insurance products can cause lapse. Product bundles including insurance covers which

are not necessary might be more often sold to customers being not that familiar with insurance

matters. Due to the usually higher premium of such contracts, those are more likely to be lapsed

afterwards when the customer discovers that the product bundle does not fit the policyholder’s

needs. Finally, the product bundle might include unnecessary or duplicate insurance coverage. As

supplementary covers often cannot be lapsed separately, the customer might decide to lapse the

entire contract.

Existence of supplementary insurance covers has not been considered as explanatory factor in

existing studies.

Policyholder sex The total lapse rate for female is 9% less than for male (see Figure 6(c)). The early

lapse rate is 17% lower, while the late lapse rate is only 6% lower. This might be explained with a

higher risk aversion of female in financial matters (see, e.g., Halek and Eisenhauer, 2001). Females

might be less willing to purchase insurance products they do not completely understand or if they

are not sure whether they can fulfill long term premium payments.

This finding of a reduced lapse rate for females is in line with Kagraoka (2005) who argues that

housewives only purchase life insurance if the household income is sufficiently large. Kagraoka

(2005) finds that the lapse rate of female policyholders is 13% less than for male customers (based

on the Poisson model; for the negative binomial model the effect is ‐11%). Due to data availability,

only Kagraoka (2005) analyzed the impact of gender on lapse rate, although all studies discuss the

relevance of this factor.


Premium payment The total lapse rate is almost 90% less for single premium business compared to

regular premium business as displayed in Figure 6(d). Policyholders investing a large amount into a

single premium policy usually have profound knowledge of the corresponding products. Additionally,

excess funds are usually used to pay the initial investment. As no obligation for future premium

payments exists, such a contract is less likely to be lapsed due to financial distress. Finally, single

premiums most often occur with policies having a rather short contract duration (e.g., deferred

annuity or endowment), i.e., shortly before the retirement phase of the customer. Single premium

business represents so far only a minor part of the analyzed portfolio in terms of exposure years,

since this business has usually only a short contract duration. Moreover, savings policies are designed

to accumulate funds through regular payments over a longer period of time. Single premium

business has been of limited relevance for the German life insurance industry so far, but its relevance

increased following the 2008 financial crisis. Many policyholders use single premium life insurance as

’parking lot’ for their money such that this type of business increased significantly. It is still not clear

whether the corresponding funds will stay long term or will be lapsed again when the financial

markets recover further. Early lapse are not relevant for single premium business as a surrender

value exists for such products starting from policy inception.

Only Milhaud et al. (2010) analyze the relationship between method of premium payment and lapse

rates. They do not only distinguish single and regular premiums, but further break down regular

premiums into monthly, bimonthly, quarterly, semi‐annual, and annual installments. Consistent with

our result, the lapse rate is smallest for single premium business, while it is largest for bimonthly

payments followed by annual payments.

The following Table 5 summarizes the results of the analysis for the nine product characteristics. In

most cases (calendar year, contract age, policyholder age and sex, premium payment) our result are

in line with existing literature. In one case we find notable differences, i.e., when product type is

considered. We neither observe large variations in lapse rates for different product types (see

Cerchiara et al., 2009) nor find consistent evidence that unit‐linked products experience higher lapse

rates as Renshaw and Haberman (1986) do. Moreover, we add new results to the existing literature

for remaining policy duration, distribution channel, and supplementary cover: (1) With decreasing

duration we observe lower lapse rates, (2) lapse rates for banks (brokers) are higher (lower)

compared to tied agents, and (3) with supplementary cover the lapse rate is higher.

4.2 GLM including interactions

Both Renshaw and Haberman (1986) and Cerchiara et al. (2009) use interactions in their lapse

analyses. Cerchiara et al. (2009) investigate interactions between product class and (a) contract age


or (b) calendar year. The authors find that the age and year effects are in general very similar across

the different product categories. They conjecture that these results are related to the somehow

arbitrary definition of the product groups. Renshaw and Haberman (1986) consider four explanatory

variables: product type, policyholder age (at entry), contract age, and company. The authors

investigate all six possible interactions of two factors and find the main interaction between product

type and contract age. For all product types, lapses reduce substantially with aging policies.

Additionally, non‐profit products experience higher lapse rates than with profit policies at each

contract age. Analyzing more detailed lapse information for one specific office, Renshaw and

Haberman (1986) find a significant interaction between product type and policyholder age which

might, however, be due to inconsistencies in the underlying data. Both Renshaw and Haberman

(1986) and Cerchiara et al. (2009) focus on interaction between two factors, since more complex

interactions are much more difficult to analyze (exponentially increasing model complexity and thus

run time).

