Within the scope of SolvencyII insurers are required to calculate the risk-based own funds needed using a standard model or their own internal risk model.
The working groups of insurance supervisors (Committee of European Insurance and Occupational Pension Supervisors [CEIOPS]) have been discussing the actual design of this new system since the summer of 2004 and published a first interim report on their discussion - inter alia on the standard model and on requirements for internal models - in November 2005.1 This report mentions the risk categories to be quantified and points out several possibilities for how these might be taken into consideration.
GDV began its research into a risk-based standard approach as early as 1997, setting itself the goal of initiating a redesign of insurance supervision with an approach that is based, to a greater extent, on risk management models. With this in mind, a risk-oriented standard model for life and casualty/property/accident insurers has been developed allowing for the particularities of specific classes. Since its publication in August 2002, the so-called "GDV model"2 has been taken up by numerous insurance companies in their risk management practice. The approach has met with a positive response at both national and international levels. Moreover, GDV has brought the model into the national and European debates on a new system of insurance supervision for Europe within the scope of the SolvencyII project.
Against this background, the model has been under revision since the spring of 2004. The objective was to check the model, which is now a few years old, to find out what adjustments should be made in the light of practical experience, the ongoing discussion and the changed economic environment. The new approach is a proposal for a standard model that is both compatible with SolvencyII and with the preparatory work done by the International Actuarial Association (IAA).3
The objective of this article is to show the progress of the work aimed at developing this standard model.
The draft calls for implementing the approach at European and national levels as a result of SolvencyII. Its general features are as follows:
- The approach, which has been developed as a coefficient and probability-based model, includes all relevant risks - unlike a scenario-based approach - and is at the same time satisfactorily simple.4
- The model has a modular structure, so that it is possible to incorporate the national particularities of other European countries.
- The approach adopts - as required due to risk-based considerations - a market-value point of view, but derives such market values, in simplified fashion, from commercial code figures. Thus, companies that do not already prepare their balance sheets according to International Accounting Standards (IAS)/International Financial Reporting Standards (IFRS), and do not have to move to international accounting rules in the foreseeable future, are not urged to switch to IAS/IFRS.
- As required by the EU Commission, asset liability management (ALM) issues are taken into consideration as part of the modelling of a change in interest rates risks for fixed interest bearing investments.
- The model allows for correlation effects in a conservative way, thus reflecting risk balancing processes in the insurance company.
- Incentives for the company to develop an internal model are provided by simplifying modelling and conservative parametrisation.5
- The parameters of the model have been - as far as this is necessary for their easy handling - predetermined in the model. In addition, where this seems necessary due to risk-based considerations, data of the individual company are used to avoid any simplified averaging in determining risk factors (personalised factor-based model). The input data of the individual company have been chosen in such a way as to ensure that they may be easily established by the insurance company and easily verified by the supervisory authority. For instance, in the life model, internal data are used to determine the risk factors included in the calculation risk. In the non-life model the technical risk is determined on the basis of the fluctuations of the combined ratio in the individual company.
- The computational formula will be made available to the companies as Excel spreadsheets, so that the burden put on insurance companies will be reduced.
Fundamental characteristics of the model
The draft standard model, compatible with Solvency II, to calculate the required risk capital (solvency capital requirements [SCR]) has the following characteristics, in addition to those already mentioned.
- As risk measure the value of risk is chosen, in line with the approach pursued at European level.6
- The risk capital needed to cover the individual risks is aggregated on the assumption of correlations to an aggregate capital requirement using the co-variance formula.
- The supervisory model takes, as required at European level, a one year's point of view.
- In both the life and the casualty/property/accident models, investment risks and operational risks are reflected according to the same approach (G1 and G2 risks). In modelling technical risks the particularities of specific classes are allowed for in each case (L and S risks).
Modelling of the investment risk
Investment risk means the risk that the market value of the investments will decrease in the next financial year. This risk category has a very significant influence on the level of own funds required which an insurer has to provide. In this context, the following sub-risks have been modelled:
- Credit risk
- The credit risk, also called failure of issuers risk, is determined for corporate bonds, mortgages and other accounts receivable. It includes the risk that debtors are unable to make the corresponding payments, for instance in the case of insolvency. Also, the risk that the credit spread increases due to classification in a worse rating class, and that the market value of the bond drops, is taken into account here. To reflect this risk, the risk factors determined on the basis of beta distributions are multiplied by the market values of the fixed interest bearing investment concerned.
- Market risk
- The market risk means the risk to which an insurance company is exposed due to fluctuations in the stock, fixed interest bearing investments and real estate markets.
- Shares: To reflect the market change risk, the volatilities and expected earnings in the stock market - depending on the respective yield in the bond market - have been estimated on the basis of historical data. In calculating the earning capacity value, the risk premium - as compared with the yield of 10 years' fixed-interest-bearing investments - has been taken as a basis. The risk factor determined on this basis is then multiplied by the market value of the shares.
