The en-bloc clause as future management action

(1)

The en-bloc clause as future

management action

I. S. Doelman

Thesis for the

Master Actuarial Science and Mathematical Finance University of Amsterdam

Faculty Economics and Business Author: I. S. Doelman Student ID: 10428380

Email: i.s.doelman@uva.nl Date: January 30, 2017 Supervisor UvA: dr. T. J. Boonen Second reader: dr. S.U. Can

(2)

(3)

The en-bloc as fma — I. S. Doelman iii

Abstract

This thesis studies the use of the en-bloc clause in disability insurance as a future management action. The en-bloc clause allows for the insurer to amend the pre-mium. If the insurer invokes the clause, the policy holder is allowed to terminate the insurance. Using the en-bloc clause as a future management action in case of a disability shock can greatly decrease the SCR. However, the Solvency II regulation prescribes that the assumptions have to be realistic. Therefore, a boundary has to be set on the maximum total premium adjustment. How this boundary is set has an impact on the SCR. Furthermore, the diversity within the portfolio, the assumed probability of lapse after premium adjustment and the maximum yearly premium adjustment affect the SCR.

Keywords Disability Insurance, Future Management Actions, AOV, Sensitivity Anal-ysis, Solvency II, En-Bloc Clause, Adverse Selection, Lapse, Disability-morbidity Risk, Article 23 Delegated Acts, Article 83 Delegated Acts, Solvency Capital Requirement, Policy Holder Behavior.

(4)

iv I. S. Doelman — The en-bloc as fma

Statement of Originality

This document is written by Irene Doelman who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it.

The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

Disclaimer

This thesis is written as part of an internship at De Nederlandsche Bank N.V. The views expressed in this thesis are those of the author and not necessarily the views of De Nederlandsche Bank.

(5)

Chapter 1 Introduction

Dutch Insurance Law (art. 7:940(4) BW) allows for a clause in the terms and conditions of an insurance contract that states that the insurer can adjust the premium and the conditions of the contract for a certain homogeneous group. This is called the en-bloc clause. If the insurer uses this clause to the detriment of the policy holder, the policy holder has the right to terminate the insurance. Since individual disability insurances usually are long term contracts and cannot be terminated by the insurer, the right to amend the conditions is very useful for the insurer. It can be necessary to amend the conditions due to a legislative change Furthermore, in case of severe financial distress, the amendment of the premium could prevent the insurer from bankruptcy. It is therefore a useful risk mitigating measure.

The use of the en-bloc clause by the insurer gives the policy holder the right to terminate the contract. While modeling the effects of the en-bloc clause, it is therefore important to take lapse behavior into account. Lapse rates have been studied in the life insurance business. In literature, lapse rates are linked to sev-eral macroeconomic and microeconomic factors (Fier and Liebenberg, 2013). Eling and Kiesenbauer (2013) analyse the German life insurance market, and conclude that both product characteristics and policy holder characteristics are important drivers for lapse rates. Because of the product differences between life insurances and disability insurances, the lapse behavior in disability insurance should there-fore be studied seperately. Moreover, the effects of premium adjustments on lapse rates could be significant. In the health insurance business, Christiansen et al. (2015) show that the long term premium development affects lapse rates.

Since the introduction of the Solvency II regulation on January 1st 2016, there are two ways in which insurers have tried to use the en-bloc clause to manage their capital position. The first one is using the clause as a contract boundary, as described in article 18 of the Delegated Acts. Kuijper (2014) studies this from an actuarial perspective. However, in my opinion this is not in line with the

(7)

2 I. S. Doelman — The en-bloc as fma regulation. Although one could argue that with the clause, the insurer can amend the premiums in such a way that they fully reflect the risks, and it therefore falls under article 18(3) sub c, article 18(7) clearly states that this is only the case if there is no circumstance under which the amount of the benefits and expenses payable under the portfolio exceeds the amount of the premiums payable under the portfolio. Since policy holders have the right to terminate their contract when the en-bloc clause is used, there is a possibility that so many policy holders exercise this right that the amount of benefits and expenses payable indeed exceed the amount of premiums payable under the portfolio. The en-bloc clause therefore cannot be used to form a contract boundary.

The second way in which insurers have tried to use the en-bloc clause to manage their capital position is as a justification for assumptions on future management actions, as described in article 23 and article 83 Delegated Acts. This is studied in this thesis. The aim is to give an operating vision on the risks this entails from both an actuarial and a legal perspective. The main questions answered in this thesis are how the use of the en-bloc clause affects the SCR and to which assumptions the SCR is sensitive.

We conclude an unlimited use of the en-bloc clause decreases the SCR by over 90%, but this requires an unrealistically large total premium increase. How a boundary on the total premium increase is set has a large impact on the SCR. Furthermore, the diversity within the portfolio, the assumed probabilty of lapse after premium adjustment and the maximum yearly adjustment affect the SCR.

First of all, Chapter 2 gives the legal framework a future management action has to comply with. After this, the use of the en-bloc clause is discussed from a legal and moral perspective in Chapter 3. In Chapter 4, literature on modeling disability insurance and policy holder dynamics is reviewed. The research design is explained in Chapter 5, after which the results are showed and analysed in Chapter 6. This is followed by a conclusion.

(8)

Chapter 2 Legal framework on future

management actions

In this chapter, the legal framework for the use of the en-bloc clause as a Future Management Action is described.

Since the introduction of the Solvency II regulation, insurers have to calcu-late their technical provisions based on realistic assumptions. This is required by article 77 Directive. This entails taking into account policy holder behavior, as described in article 26 Delegated Acts. However, insurers are also allowed to take into account future management actions. This can have a large impact on the technical provision. Therefore, article 77 Directive requires the assumptions on future management actions to be realistic. Although article 23 Delegated Acts gives some conditions the future management actions have to comply with in or-der to be consior-dered realistic, the conditions are defined rather loosely. It could therefore be debatable whether and to what extend an assumption is realistic. The use of the en-bloc clause as a future management action could in some cases be realistic.

When calculating the SCR for a shock scenario, assumptions on future man-agement actions can also be taken into account. However, according to article 83(2)(b) Delegated Acts, any material impact of the future management actions on the policy holder behavior has to be considered. We therefore have to take into account the possibility of an increased lapse rate if the en-bloc clause is used.

The supervisory authority has to assess to what extent the assumptions on future management actions are realistic. Article 23 Delegated Acts gives a guide-line, but not a clear boundary. In Chapter 6, we see a case where a boundary has to be set to an assumption, but it is not clear where.