We follow the approach of the existing literature when considering interactions between only two

factors. We, however, do not only analyze interactions including product type, but also consider

distribution channel, (non‐)existence of supplementary cover, and premium payment. Since the

model complexity increases tremendously when interactions are added, we use a simplified

modeling approach for remaining policy duration and policyholder age in order to reduce that

complexity. Instead of considering each level separately, we group the levels into five classes each.24

When presenting the results of the analyses in the following, we restrict ourselves always to total

lapse in terms of number of contracts. Additionally, we do not present the results for all interactions

considered, but focus on significant interactions.

4.2.1 Interactions between product type and other characteristics

Since empirical evidence suggests that the most significant interactions exist for product type, we

consider interactions of product type with all other explanatory variables. The interaction effects

between product type and calendar year, contract age, and distribution channel, respectively, for

total lapse in terms of number of contracts are displayed in Table 6. Note that missing values in this

and the following tables indicate variable combinations for which no lapse event exists in the data

and hence a lapse rate cannot be estimated, e.g., the first Riester pensions have been lapsed in 2003

although being introduced already in 2002. For comparison, the respective effects for the simplified

model neglecting interactions, i.e., modeling remaining policy duration and policyholder age with

24 For policy duration, we distinguish policies with a remaining duration of ≤ 5, 6−15, 16−25, 26−55, and ≥ 36 years. The

policyholder age is grouped into 18−25, 26−35, 36−45, 46−55, and ≥ 56 years.


classes, have been included in the first row and last column, respectively. The results of this

simplified model deviate only gradually from the results presented in Section 4.1.

Considering calendar year effects by product type (see Panel A in Table 6), these effects are broadly

consistent with the results for the GLM not taking into account interactions. The lapse rate level for

unit‐linked products is higher than for the traditional counterparts (both for annuities and Riester

pensions) during and after the 2008 financial crisis. These might indicate that many customers get

nervous during falling stock markets as unit‐linked products are directly linked to stock market

returns. Helfenstein and Barnshaw (2003) find a significant positive relationship of single‐premium

unit‐linked life insurance sales and stock market performance in the U.K. using data from 1972 to

2001. Based on this observation, Helfenstein and Barnshaw (2003) conjecture that lapse rates vary

with substantial changes in market conditions as policyholders may want to participate from gains in

booming markets and limit losses in declining markets. Lapse rates have increased for all products

(except term life) during and following the 2008 financial crisis which is assumed to be a

consequence of the financial crisis (Lier, 2010). This provides further evidence for the emergency

fund hypothesis as a short term economic downturn accompanied the financial crises. For all product

categories, lapse rates constantly decrease with decreasing policy duration as displayed in Panel B of

Table 6, except for Riester, endowment, and term life policies with a very short remaining duration of

less than six years. For term life, this effect supports the above conclusion of lapsing when the risk

coverage is no longer required. For endowments and Riester pensions, this effect is rather

unexpected. If might, however, be explained with the portfolio selection including new business

since 2000. As those contracts usually have a long duration, only a limited number of contracts have

such a short remaining duration, e.g., less than 0.2% of all Riester pensions. Therefore, the lapse

rates are strongly influenced by single lapse events. No major deviations between product categories

can be identified when distribution channels are considered except that the overall lapse rate levels

differ by product type (see Panel C in Table 6). The bank channel exhibits a higher lapse rate than tied

agents, while brokers experience the smallest lapse rate. This result is identical with the GLM without

consideration of interactions. For all other policy(holder) characteristics, the effects are very similar

across product type and in line with the above discussed GLM without interactions. Only the overall

lapse rate level differs by product type. Detailed results are available upon request.

The results regarding interactions including product type are consistent with Renshaw and Haberman

(1986) and Cerchiara et al. (2009) in so far as we find (at least) some significant interactions for each

combination of product type and any of the other policy(holder) characteristics. The magnitude of

the effects is, however, different which can probably be attributed to the different products

considered.


4.2.2 Interactions between distribution channel and other characteristics

Being the first study having data on distribution channels, we additionally consider interactions of

distribution channels with the other product and policy(holder) characteristics. The results are very

consistent for most characteristics compared to the results of the GLM without interactions, except

for the difference in the overall lapse rate level for the different distribution channels (i.e., lapse

rates for banks are higher than for tied agents, while broker have the lowest lapse rate). Only for

policyholder age and supplementary cover major deviations can be observed (see Table 7).