- Real estate/property: In determining the risk arising from real estate and property, a similar approach is applied as for the share risk. Here too, the volatilities and expected earnings are estimated by means of experience gathered in the past. Again, the market values of the real estate are weighted by the risk factor thus calculated.
- Fixed interest bearing investments: The change in interest rates risk has been redrafted in the present version of the model. With a view to better taking account of ALM aspects in the model, the guarantee risk, which before was considered separately, has been included in the change in interest rates risk, as is in accordance with reality. The reduction of interest rates risk is reflected as shown in Figure 2.
The reinvestment or, better, the reduction of interest rates risk is determined by first using the stochastic interest rate model to calculate the market interest rate that corresponds exactly to the (lower) 0.5% quantile of the corresponding distribution. The assumed interest rate reduction corresponds to the difference between the current and the calculated market interest rates. For the interest rate thus established, the basic idea is that both the market values of assets and the market values of liabilities (giving rise to the payment of interests) are determined. The reduction of interest rates risk is defined as the difference between the increase in the market values of liabilities and the increase in the market values of assets. For reasons of methodology, market values are determined based on approximate figures using the modified duration of bonds or liabilities. Also, the increase in interest rates risk is modelled as shown in Figure 3.
In the case of a shock-like increase in interest rates (again, the shock interest rate is calculated using the stochastic interest rate model), the consequence is a decline in values on the assets side, faced, in the case of guaranteed surrender values, by the unchanged liabilities of the insurance company. An interest rate induced cancellation risk arises for the insurance company when the surrender value of a contract exceeds the market value of the matching assets, after the occurrence of the interest-rate shock. This scenario applies only in the case of guaranteed surrender values. In fact, in the case of a sharp increase in interest rates, clients will be more inclined to consider the cancellation of an existing contract and a new investment bearing higher interests, so that the insurance company will be forced to sell bonds at the resulting lower market value.
The amount of the economic loss is determined by the difference between the book value of the mathematical provisions, with guaranteed surrender values, and the market value of the matching assets after the interest rate shock and by the ALM cancellation rate which reflects the (interest rate induced) cancellation behaviour of clients. The first step is to calculate the SCR that would be needed if all clients cancelled. Since this would result in exaggerating the risk, cancelling behaviour is modelled assuming a certain client behaviour depending on the current level of interest rates. The total interest rate risk is determined as the maximum of the increase in interest rates risk and the reduction of interest rates risk. This value is adjusted for the average guaranteed interests paid on liabilities, less the expected yield from the bond portfolio in order to model the update during the accounting year.
- Currency risk
- The currency risk, which results from non-matching representation, is taken into account in respect of bonds and real estate. Risk factors for different currencies are derived by means of the normal distribution.
- Concentration risk
- With regard to the concentration risk, which results from a small spread of investments, the approach of the old GDV model remains fundamentally unchanged. It is based on the limits according to European Directives. In the future, it will not be the book values that are used as a basis, as is currently the case, but the market values of investments.
The own funds requirements resulting from these four risk categories have then to be aggregated to the investment risk. Since no stable positive or negative correlations can be proven over time, a zero correlation has been assumed for the purpose of simplification.
Calculation of the underwriting risk
Due to the particularities of specific classes, this risk category is modelled differently for life and casualty/property/accident insurers.
- Life (L risk)
Underwriting risks for life insurers can be subdivided into:
- Costs risk
- Default risk of receivables due from agents and policyholders
- Biometric risk
Since a quantile-based approach does not seem possible, these sub-risks are reflected via risk scenarios. This approach is consistent with the International Actuarial Association (IAA) proposals suggesting such a procedure. In the case of the costs risk, which arises from possible changes in cost structures, it is assumed that in the following year a discontinuation of new business will occur, with the company nevertheless having to incur expenditure to the amount of the fixed acquisition costs and administrative expenses. Capital to the same amount has to be provided for this risk. However, deductions are allowed for the income from expenses derived from business in force, amortisation loadings and the balance from other income and expenditure.
Another risk is constituted by the default of receivables due from agents and policyholders. First, the reduction of Zillmer claims due to the premature termination of contracts, less reversed commission entries due to premature termination, plus depreciation and value adjustments regarding receivables due from insurance agents is determined. In this respect, the value is considered in relation to Zillmer claims and receivables due from insurance agents. The biometric risk is composed of the fluctuation, cumulation and trend risks, which are modelled separately:
- Fluctuation risk: In this case, standard deviations of the distributions - separately for insurances against death, on survival, occupational disability insurances and remaining insurances - are approximated, with the size of the portfolio, the actual expenditure and the capital at risk being included as parameters. In accordance with the preset quantile, the risk capital is determined as a multiple of the distribution.
