Solvency II. A comparison of the standard model with internal models to calculate the Solvency Capital Requirements (SCR)

Master's Thesis, 2015

67 Pages



List of Figures

List of Tables


1 Introduction

2 Solvency II
2.1 The need for a new solvency regime
2.2 Basic architecture of Solvency II
2.2.1 Pillar I: Quantitative Requirements
2.2.2 Pillar II: Qualitative Requirements
2.2.3 Pillar III: Transparency Requirements

3 Solvency Capital Requirements
3.1 The Solvency Balance Sheet
3.2 Definition of SCR
3.3 Standard Model
3.3.1 Basic Solvency Capital Requirements
3.3.2 Market Risk Module Interest Rate Risk Equity Risk Property Risk Currency Risk Spread Risk Concentration Risk Illiquidity Risk
3.3.3 Life Module Mortality Risk Longevity Risk Disability and Morbidity Risk Lapse Risk Expense Risk Revision Risk CAT Risk
3.3.4 Non-Life Module Premium and Reserve Risk Non-Life Lapse Risk Non-Life CAT Risk
3.3.5 Counterparty Default Risk
3.3.6 Intangible Asset Risk Module
3.3.7 Operational Risk
3.4 Internal Model
3.4.1 The Internal Model Approval Process
3.5 Summary

4 Current Topics on Solvency II
4.1 Long Term Guarantee Assessments

5 Quantitative Comparison
5.1 Literature Review
5.2 Research Question
5.3 Model Framework
5.3.1 Calculating SCR in the standard approach
5.3.2 Calculating SCR in the internal approach
5.4 Input parameter and calibration
5.5 Results

6 Conclusion



List of Figures

Figure 1: The Three Pillars of Solvency II (According to Rühlicke (2013, p. 22))

Figure 2: The Solvency Balance Sheet (According to CEIOPS Consultation Paper (2006, p. 14))

Figure 3: SCR regarding Value-at-Risk Approach (According to Gründl/Schlütter/Post (2014, p.45))

Figure 4: The overall Structure of the Standard Formula (Source: EIOPA (2014, p. 6))

Figure 5: The Internal Model Review Process (Source: Cadoni, Paolo: Internal Models and Solvency II (2014, p. 46))

Figure 6: Main Factors in Comparison (Source: Gillespie et al. (2008) / Towers Watson (2011))

Figure 7: CIR Term Structure at time t=

Figure 8: SCR of the Initial Portfolio calculated by the Standard and the Internal Model

Figure 9: 3D Plot of Estimated Term Structure at t=1 (1 path)

Figure 10: Equity Scenarios calculated by the Standard model

Figure 11: Equity Scenarios calculated by the Internal Model

Figure 12: Real Estate Scenarios calculated by the Standard Model

Figure 13: Real Estate Scenarios calculated by the Internal Model

Figure 14: Corporate Bond Scenarios calculated by the Standard Model

Figure 15: Corporate Bond Scenarios calculated by the Internal Model

Figure 16: Asset Quality Analysis via Standard Model

Figure 17: Asset Quality Analysis via Internal Model

List of Tables

Table 1: BSCR Correlation Table

Table 2: Main Characteristics of Standard Model and Internal Models

Table 3: Ratio of Internal Model SCR to Standard Formula SCR (Source: QIS5 Final Report (2013, p. 114))

Table 4: Correlations in the Equity Risk Sub-Module of the Solvency II Standard Model (Souce: EIOPA (2014, p. 115))

Table 5: Spread Shock for Corporates and Non-EEA Government in the SII Standard Approach (Source: EIOPA (2014, pp. 122-123))

Table 6: Correlation in the Market Risk Module in the SII Standard Approach (Source: EIOPA (2014, pp. 108-109))

Table 7: Bond Portfolio

Table 8: Calibration Parameters Applied in the Numerical Analysis

Table 9: Test Scenarios for the Asset Type Quality Analysis

Table 10: Risk Free Interest Rate Shock Parameter determined by EIOPA


Abbildung in dieser Leseprobe nicht enthalten

1 Introduction

The Solvency II Directive, which will come into effect from January 2016, is a very im- portant project of the European insurance industry. It will set new rules to the European insurance business. Because of being the biggest insurance market of the world - European insurers generate more than € 1,100 bn p.a. and invest around € 8,600 bn in the economy1

- the new directive will also act as a signal for the worldwide regulation of insurance companies. So it is also intended to have a framework, which is in line with the international developments in solvency, risk management, supervisory and accounting.

After 15 years of planning and development the regulation is now implemented step-by- step. The aim of the EU Solvency II Directive is to prevent insurers from becoming insol- vent. For this purpose, among other things, a uniform capital adequacy for all European insurance companies is provided. Core of the proposed amendments with respect to the investment is that eligible capital at any time must be higher than the calculated risk.

One of the main parts of the Solvency II project is the determination of the capital re- quirements. The idea is to asses both the assets and the liabilities with the aim of a more realistic modelling and assessments of the risk to which an insurer may be exposed to. The solvency capital requirements (SCR) for an one year horizon is then calculated on the 99.5% Value-at-Risk. The determined SCR answers the question how much capital is re- quired today to cover losses, which may occur during the next 12 months, with a probabil- ity of 99.5%.