While lapse rates are rather flat for the bank and other channel across the different age groups, it is

not for tied agents and brokers (see Panel A of Table 7). For tied agents, the lapse rates for the

youngest and oldest age group are substantially less than for the other age groups. This can be

interpreted as indication for different relationship levels. Agents seem to have a closer relationship

with young customers and people shortly before retirement. This might be explained with increased

business opportunities in these age groups (young people just start to build their insurance portfolio,

while the above 55 years old prepare for the retirement phase and need to adjust their insurance

portfolio). For brokers, lapse rates are increasing with age, in particular for the age groups older than

45 years. One possible explanation might be the increasing mobility of customers today. It becomes

less likely that people stay in one place for the whole life. When they move to another place, they

usually change the insurance broker. The new broker might tend to switch contracts in order to earn

commission. As displayed in Panel B of Table 7, we observe that lapse rates for the bank and other

channel are higher for policies including supplementary coverage. For tied agents and brokers,

however, lapse rates are almost identical, independent of the (non‐)existence of a supplementary

cover. This supports the above discussed hypothesis regarding service quality which should be

highest for brokers followed by tied agents and banks.

4.2.3 Interactions between supplementary cover and other characteristics

In order to further understand the drivers behind the higher lapse rate for policies including a

supplementary cover, we analyze the interactions between supplementary cover and all other

product and policy(holder) characteristics. The result of higher lapse rates for business with

supplementary cover is consistent across all levels of the other characteristics, except for product

type. Moreover, the development of lapse rates with and without supplementary cover is similar but

at different levels, except for policyholder age. We thus focus on the results for interactions with

product type and policyholder age in Table 8.

Lapse rates for annuities and endowments are higher when they include a supplementary cover,

while the corresponding lapse rates are smaller for all other product categories (see Panel A of Table


8).25 Therefore, the overall effect is driven by annuities and endowments which account for 40% of

the portfolio, but represent almost 60% of all contracts with supplementary coverage (both in terms

of exposure). The relationship of premium payment and policyholder age is displayed in Panel B of

Table 8. While for the youngest customers the lapse rate with supplementary cover is smaller, it is

larger for all other age groups and the gap to business without supplementary cover is increasing

with age. In particular, lapse rates for business with supplementary cover are significantly higher for

policyholders older than 45. This might support the above conclusion regarding unnecessary

coverage. When the mortgage is repaid or the children leave the family home, the term life or

disability cover might not be required anymore. As these supplementary covers cannot be lapsed

separately, the entire contract will be lapsed.

4.2.4 Interactions between premium payment and other characteristics

Single premium business significantly increased during and after the 2008 financial crisis. Customers

and investors exited the stock markets and used this vehicle as ’safe haven’ for their money. Some

insurers very actively promoted the single premium business.26 As the German regulator assumed

the liquidity risk to be substantial for such business in case of lapse, a cap for the capitalization

business has been introduced but for single premium business only qualitative requirements have

been defined (i.e., the actuarial reserve of capitalization products needs to be less than 3% of the

total actuarial reserve; see BaFin, 2010a,b). For both the German regulator and insurance managers,

it is thus very relevant to analyze the lapse characteristics of the single premium business and

especially if it suffers an increased lapse in recent years. We analyze interactions between premium

payment and all other characteristics to assess the differences between regular and single premium

business. Significant interactions are only found for product type, calendar year, and contract age.

The results focusing on these main effects are displayed in Table 9 for total lapse (in terms of number

of contracts). Consistent with the GLM without interactions, the lapse rate level for single premium

business is much smaller than for regular premium business. The lapse rate development of regular

and single premium business, however, varies for certain characteristics. The lapse rates of single

premium are consistently much smaller than for regular premium business for all product types as

displayed in Panel A of Table 9. This can be attributed to the same reasons as mentioned above

(better insurance knowledge, no further premium payments required, and policy inception shortly

before retirement). While the lapse rate for regular premium business increased starting from 2007,

the lapse rate of single premium business decreased even further (see Panel B of Table 9). As

25 Note that the Riester pension is designed to increase private pension savings and are federally subsidized. Therefore,

supplementary covers cannot be included in these policies. 26 Single premium payments are available for all product categories considered, except for Rürup pensions. It is, however,

not limited to those products. In particular, capitalization products are explicitly designed for this purpose. No information on this product category is available for our analysis.


mentioned above, volume of single premium business increased during and following the 2008

financial crisis. As lapse volumes seem to remain stable, decreasing lapse rates are the consequence.