(9)

Chapter 3 The en-bloc clause in a legal and

moral perspective

Although the so-called en-bloc clause has been used by insurers on various occa-sions, there are legal and moral objections to its use. In this chapter some of these objections will be discussed.

From a risk management perspective, having an en-bloc clause in general is a good way to mitigate risk. However, the use of the en-bloc clause is meant as a last resort in case of severe financial distress. The decision to use the en-bloc clause to increase the premium should not be taken lightly.1 _{In this context, anticipating}

the use of the en-bloc clause in order to reduce the required capital is not desirable, because it increases the chance that the en-bloc clause has to be invoked: a self-fulfilling prophecy is created. One can wonder if the anticipation of the use of the en-bloc clause reflects the required prudent management of the business.2

Moreover, there are multiple objections to the use of an en-bloc clause. The first objection has to do with the essence of insurance: the transferal of risk in exchange for a premium. Raising the premium because the development of the portfolio is different than expected, either because the risks have been wrongly assessed or because of a simple case of bad luck, is in essence a form of transferring the risk back to the policy holder. In my opinion this is contrary to the nature of an insurance contract. This view is shared in literature, for instance by Hendrikse (2012).

Although the clause has been used by Dutch insurers to raise the premium on various occasions in the past, the legal status is quite uncertain. There is a distinction to be made between the amendment of the premium before the date the policy holder can terminate the insurance (the expiration date), and after this date. There have been a few cases in which the insurer has tried to amend

1 _{Kamerbrief minister van Financi¨}_{en, 25 maart 2014; kenmerk FM/2014/436 U.} 2 _{Art. 41(1) Solvency II Directive.}

(10)

The en-bloc as fma — I. S. Doelman 5 the premium before the expiration date. This seems to only be possible in case of severe financial distress on the side of the insurer.3 There have not been any cases on the use of the clause after the expiration date. However, there seem to be multiple ways to legally challenge the use of this clause in the case of individual disability insurance, even though the Dutch legislator seems to have provided room for this clause. The financial situation of the insurer will likely be taken into consideration.

The contracts for individual disability insurance are consumer contracts. There-fore it has to be verified whether the premium adjustment clause is an unfair term as described in the European directive on unfair terms in consumer contracts.4

If the clause is deemed unfair, the clause will not bind the consumer.5 _This

di-rective is incorporated in Dutch law,6 _{but the wording differs from the wording}

in the directive. According to the directive, the clause is unfair if contrary to the requirement of good faith, it causes a significant imbalance in the parties’ rights and obligations arising under the contract, to the detriment of the consumer.7 The wording of the Dutch article is significantly different: if the clause, given the nature and the content of the contract, the manner in which the clauses have been established, the mutually known interests of the parties and other circumstances of the case, is unreasonably burdensome on the other party.8 _{However, judges will}

have to interpret the Dutch law in conformity with the directive.

Although the annex to the directive provides an indicative list of clauses that may be unfair, a term on this list is not necessarily unfair and a term that is not on the list may still be unfair.9 _{It is debatable whether the premium adjustment}

clause is on the list.10

3 _{Rechtbank Utrecht, ECLI:NL:RBUTR:2007:BA6717 (ONVZ), paragraph 5.17; Rechtbank}

Amsterdam, ECLI:NL:RBAMS:2013:7138 (Delta Lloyd), paragraph 4.7.

4 _{Council Directive 93/13/EEC of 5 April 1993 on unfair terms in consumer contracts.} 5 _{Art. 6(1) Directive.}

6 _{Art. 6:233 to 6:239 BW.} 7 _{Art. 3(1) Directive.} 8 _{Art. 6:233 BW.}

9 _{European Court of Justice 7 mei 2002, C-478/99, ECLI:EU:C:2002:281, (Commission v.}

Sweden), paragraph 20; European Court of Justice 1 april 2004, C-237/02, ECLI:EU:C:2004:209, (Freiburger Kommunalbauten), paragraph 20.

10 _{Sub j of the annex: enabling the seller or supplier to alter the terms of the contract}

unilat-erally without a valid reason which is specified in the contract. Paragraph j is without hindrance to terms under which a seller or supplier reserves the right to alter unilaterally the conditions of a contract of indeterminate duration, provided that he is required to inform the consumer with reasonable notice and that the consumer is free to dissolve the contract. In my opinion, the individual disability insurance is not a contract of indeterminate duration, because it automati-cally ends on a date mentioned in the contract, usually the pension age. The exception therefore does not apply. Art 7:940 (4) BW does not specify an obligation to give a valid reason which is specified in the contract. In my opinion, the clause therefore falls within the scope of the list.

(11)

6 I. S. Doelman — The en-bloc as fma The clause gives the insurer the right to unboundedly increase the premium, whereas it gives the policy holder the right to terminate the contract.11 The sig-nificance of this right, however, should not be overstated. Contracting elsewhere is both costly and time consuming, because a new insurer will want to assess the health of the policy holder before contracting. Furthermore, a new insurance will be more expensive, because the policy holder is older and the risks there-fore have changed. Moreover, if the policy holder has been disabled in the past or has complaints, new insurers might not accept him at all or with exemptions. The question whether the right to terminate is purely formal or can actually be exercised should be taken into account while determining if a clause is unfair.12

It is therefore defensible that the en-bloc clause causes a significant imbalance in the parties rights, to the detriment of the consumer, and is therefore unfair. Fur-thermore, the European Court of Justice concluded that a term which was solely to the benefit of the seller and contained no benefit in return for the consumer, is always unfair.13 _{Hendrikse (2012) concludes that as the option to terminate}

the contract provides no real benefit for the consumer, an en-bloc clause is unfair in any contract. Since for many other insurance contracts it is easy to switch to another insurer, this is an even more convincing argument in the case of disability insurance.

If this argument fails, there are two more ways to challenge this clause. Both are based on general principles of Dutch contract law. The first principle is the demands of reasonableness and fairness.14 The second is the abuse of power.15 The success of these reasonings will depend on the circumstances of the case. The argument with respect to reasonableness and fairness has been successful in a case where the insurer tried to amend the premium before the expiration date.16

The lack of altenatives for the consumer constitutes an important factor to consider before the use of the en-bloc clause. Even if the policy holder is healthy, the process of switching to another insurer places a significant burden on him. Apart from the one-off costs, the premium will most likely be higher because of his less favorable age. For policy holders who have complaints or have been disabled in the past, it is even more unlikely they have a realistic alternative for the insurance.