- Cumulation risk insurances against death/occupational disability insurances: In the case of this risk it is assumed that risk expenditure will double over the preceding year. The actual expenditure is deducted from the risk expenditure. The risk capital is once again maximised over the three preceding years.
- Trend risk: Here annuities only are considered. As risk capital, a proportion of the mathematical provisions for annuities is assumed.
- Non-life (S1 and S2 risks)
- The insurance technique of a casualty/property/accident insurer is reflected by considering the following sub-risks:
- Premium and provisioning risk
- Failure of reinsurance risk
The premium and provision risk (S1 risk) reflects the risk arising from application of insufficient premium rates and insufficient provisions. At first, the business of a casualty/property/accident insurer is divided into 11 lines of business (LoB), based on the First Non-Life Coordinating Directive.
The risk capital requirement is calculated using the company's individual combined ratios for each line of business, taking into account the correlations among the lines of business calculated on market basis. In addition, it is considered whether a company applies insufficient or sufficient premium rates to a class. Similar to the life model, risk bearer and risk factor per LoB are multiplied. For reasons of simplification, proportional reinsurance only is taken into account. A conservative estimate is made of the correlations applied, so that the model takes diversification effects into account - as they are typical of the activity in an insurance company - but still provides incentives to work on internal models. Another important advantage of the model, contrary to other proposals put forward in the international debate, is that a standard model is based on internal company data, but nevertheless the approach remains sufficiently simple.
Unlike in the first version of the model, the risks related to premium rates and provisioning are integrated. This procedure is aimed at preventing the model from providing false incentives. For instance, if in the provisioning risk, where the provisions would serve as a risk bearer, the own funds requirements rose in line with the increase in provisions. In addition, the following reasons may be given for such an integrated approach: It seems right to use the combined ratio because the model can fall back on internal company data, which can be easily verified by the supervisory authority. If the premium risk and the provisioning risk are separated, this results in greater instability of the data, especially in small companies, than if the calculation is based on the combined ratio. Moreover, as is shown by some test calculations, the combined ratio is the more stable measure in the case of transition to the fair value approach because artificial volatilities may arise, particularly on the provisions side.
As usual in international debates, natural disaster risks have been integrated into the non-life model. Natural disaster risks are treated in the model as separate LoB with a zero correlation towards other lines of business. The basis is a market loss distribution. The premium portion related to natural disaster risks is derived from market data as a loss portion of all identified severe losses and preset as a uniform percentage in the model. Reinsurance cover - proportional or non-proportional - is taken into account. For the purpose of simplification, only storm risks are included in this first step. A later modelling of further natural hazards is possible. Additionally, the model does not take into account regional differences between the exposures of individual insurance companies in Germany or company probable maximum loss (PML). Such a procedure is left to internal models. The failure of reinsurance risk (S2 risk) is also modelled. In the new model the risk factors are determined on the basis of the system applied by major rating agencies. Reinsurers rated inferior to BBB, but submitted to supervision by European authorities, are weighted by the probability of failure on which the supervisory concept for reinsurers is based.
Reflection of the operational risk
The operational risk is generally defined as the risk of losses occurring as a result of inadequacy or failure of internal procedures, persons or systems or due to external events. The own funds requirements, to this effect, are calculated in the model as the maximum of a percentage of gross premiums earned and of a proportion of technical provisions.
The submitted proposal is compatible with the requirements imposed by the EU Commission in its working documents relating to the SolvencyII project, and which have become apparent, for instance, in the first CEIOPS Interim Report.7 At the same time it meets the requirements put forward by the IAA. Therefore, the model proposed is to be understood as a contribution to the discussion within the scope of the SolvencyII project and intends to demonstrate how the various questions raised by the EU Commission can be solved. As a positive observation, it can be pointed out that many proposals for modelling that have been submitted have since been included in the CEIOPS Interim Report. GDV plans to continue to bring the standard model actively into the international debate, so as to influence European opinion in this respect and ensure the German business model is reflected in a risk-adjusted manner in the standard approach. Moreover, the approach, which has a modular structure, can be easily adjusted to the circumstances existing in other countries. However, it is likely that no purely national proposal can be enforced at European level and that only a common solution between EU member countries can be implemented. Following concluding internal work on the standard model and its validation by the association bodies, the model documentation and the Excel calculation sheets will be published on the website of GDV.
Dr. Thomas Schubert is head of the Business Administration Institute at GDV. Gundula Griessmann works in the Business Administration Institute at GDV. The authors would like to thank all members of the project groups who devoted much time to elaborating on this standard model.
CEIOPS (2005)A Draft
Answers to the European Commission on the 'second wave of Calls for Advice in the framework of the Solvency II project www.ceiops.org
CEIOPS (2005)B: Amended Framework for Consultation on Solvency II www.ceiops.org/texte/solvII_framework_ec.pdf.
GDV Modell (2002) Neues Aufsichtsmodell fur europaische Versicherungsunternehmen www.gdv.de/fachservice/20716.htm
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