This effect, however, might be reversed in the future if lapse volume increases and/or new business

volume decreases. It is thus important to analyze whether single premium business suffers increased

lapse in the future. As shown in Panel C of Table 9, the lapse rate of regular premium business

decreases more or less linearly from the second contract year. Overall, single premium business

shows the same decreasing pattern, but with variations. Single premium business represents only a

minor part of the portfolio (1.3% of the total exposure). Lapse rates are thus more volatile with

regards to changes in lapse volume.

5 CONCLUSIONS

In this paper we assess the impact of nine product and policy(holder) characteristics on life insurance

lapse, including product type, policyholder age, and policyholder sex. Following analyses for U.K.

(Renshaw and Haberman, 1986), Japan (Kagraoka, 2005), Italy (Cerchiara et al., 2009), and Spain

(Milhaud et al., 2010), generalized linear models (GLMs) are used to assess the relationship between

lapse rates and those characteristics. We consider the largest database ever used for this purpose

and extend the existing empirical literature by studying a time period of particular interest (two

market turmoils) and factors that were not yet analyzed (remaining policy duration, distribution

channel, supplementary cover).

The main findings of this paper are threefold. First, all considered product and policy(holder)

characteristics have a statistically significant impact on lapse rates. The spread of lapse rates is

largest for calendar year (increasing lapse rates, especially in phases of crisis), contract age

(decreasing lapse rate with increasing contract age), and premium payment (lapse rate for single

premium business 90% lower compared to regular premiums). Second, there are no major

differences between unit‐linked and traditional products which is a major difference compared to

existing studies on this topic from other insurance markets. Lapse rates for unit‐linked annuities are

below those of traditional annuities, while this effect is opposite for Rürup pensions, a special

German annuity product. Starting with the 2008 financial crisis, we find that lapse rates for unit‐

linked products are above those of traditional products (see analysis including interactions with

product type). This effect is, however, limited and the time horizon is too short to draw final

conclusions on the sustainability of this effect. Third, interactions of premium payment,

supplementary cover, and distribution channel with all other characteristics are analyzed: (a) Starting

from 2007, lapse rates for regular premium business are increasing, while lapse rates for single


premium business decrease which might be related to a shift towards more volatile single premium

business; (b) the observed higher lapse rates for policies with supplementary cover is exclusively

driven by endowments and annuities as the opposite effect is observed for all other product types;

and (c) the lapse rate development for the distribution channels considered varies by policyholder

age (rather stable for banks, increasing for brokers, and decreasing for tied agents).

This work focuses on providing an initial empirical assessment of lapse determinants for the German

life insurance market. Future research can build upon these results, e.g., in order to develop a

prediction model for future lapse rates. This can help life insurers to implement measures in terms of

risk and value based management, e.g., to setup of a customer retention program focusing on

customers which are most prone to lapse (Prestele, 2006). This requires additional model validation

procedures, e.g., splitting the data set into a fitting and testing sample (see, e.g., Cerchiara et al.,

2009; Kiesenbauer, 2011), which goes beyond the scope of this paper. Additionally, calendar year

effects might be linked to economic indicators such as unemployment rate, interest rate, or growth

of gross domestic product. Moreover, within the new European regulatory framework for insurance

companies (Solvency II), lapse has been identified as one of the main risk drivers for life insurers. The

Solvency II model itself, however, only differentiates lapse rates for retail and non‐retail business.

Obviously, Solvency II thus neglects numerous important drivers of lapse that might be integrated in

a company‐specific (partial) internal model. Finally, it is surprising to see that lapse drivers have not

been studied using U.S. data. There is thus significant room for future research to further validate the

findings presented here.


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FIGURE 1

Overview of empirical literature studying drivers of life insurance lapse


TABLE 1

Overview on empirical literature regarding analysis of product and policyholder characteristics


FIGURE 2

Lapse rate development in the German life insurance market – 1997 to 2009


TABLE 2

Extent of available data by product typ


TABLE 3

Possible values of all considered product and policy(holder) characteristics


TABLE 4

GLM results for total lapse without interactions


TABLE 4

Continued


FIGURE 3

Effect of product type on lapse rates (reference level: Annuity)


FIGURE 4

Effect of policy and policyholder characteristics on lapse rates


FIGURE 5

Effect of policy and policyholder characteristics on lapse rates


TABLE 5

Summary of results for the GLM without interactions compared to existing literature


TABLE 6

Interaction effects between product type and selected policy(holder) characteristics on total lapse

rates


TABLE 7

Interaction effects between distribution channel and selected policy(holder) characteristics on total

lapse rates

TABLE 8

Interaction effects between supplementary cover and selected policy(holder) characteristics on total

lapse rates


TABLE 9

Interaction effects between premium payment and selected policy(holder) characteristics on total

lapse rates

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