11 _{7:940(4) BW.}

12 _{European Court of Justice 21 March 2013, C-92/11, ECLI:EU:C:2013:180, (RWE Vertrieb}

AG v Verbraucherzentrale Nordrhein-Westfalen e.V.), paragraph 54.

13_{European Court of Justice 1 april 2004, C-237/02, ECLI:EU:C:2004:209, (Freiburger}

Kom-munalbauten), paragraph 23.

14 _{Art. 6:248 BW.} 15 _{Art. 3:13 BW.}

(12)

The en-bloc as fma — I. S. Doelman 7 Moreover, disability insurances are expensive. According to the Sociaal-Economische Raad (2010), the costs of disability insurance are often named as a reason for con-sumers not to insure. An unexpected raise of the premium could therefore give the policy holder financial problems.

Finally, since the scandal with investment insurances in 2006, the woeker-polisaffaire, insurers have been struggling with earning back the trust of the con-sumers. The lack of transparency of products was a big problem. The unexpected use of the en-bloc clause will not help the insurer with regaining the trust of its policy holders. Consumer television program Radar has already criticized the in-surers for a lack of transparency with regards to the use of the en-bloc clause and the consequences it has for the policy holders.17

(13)

Chapter 4 Literature review

This thesis aims to analyse the risks involved when the en-bloc clause is used as an assumption on future management actions. Therefore, the disability insurance needs to be modeled. In this chapter, literature on the modeling of individual disability insurance will be reviewed. Furthermore, the possible influence of the use of the en-bloc clause on the policy holder dynamics and adverse selection effects will be discussed.

Modeling individual disability insurance

Individual disability insurances in the Netherlands are typically modeled as a Markov process. This means it complies with the well-known Markov property:

P[S(t + 1) = st+1|S(t) = st, S(t − 1) = st−1, ..., S(0) = s0] =

P[S(t + 1) = st+1|S(t) = st]. (4.1)

One of the models, as described by Haberman and Pitacco (1999) is a three-state model. This is illustrated in Figure 4.1.

The property of a Markov process is that the probability of transitioning to another state is independent of the history. This means that the probability of recovery (transitioning from State I to State A) is independent of the time one has been disabled. In practice, this is not realistic. In this thesis, we consider a more general model.

The Dutch Association of Insurers (Verbond van Verzekeraars) has done mul-tiple studies on the modeling of disability insurance. A differentiation is made between short term (first year) and long term disability. In this thesis, only the long term disability will be discussed. The studies by Gregorius (1992), the revi-sion in 2000 and the revirevi-sion in 2009 by Santoso are not public. However, Makhan (2011) and Brethouwer (2011) describe these models. The models are one year multiple state models which can be illustrated by Figure 4.2.

(14)

The en-bloc as fma — I. S. Doelman 9

Figure 4.1: Three-state Markov model by Haberman and Pitacco (1999). ’A’ rep-resents the state Active, ’I’ reprep-resents the state Disabled and ’D’ reprep-resents the state Deceased.

Figure 4.2: Multiple state model. ’A’ represents the State Active, ’I(y)’ the yth

year of disability and ’D’ represents the State Deceased.

The problem with recovery rates dependent on the length of the disability is reduced in this model. It is assumed that after 5 years of disability, the probability of recovery is zero. Furthermore, all transition probabilities are dependent on age, gender and occupation. Makhan (2011) lists the estimated probabilities. In this thesis, only the probabilities of males in occupation group 1 are used, which are included in Appendix A.

Policy holder dynamics and adverse selection

ef-fects

Since policy holders have the right to terminate their contract in case of premium adjustment, this needs to be incorporated into the model.

Little is known about the behavior of the policy holder in this situation. It is very likely to depend on the specifics of the portfolio among other things. For instance, according to Kuijper (2014), NN Group uses the en-bloc clause frequently

(15)

10 I. S. Doelman — The en-bloc as fma without shocks in lapse rates for one portfolio, but fears large lapse if it is used for another portfolio.

Christiansen et al. (2015) study lapse rates in combination with premium adjustments in the German health insurance market. They find that policy holders with a long term increasing or strongly increasing premium lapse significantly more often than policy holders with a long term stable premium. However, they also suggest that health insurance policy holders in Germany are used to premium adjustments. This might influence the lapse behavior in their study.

Some might argue that policy holders will not lapse because it is not rational. Although it will be analysed when a policy holder is theoretically locked in, this does not mean the probability of lapse is zero. First of all, humans generally do not behave rationally in an economical sense all the time. Second of all, instead of an insurance, a policy holder might consider other options, for instance participating in a so-called broodfonds or saving up for the possibility of disability.

In most models, it is assumed that the disability rates of the policy holders who lapse is the same as the disability rates of the policy holders who do not lapse: no adverse selection takes place.

A lot of theoretical research has been done on competitive insurance markets with asymmetric information. Important work is done by Rothschild and Stiglitz (1976). They take a game-theoretical approach to the problem. Using a stylised model, they show that in a market with both high-risk and low-risk customers and imperfect information, there is not always an equilibium. Furthermore, the high-risk customers form a negative externality to the low-risk customers.

Siegelman (2004) argues that in practice, the threat of adverse selection caused by informational asymmetry in insurance markets is exaggerated, since there is no overwhelming empirical evidence. He argues that one of the reasons for this is that where adverse selection is often linked to the eventual collapse of the entire insurance pool, this is usually not the case, since people do not make decisions as rationally as these decisions are often modeled. There are also factors that insurers cannot use in pricing, even though they might have an influence. These factors may have led to some degree of adverse selection, but this is not extreme.

A large difference between the literature on adverse selection and this thesis is that, whereas in literature the moment of conclusion of the contract is considered, this thesis focusses on adverse selection with regards to lapse. Therefore, the solution that insurers use to prevent adverse selection, a thorough health test before contract conclusion, cannot be used. This thesis does not aim to research this problem from a theoretical approach. Instead, a more practical approach is taken: the possible implications of adverse selection are taken into account.

(16)

Chapter 5 Research design

In this chapter, the research design is described. This entails the model, the as-sumptions made, the portfolio and the scenarios that will be analysed.

The model

To model the disability, we use a one year model. Let S(t) be the state of the policy holder in year t. Besides the states Active, Deceased and Lapsed, there are several states Disabled, representing the length of the disability. Since the probability of recovery after five years disability is assumed zero, there are no seperate states for disability after the sixth year: all policy holders who are disabled for six years or longer are aggregated in the 6th _{Disability State. The model from Figure 4.2}

is extended with a possibility for lapse. It is assumed lapse only occurs from policy holders who are active, since it would not be rational for disabled policy holders to lapse (while disabled, they receive the benefits without having to pay the premium). The model is illustrated in Figure 5.1. The various states policy holders can be in are listed in Table 5.1.

The probability of a policy holder with age x to transition from state i to state j after t years is defined as:

tpijx := P[S(x + t) = j|S(x) = i]. (5.1)

The original disability (transition from state Active to state Disabled (first year)) and recovery (transition from the various states of Disabled to Active) probabilities are calculated according to the formulas in Appendix A. The AG 2016 mortality table is used for the transitions to the state Deceased.

Since our model complies with the Markov property as described in For-mula 4.1, it is a Markov model.

We assume a constant interest rate r. Furthermore, it is assumed that there is no partial disability and no partial lapse (by changing the amount insured). The

(17)

12 I. S. Doelman — The en-bloc as fma Abbreviation State

A Active

I(1) Disabled (first year) I(2) Disabled (second year) I(3) Disabled (third year) I(4) Disabled (fourth year) I(5) Disabled (fifth year)

I(6) Disabled (sixth year or longer) D Deceased

L Lapsed

Table 5.1: The possible states policy holders can be in.

Figure 5.1: The model used in this study. See Table 5.1 for the meaning of the abbreviations. Compared to Figure 4.2, the model is augmented with a possibility for lapse.

insurance is assumed to end at age 67. The policy holder is assumed to not pay a premium in the last year (at age 66). Moreover, n is defined as the number of years until the age of 67 is reached by the policy holder.

The initial premium per yearly benefit of 1 is calculated as the leveled actuar-ially fair premium plus 10 percent. There is no implicit profit margin. The leveled actuarially fair premium per policy holder is calculated by discounting the cash flows and setting them equal:

n−1 X t=0 Paf · E[At] · (1 + Ip)t· (1 + r)−t = n X t=0 E[Bt] · (1 + Ib)t· (1 + r)−t, (5.2)

where Paf is the leveled actuarially fair premium, Ip is the indexation precentage

(18)

The en-bloc as fma — I. S. Doelman 13 fraction of policy holders in the state Active at time t, and E[Bt] is the expected

amount of benefits to be paid at time t. This leads to: Paf = Pn t=0E[Bt] · (1 + Ib) t_{· (1 + r)}−t Pn−1 t=0 E[At] · (1 + Ip)t· (1 + r) −t. (5.3)

In all scenario’s where the use of the en-bloc clause is in order, the assumed premium adjustment policy is that the premium is adjusted when the Combined Ratio is larger than 1 for two years consecutively. The Combined Ratio (CoR) in year t is given by:

CoRt=

Bt+ ∆T Pt+ r · T Pt−1

Pt

, (5.4) where Bt are the benefits payed in year t, T Pt is the technical provision in the

year t, and Pt is the premium income in year t. The technical provision that is

used for the calculation of the CoR is calculated beforehand and not adjusted for the shock in disability rates. This implies the insurer will not adjust the premium at the precise moment of shock, but only after a few years. It is as if the insurer does not know the shock has taken place. The insurer raises the premium but does not adjust the disability rates when the premium income and benefit payments are not in balance anymore.

It is assumed that a combined ratio larger than 1 for the second year in a row will lead to a premium adjustment such that the premium in the following is equal to the premium that would have led to a CoR of 0.95 in the current year, with a maximum increase of 20%. This premium adjustment policy is a strong assumption, but non-life insurers often use the CoR as a means to estimate the portfolio performance and base business decisions on it.

The effects of all scenarios are calculated for a portfolio of 15,000 policy holders. This corresponds to the size of a medium-sized disability insurer. The portfolio is described in Appendix B, in Table B.1. It is assumed all these policy holders get the same benefits in case of disability, which is set at 1 per year (before indexation). The assumed indexation of benefits is 1%, while the indexation of premiums is 0%. The interest rate r is assumed to be constant at 2%.

Base scenarios

The Solvency II directive prescribes a disability shock where the probability of disability increases with 35% in the first year, and with 25% in the years after that. The probability of recovery decreases with 20%. The Best Estimate of the technical provision after disability shock (E[T PDS]) minus the Best Estimate of the technical

(19)

14 I. S. Doelman — The en-bloc as fma shock (SCRDS). This can be expressed mathematically as:

SCRDS = E[T PDS] − E[T PBS]. (5.5)

The necessary technical provision is calculated for three scenarios: one where there is no disability shock (Base scenario), one where there is a disability shock and the en-bloc clause is used (Scenario I), and one where there is a disability shock but no en-bloc clause is used (Scenario II). The Solvency Capital Requirement (SCR) for the disability shock with and without the use of the en-bloc clause is then calculated by subtracting the technical provision of the scenario without shock from the scenario with shock and with and without the use of the en-bloc clause respectively. An overview of this is given in Table 5.2.

Both the technical provision and the SCR are best estimates. Since we use simulation to find the necessary technical provision, some uncertainty remains. Therefore, we calculate an interval CI, given by the 5th and 95th percentile of the technical provision after shock minus the best estimate of the technical provision without shock.

Name Description

Base Scenario Scenario where no disability shock takes place.

I A disability shock takes place and the en-bloc clause is used given the assumptions in Table 5.3.

II A disability shock takes place but the en-bloc clause is not used.

Table 5.2: Description of Base scenario, scenario I and scenario II.

In these scenarios, all assumptions described above are used. These assump-tions are listed in Table 5.3. The third column shows whether the sensitivity of the results to this parameter are studied. The SCR for the disability shock with the use of the en-bloc clause, SCRI is compared to all other results with varying

(20)

The en-bloc as fma — I. S. Doelman 15 Variable Starting value Studied Number of policy holders 15,000 Yes Portfolio composition See Table B.1 No Portfolio diversity No diversity Yes Premium stucture Leveled No Profit margin 10% No Interest rate 2% No Indexation of premiums 0% No Indexation of benefits 1% No

Lapse 5% Yes

Adjustment policy CoR > 1 twice consecutively No Maximum premium increase per year 20% Yes Maximum total premium increase Unlimited Yes Shock size Solvency II No Theoretically locked in dependence No Yes Table 5.3: Overview of all input parameters and whether the sensitivity of the SCR to this parameter is studied.

Sensitivity of assumptions

Number of policy holders

We assume a portfolio of 15,000 policy holders, which corresponds with a medium sized disability insurance portfolio in the Netherlands. A large Dutch disability insurance portfolio consists of approximately 30,000 policy holders. We check the robustness of the results by testing the effect of having 30,000 policy holders instead of 15,000 policy holders.

Maximum premium adjustment

It is assumed that there is a maximum premium increase of 20% per year. In a publication from the Dutch Association of Insurers (Verbond van Verzekeraars, 2016), Dutch insurers have stated that they aim to prevent substantial premium shocks. Using a maximum allowed premium increase of 20% per year is a mild interpretation of this statement. A maximum allowed increase of 10%, 30% and 40% is studied. The total premium increase in the base scenarios is unlimited. This assumption is also studied. Assumed are maximum total premium increase rates of 20%, 40%, 60% and 100%. An overview of the scenarios studied is listed in Table 5.4.

(21)

16 I. S. Doelman — The en-bloc as fma Name Maximum increase per year Maximum total increase

I 20% Unlimited 10% p/y 10% Unlimited 30% p/y 30% Unlimited 40% p/y 40% Unlimited 20% total 20% 20% 40% total 20% 40% 60% total 20% 60% 100% total 20% 100%

Table 5.4: Overview of scenarios studied for the maximum premium adjustment.

Portfolio diversity

Insurers can deal with possible lapse in their models in multiple ways. They can leave it out of their models, assume a constant lapse rate or they can model a higher lapse at the moment the en-bloc clause is used. Usually, it is assumed lapsing policy holders are equally healthy as non-lapsing active policy holders. However, this is not completely realistic. For policy holders who have been disabled in the past or experience symptoms it is not feasible to get an insurance elsewhere, since their chances of becoming disabled (again) are higher. This means they are less likely to lapse in the case of premium adjustments. Therefore, we assume that the policy holders who lapse are on average less likely to become disabled than other active policy holder. With healthier policy holders lapsing, the disability rates of the remaining group will increase. It is unknown how big this effect is, which is why several scenarios will be analysed.

In order to model the effects of adverse selection, the policy holders are dev-ided into groups. These groups are assigned a risk factor which influences their probabilities of becoming disabled. For instance, policy holder k will have the following disability probability at age x:

1pA,I(1)_k,x =1pA,I(1)x · rfk, (5.6)

where rfkis the risk factor for policy holder k. The average risk factor over all

pol-icy holders in all groups will be 1, which means the average disability probability is not altered. Aside from a risk factor, the groups will be assigned a probability of lapse in case of premium adjustment. This will be assigned in such a way, that the healthier policy holders have a higher lapse probability. The average lapse probability remains 5%. Because of the different lapse probabilities, the average health of the remaining policy holders is reduced when the premium is adjusted. The variation in risk factors and corresponding lapse probabilities that are

(22)

The en-bloc as fma — I. S. Doelman 17 studied are listed in Table 5.5.

Name Portfolio structure

Group size Risk factor Lapse probability

I 100% 1 5% A 50% 1.2 3% 50% 0.8 7% B 50% 1.5 3% 50% 0.5 7% C 50% 1.2 0% 50% 0.8 10% D 50% 1.5 0% 50% 0.5 10%

Table 5.5: Overview of scenarios studied for the portfolio diversity.

Lapse probability after premium adjusmtent

In Scenario I, the probability of lapse after premium adjustment is set at 5%. We study scenarios with a lapse probability of 2%, 10% and 15% after premium adjustment. Since the lapse probability could be dependent on the total premium adjustment up until that point, one other scenario is studied as well. The lapse probability at time t, λ, in this scenario is given by:

λt= 5% · (1 + it), (5.7)

with it the total premium adjustment up until time t. Table 5.6 gives an overview

of the scenarios that are studied.

Name Lapse probability after premium adjustment

I 5%

2% 2% 10% 10% 15% 15% 5%+ increase 5%·(1+it)

Table 5.6: Overview of scenarios studied for the lapse probability after premium adjustment.

(23)

18 I. S. Doelman — The en-bloc as fma

Theoretically Locked In

Since the disability rates depend on age and the premium is calculated at the beginning of the contract, the premium depends on the age of the policy holder at the start of the contract. A healthy policy holder is theoretically locked in if the premium (after using the premium adjustment clause) is lower than the premium the policy holder would pay if he purchased a new insurance under the same condition. One-off costs are not taken into account.

Being or not being theoretically locked in could influence the lapse behavior of the policy holder. Therefore, a scenario is studied where only policy holders who are not theoretically locked in, have a lapse probability of 5%. The lapse probability of policy holders who are theoretically locked in is zero.

For this scenario, the starting premiums of policy holders of all ages is calcu-lated first.

(24)

Chapter 6 Results and analysis

In this chapter, the results of the research will be discussed. First, the Solvency Capital Requirement for the disability shock is calculated in the case that the en-bloc clause is used and the case that the clause is not used. Then, the sensitivity of the result is studied for some assumption amendments.

Solvency Capital Requirement

Using the assumptions listed in Table 5.3, the technical provision is calculated in the case of no shock, in case of a shock without an en-bloc clause and in case of a shock with an en-bloc clause. The SCR of the shock is calculated afterwards, using Formula 5.5. The results are given in Table 6.1, and graphically illustrated in Figure 6.1. The red square is the SCR. The black line is the interval CI.

Best Estimate 5th percentile 95th percentile Technical provision before

shock (Base scenario)

8,253 6,965 9,583 Technical provision after shock

without en-bloc (Scenario II)

18,208 16,906 19,767 Technical provision after shock

with en-bloc (Scenario I)

8,970 8,338 9,549 SCR for shock without en-bloc

(SCRII)

9,955 8,653 11,515 SCR for shock with en-bloc

(SCRI)

717 85 1,296 Table 6.1: Technical provision and SCR in the different scenarios as described in Table 5.2.

(25)

Figure 6.1: The SCR and interval CI if the use of the en-bloc clause is assumed and the SCR and interval CI if the en-bloc clause is not used. The red square is the SCR. The black line is the interval CI.

The results show that the use of the en-bloc clause in case of disability shock decreases the SCR by over 90%. This is very beneficial for the insurer. However, this also means that if the SCR is calculated with the use of the en-bloc, a le-gal challenge on the legitimacy of the use of the en-bloc clause, as described in Chapter 3 could have a significant impact. Furthermore, the en-bloc clause is used very extensively: policy holders with a long duration face a premium increase of 274% on average. It therefore fails to meet the requirement of being realistic, as described in Chapter 2. Therefore, the SCR has also been calculated for a scenario where a restriction on the premium increase of 40% has been set. Even this total increase has a large impact on the policy holder. This will be denoted by SCRIII.

Using this restriction leads to the results listed in Table 6.2.

SCR 5th percentile 95th percentile SCR for shock with restricted

en-bloc (SCRIII)

4,649 3,567 5,805 Table 6.2: SCR and interval CI for Scenario III. This is the scenario where the en-bloc is used with a restriction on the total premium increase.

The results show that even though the effect of the restricted en-bloc clause is a lot smaller than the effect of the unrestricted en-bloc, it still reduces the SCR by more than half compared to the scenario without use of the en-bloc clause.

(26)

Figure 6.2: The SCR and interval CI for Scenario I, II and III. The red square is the SCR. The black line is the interval CI.

Robustness checks

The robustness of the results is studied for the use of 30,000 policy holders instead of 15,000 policy holders and for the use of the theoretically locked in constraint. The results are given in Appendix C and Appendix D respectively.

We conclude that the influence of having 30,000 policy holders instead of 15,000 policy holders is marginal. The use of the theoretically locked in constraint has an influence on the SCR if the en-bloc clause is used without restriction. However, in the more realistic case that the use of the en-bloc clause is restricted, this influence evaporates.

Maximum premium adjustment

In Scenario I, the premium adjustments are limited to 20% per year. The total premium increase is unlimited. In the simulations, this leads to total premium increases up to 550%. In this section, the influence of both assumptions is stud-ied. For the maximum premium adjustments per year, we study scenarios with a maximum of 10%, 30% and 40%. For the total premium increase, a maximum of 20%, 40%, 60% and 100% is studied. Recall Table 5.4 for an overview of the scenarios studied. The results are listed in Table 6.3, and graphically illustrated in Figure 6.3 for the maximum yearly adjustment and Figure 6.4 for the maximum total adjustment.

The results clearly show that having a restriction on the maximum total pre-mium adjustment has a very large influence on the SCR. How the maximum for

(27)

22 I. S. Doelman — The en-bloc as fma Name SCR 5th percentile 95th percentile

I 717 85 1,296 10% p/y 1,937 1,162 2,853 30% p/y 363 -491 1,141 40% p/y 125 -1,016 1,209 20% total 6,732 5,454 8,216 40% total (III) 4,649 3,567 5,805 60% total 3,329 2,299 4,326 100% total 1,421 550 2,316

Table 6.3: The SCR and interval CI for the scenarios for the maximum premium adjustment. Recall Table 5.4 for an overview of the scenario names.

the total premium adjustment should be set is dependent on what can be con-sidered realistic, as explained in Chapter 2. It is also an ethical question. Along with the legal and moral objections to the use of the en-bloc clause in general, as described in Chapter 3, it is important to keep in mind that large premium ad-justments could lead to policy holders being forced to terminate their policy even though they already experience complaints leading to disability. In the remainder of this thesis, we take a maximum of 40% total premium adjustment as an extra restriction in some cases. It is indicated when this extra restriction is imposed.

Name Average maximum premium increase 10% p/y 313%

30% p/y 266% 40% p/y 272%

Table 6.4: Average maximum premium increase for the scenarios for the maximum premium adjustment. Recall Table 5.4 for an overview of the scenario names.

Table 6.4 shows that in the scenarios where the maximum yearly premium adjustment is tested, the en-bloc clause is used very extensively, so that it does not meet the requirement of being realistic (see Chapter 2). Therefore, both scenarios have also been tested with the extra restriction of a maximum total premium increase of 40%. This leads to the results in Table 6.5 and Figure 6.5.

The results for the maximum yearly premium adjustment show that if the total premium adjustment is unlimited, the boundaries set for the maximum yearly adjustment have a large influence on the SCR. A lower yearly maximum gives a larger SCR, and a higher yearly maximum gives a lower SCR. This effect is still present if the total premium adjustment is restricted, but a lot smaller. A

(28)

Figure 6.3: SCR and interval CI for Scenario I and the scenarios for the maximum yearly premium adjustment. The red square is the SCR. The black line is the interval CI.

Name SCR 5th percentile 95th percentile III 4,649 3,567 5,805 10% p/y (restricted) 4,989 3,790 6,249 30% p/y (restricted) 4,666 3,471 5,788 40% p/y (restricted) 4,567 3,340 5,721

Table 6.5: SCR and interval CI for the maximum yearly premium adjustment with restriction. Recall Table 5.4 for an overview of the scenario names.

maximum yearly premium adjustment of 10% instead of 20% gives a SCR increase of 7%.

(29)

Figure 6.4: SCR and interval CI for Scenario I and the scenarios for the maximum total premium adjustment. The red square is the SCR. The black line is the interval CI.

Figure 6.5: SCR and interval CI for Scenario III and the scenarios for the max-imum yearly premium adjustment with restriction. The red square is the SCR. The black line is the interval CI.

(30)

Portfolio diversity

Recall Table 5.5 for the scenarios studied with regards to the portfolio diversity. Table 6.6 gives the SCR and the interval X for the scenarios. These are graphically illustrated in Figure 6.6.

Name SCR 5th percentile 95th percentile I 717 85 1,296 A 773 181 1,398 B 783 166 1,409 C 914 239 1,520 D 1,117 494 1,697

Table 6.6: SCR and interval CI for the portfolio diversity. Recall Table 5.5 for an overview of the scenario names.

Figure 6.6: SCR and interval CI for Scenario I and the scenarios for the portfolio diversity. The red square is the SCR. The black line is the interval CI.

In these scenarios, the en-bloc clause is used very extensively. Table 6.7 gives the average maximum premium increase. The is the premium increase policy hold-ers with the longest duration will face if they do not lapse. Since using the en-bloc clause to this extent is not realistic and therefore does not meet the require-ments for a future management action, we again impose an extra restriction: the premium can maximally be increased with 40%. The results of the calculations given this extra restriction are displayed in Table 6.8 and graphically illustrated in Figure 6.7.

Both with and without the restriction, the portfolio diversity increases the SCR. Within the diversity scenarios a larger diversity within the portfolio causes

(31)

26 I. S. Doelman — The en-bloc as fma Name Average maximum

premium increase A 291%

B 308% C 303% D 384%

Table 6.7: Average maximum premium increase for the portfolio diversity. Recall Table 5.5 for an overview of the scenario names.

Name SCR 5th percentile 95th percentile III 4,649 3,567 5,805 A (Restricted) 4,804 3,612 6,025 B (Restricted) 4,785 3,594 5,966 C (Restricted) 5,182 3,918 6,364 D (Restricted) 5,552 4,245 6,759

Table 6.8: SCR and interval CI for Scenario III and for the scenarios for the portfolio diversity given the restriction.

a higher SCR for the scenarios tested. Compared to the scenarios without portfolio diversity (Scenario I and III), the SCR of the scenario with the largest diversity is about 20% higher with the extra restriction and about 55% higher without the extra restriction. We can conclude that portfolio diversity is an important factor to take into consideration.

(32)

Figure 6.7: SCR and interval CI for Scenario III and the scenarios for the influence of the portfolio diversity given the restriction. The red square is the SCR. The black line is the interval CI.

Lapse probability after premium adjustment

In Scenario I, a lapse probability of 5% is assumed when the en-bloc clause is used. Several lapse probabilities are studied; recall Table 5.6. The results are displayed in Table 6.9, and graphically illustrated in Figure 6.8.

Name SCR 5th percentile 95th percentile I 717 85 1,296 2% 1,267 608 1,907 10% -126 -651 402 15% -286 -902 419 5%+increase 781 32 1,488

Table 6.9: SCR and interval CI for the lapse probability after premium adjust-ment. Recall Table 5.6 for an overview of the scenario names.

Table 6.10 shows that the en-bloc clause has been used very extensively. Again, we impose the extra restriction of a maximum premium increase of 40%. Table 6.11 gives the results given the extra restriction. These are graphically illustrated in Figure 6.9.

The results show that both with and without the extra restriction, the higher lapse percentages cause a decrease in the SCR. This can partially be explained by the the extreme increase in premiums, and partially by the release of technical provision in case of lapse. The effect of the premium release could be different if, instead of a leveled premium, another premium structure is used. It should also

(33)

Figure 6.8: SCR and interval CI for Scenario I and the scenarios for the lapse probability after shock. The red square is the SCR. The black line is the interval CI.

Name Average maximum premium increase

2% 231%

10% 428% 15% 936% 5%+increase 1,143%

Table 6.10: Average premium increase for the lapse probability after premium adjustment. Recall Table 5.6 for an overview of the scenario names.

be noted that in our model, the released technical provision of the lapsing policy holders stays within the portfolio. In practice, an insurer might be inclined to use the released technical provision for another portfolio or for dividend.

Furthermore, the results show that it is important not to overestimate the lapse probability after premium adjustment.

(34)

Name SCR 5th percentile 95th percentile III 4,649 3,567 5,805 2% (Restricted) 4,999 3,803 6,280 10% (Restricted) 4,282 3,124 5,429 15% (Restricted) 4,204 3,101 5,337 5%+ increase (Restricted) 4,603 3,354 5,898

Table 6.11: SCR and interval CI for Scenario III and the scenarios for the lapse probability after premium adjustment given the restriction. Recall Table 5.6 for an overview of the scenario names.

Figure 6.9: SCR and interval CI for Scenario III and the scenarios for the lapse probability after premium adjustment given the restriction. The red square is the SCR. The black line is the interval CI.

(35)

Chapter 7 Conclusion

In this thesis, we studied the risks of using the en-bloc clause as a future manage-ment action. One of the risks of using the en-bloc clause as a future managemanage-ment actions is a legal risk. The use of en-bloc clause is debatable, and therefore it might not be enforceable.

We have seen that the unlimited use of the en-bloc clause decreases the SCR by over 90%. However, the total premium increase in that case is unacceptable and unrealistic. How large the effect of a restriction on the total premium increase is, is very dependent on the boundaries set. In setting these boundaries, two things have to be taken into account. First of all, according to article 77 of the Solvency II Directive and article 23 Delegated Acts, the assumption has to be realistic. Secondly, ethical considerations have to be acknowledged.

The results are relatively robust for the number of policy holders. Furthermore, if the total premium adjustment is restricted, the results are also robust for the case where policy holders only lapse if they can get a lower premium elsewhere.

Portfolio diversity is a very important factor to take into consideration when calculating the SCR. A larger policy holder diversity leads to a higher SCR. In the scenario with the largest portfolio diversity, the SCR was about 55% higher in the case of a restricted total premium adjustment and about 20% higher in the case with unlimited premium adjustment.

Furthermore, limiting the maximum yearly premium adjustment influences the SCR. A lower yearly maximum gives a larger SCR, and a higher yearly maximum gives a lower SCR. This effect exists both if the total premium adjustment is limited and unlimited.

The assumend lapse probability after premium adjustment also has influence on the SCR. Both with and without a restricted total premium adjustment, it is important not to overestimate the lapse probability, since this might lead to a capital deficit.

(36)

Suggestions for further research

Since so little is known on this subject, it would be very interesting to study policy behavior in disability insurance after premium adjustment. This could entail both lapse rates in general or a study on the health of lapsing policy holders. It would be interesting to study how this lapse influences the average health of the portfolio.

Insurers might also want to research the effect of the portfolio structure and adjust the model to their own portfolio. Differences in insured capital and partial lapse by changing the insured capital might alse be taken into account in that case.

Furthermore, the Solvency II directive seperates the risks for disability, lapse, interest rates and so forth by calculating the effects of different shocks seperately. It might be interesting to model these shocks in conjunction or to give a better insight in the way these risks interact.

(37)

References

Brethouwer, S. (2011). Arbeidsongeschiktheidsverzekeringen (Bachelor’s Thesis, University of Amsterdam). Retrieved from http://www.scriptiesonline. uba.uva.nl/scriptie/399622.

Christiansen, M. C., Eling, M., Schmidt, J. P. & Zirkelbach, L. (2015). Who is changing health insurance coverage? Empirical evidence on policyholder dy-namics. Journal of Risk and Insurance, 83(2), 269299.

Eling, M., & Kiesenbauer, D. (2013). What policy features determine life insurance lapse? An analysis of the German market. Journal of Risk and Insurance, 81(2), 241-269.

Fier, S. G., & Liebenberg, A. P. (2013). Life insurance lapse behavior. North American Actuarial Journal, 17(2), 153-167.

Haberman, S., & Pitacco, E. (1998). Actuarial models for disability insurance. CRC Press.

Hendrikse, M. L. (2012). De en-bloc-clausule: een vreemde eend in de verzeker-ingsrechtelijke bijt. Nederlands Tijdschrift voor Handelsrecht 2012-1, 1-15. Kuijper, Y. (2014). How should a disability insurance company interpret the

con-tract boundaries imposed by the Solvency II regulation? (Master’s Thesis, Uni-versity of Amsterdam). Retrieved from http://www.scriptiesonline.uba. uva.nl/scriptie/560252.

Makhan, V. (2011). Het prijzen van arbeidsongeschiktheidsverzekeringen (Bach-elor’s Thesis, University of Amsterdam). Retrieved from http://www. scriptiesonline.uba.uva.nl/scriptie/399624.

Rothschild, M. & Stiglitz, J. E. (1976). Equilibrium in competitive insurance mar-kets: An essay on the economics of imperfect information. Quarterly Journal of Economics 90, 629-650.

Siegelman, P. (2004). Adverse selection in Insurance Markets: An Exaggerated Threat. The Yale Law Journal 113, 1223-1281.

Sociaal-Economische Raad (2010). Zzpers in beeld: Een integrale visie op zelfs-tandigen zonder personeel.

(38)

The en-bloc as fma — I. S. Doelman 33 Verbond van Verzekeraars (2016). Regeling spelregels bij en-blocwijzigingen AOV.

(39)

Appendix A: Transition

probabilities

The following transition probabilities are used in this thesis. These are taken from Makhan (2011). These are the probabilities for a male in occupation group 1.

1pA,I(1)x = 0.00149 · 1.0362 x_, 1pI(1),Ax = 1.04056 − 0.01838 · (x − 1), ∀x ≥ 30, 1pI(2),Ax = 0.73521 − 0.01076 · (x − 2), ∀x ≥ 30, 1pI(3),Ax = 0.52170 − 0.00874 · (x − 3), ∀x ≥ 30, 1pI(4),Ax = 0.25695 − 0.00429 · (x − 4), ∀x ≥ 30, 1pI(5),Ax = 0.25941 − 0.00464 · (x − 5), ∀x ≥ 30, 1pI(6),Ax = 0, 1pI(y),Ax =1p I(y),A 30 , ∀x < 30, y ∈ {1, 2, 3, 4, 5}. 34

(40)

Appendix B: Portfolio of policy

holders

The portfolio used for the calculations consists of 15,000 policy holders, equally distributed over the ages at the moment of shock and at the start of the insurance as displayed in Table B.1.

Age at moment of shock Age at start insurance

20 20 30 20 30 30 40 20 40 30 40 40 50 20 50 30 50 40 50 50 60 20 60 30 60 40 60 50 60 60

Table B.1: Portfolio of policy holders used in all calculations of Chapter 6.

(41)

Appendix C: Robustness check

on portfolio size

Since the results are obtained by simulation, having a finite number (15,000) of policy holders could influence the results. Therefore, the robustness of result is verified by simulating with a portfolio of 30,000 policy holders. The results are given in Table C.1 and graphically illustrated in Figure C.1.

Figure C.1: Average SCR per policy holder and interval CI for Scenario I and the scenario for the portfolio size. The red square is the average SCR per policy holder. The black line is the interval CI.

The difference between the average necessary capital per policy holder in the two scenarios is caused by the fact that the amount of simulations done is limited. The interval X is only slightly decreased. When the extra restriction of a total maximum premium increase of 40% is enforced, this does not alter. The results given that restriction can be found in Table C.2 and Figure C.2. We can therefore conclude that having 30,000 policy holders instead of 15,000 has little influence.

(42)

The en-bloc as fma — I. S. Doelman 37 Name Average SCR

per policy holder

5th percentile 95th percentile Average maximum premium increase I (15,000 pol-icy holders) 0.0478 0.0056 0.0864 274 % 30,000 policy holders 0.0525 0.0157 0.0860 269 % Table C.1: Average SCR per policy holder, interval CI and average maximum premium increase for the scenarios on the portfolio size.

Figure C.2: Average SCR per policy holder and interval CI for Scenario III and the scenario for the portfolio size with the extra restriction. The red square is the average SCR per policy holder. The black line is the interval CI.

Name Average SCR per policy holder

5th percentile 95th percentile III (15,000

pol-icy holders, re-stricted) 0.3100 0.2378 0.3870 30,000 pol-icy holders (restricted) 0.3120 0.2570 0.3690

Table C.2: Average SCR per policy holder and interval CI for Scenario III and the scenario for the portfolio size with the extra restriction.

(43)

Appendix D: Robustness check

on theoretically locked in

constraint

In order to analyse a scenario where policy holders only have a 5% lapse probabil-ity if they are not theoretically locked in, we first calculate the size of the starting premium over the ages. This is illustrated in Figure D.1. The assumptions from Table 5.3 are applied. A policy holder would be theoretically locked in if his start-ing premium plus the (accumulated) increase is lower than the startstart-ing premium at that point in time. For instance, a policy holder who purchased the insurance at age 20 with a accumulated increase of 20% would not be theoretically locked in at age 30, but the policy holder would be theoretically locked in at age 40.

Figure D.1: Starting premium over ages, given the assumptions from Table 5.3. The pattern of premium size can be explained qualitatively. For the lower ages, the starting premium rises with age because the average disability rates over the duration of the insurance rises. For higher ages, the starting premium declines

(44)

The en-bloc as fma — I. S. Doelman 39 with age because even though the probability of disability rises, the benefits only have to be paid out for a small number of years.

Given the theoretically locked in constraint, the SCR is calculated. The results are listed in Table D.1 and graphically illustrated in Figure D.2.

Name SCR 5th percentile 95th percentile Average maximum premium increase I 717 85 1,296 274%

Theoretically Locked In

1,503 586 2,467 116%

Table D.1: SCR, interval CI and average maximum premium increase for the theoretically locked in constraint.

Figure D.2: SCR and interval CI for Scenario I and the scenario for the theo-retically locked in constraint. The red square is the SCR. The black line is the interval CI.

Name SCR 5th percentile 95th percentile III 4,649 3,567 5,805 Theoretically Locked

In (Restricted)

4,745 3,583 6,016

Table D.2: SCR and interval CI for Scenario III and the scenario for the theoret-ically locked in constraint with the extra restriction.

(45)

Figure D.3: SCR and interval CI for Scenario III and the scenario for the theo-retically locked in constraint and the extra restriction. The red square gives the SCR. The black line gives the interval CI.

We see that the locked in constraint has a large influence on the SCR if the en-bloc clause is used without restriction. However, in the more realistic case of a restricted en-bloc clause, this influence has evaporated.

The en-bloc clause as future management action