For the calculation of the SCR the insurer can choose between standard model, internal models or a hybrid model. Since internal models allow a better assessment of the compa- nies risk than the standard model, insurers are encouraged to implement such stochastic internal models. But the implementation of internal model is as well costly as sophisticat- ed. That is why the European Commission with support of the Committee of Insurance and Occupational Pension Supervisors (CEIOPS) has established a scenario based standard model. The standard model defines in a first step different sub modules (e.g. market risk, operational risk) for which the capital requirements are calculated. The different SCR’s are “then aggregated under the assumption of a multivariate normal distribution with prespecified correlation matrices to allow for diversification effects”2.

The calibration of the standard model is assessed by a series of Quantitative Impact Studies (QIS), which analyse the effect of the capital requirements. Although the standard model reveals some shortcoming most of the small and medium-sized companies committed to rely on the model. Larger companies are more likely to implement a fully internal model. But there are also some larger companies using partial models meaning that some parts of the standard model are used as well.

Since the regime will come into effect in the near future both models cannot be compared using real data. Therefore some paper compare both models using a stylized insurer3. Their results say that the standard model overestimates the risk in many cases and therefore de- termines a higher SCR than the internal model. But there might also be circumstances in which the internal model underestimates the risk and results in a lower SCR than really necessary.

The aim of this thesis is a comparison of the standard model with the internal model to calculate the SCR. For this purpose the analysis only concentrates on the assets of a lifeinsurer, which are invested in the asset classes stocks, real estates, government and corporate bonds. A stochastic internal model is then implemented. At the center of the thesis is the analysis of the effects on the SCR altering the portfolio weights of the corresponding asset classes using both the standard and the internal model.

The structure of this thesis is organized as follows: In Section 2 a short introduction in Sol- vency II is given by describing the need of a new regime and the basic architecture of the regime. Section 3 defines in a first step the solvency balance sheet and SCR. Secondly the standard model and the internal model are described and compared on a qualitative basis. Section 4 covers the topic of the Long Term Guarantee Assessments. The model frame- work of both models used for the analysis is described in detail in section 5. This section also includes the numerical result of the analysis. Finally, section 6 gives a short conclu- sion of the thesis.

2 Solvency II

The Solvency II Directive (SII Directive) is an EU Directive4 that is redesigning the capital adequacy regime for European insurers and reinsurers. It contains a new set of regulatory requirements. It aims to harmonize the EU insurance regulation and preserving “a level playing field” for all market participants in a single rule book5. According to Cadoni (2014, p. 1) the new rules will continue the trend, placing demanding requirements on firms’ risk management. It also establishes a solvency system better matched to the risks of each (re)insurance firm than current regulations.

The goal of Solvency II (SII) is to protect the policyholder as well as providing stability to the financial system as a whole. It provides incentives to the insurers to measure and man- age the risks of their undertakings. It determines the quality of assets and the minimum amounts of financial resources insurers must have to cover the liabilities and risks. Actuar- ies now follow a total balance sheet approach and valuate both assets and liabilities by a common market value. Additionally, in order to manage their own risk, insurers are re- quired to disclose information to supervisors and market participants. This leads to an early warning system, where supervisors can improve and restore a company’s financial health by making demands.

In the next section, the need for a new solvency regime will be described. The following sections will give an overview of the basic architecture and current topics on Solvency II.

2.1 The need for a new solvency regime

Insurance companies take on and pool risks from its customers, sharing the risk among them6. So the company faces risks, which stem directly from this business. These risks are called underwriting risks7. The regulation of insurance companies has been mainly focused on underwriting risk. The capital requirement for insurer, a solvency margin and a mini- mum guarantee fund are derived from earned premiums, claims and mathematical reserves, all of which are related to underwriting. During developing the Solvency I Directive, the insurance Committee agreed, that “a more fundamental and wider-ranging review of the overall financial position of an insurance undertaking, including investment risk, (Solvency II) should be commenced”8.

An evidence supporting the necessity of the rework was provided by the Sharma Report: Between 1996 and 2001 the “London working group”, a group of supervisors, investigated 21 cases of failures and “near misses” in 17 European countries. Their findings were made public in 2002 in a report, which is called the Sharma report9. The conclusions were that the current solvency framework does not consider crucial risk factors (i.e. market risk, credit risk or operational risk). And they suggested that a new directive (Solvency II) should include requirements for governance and risk management within the companies and all firm activities should implement tools to monitor and mitigate risks at all levels. In many of the investigated cases, there was a chain of multiple underlying causes for failure. That’s why the report says: “Capital is only the second strategy of defence in a company, the first is good risk management”10.

The new SII Directive is risk-adjusted and based on a market-consistent valuation of assets and liabilities. The goal is an increased consistency between the companies’ real risk exposure and the solvency margin capital as well as harmonization of the regulatory regimes, which results in a better approach to the industry’s risk management. The framework also includes incentives for companies to assess and manage their risks.

2.2 Basic architecture of Solvency II

The structure of SII can be grouped into three pillars, inspired by Basel II accord from the banking industry. Figure 1 gives an overview of the pillars.

The first pillar focuses on the quantitative capital requirements and contains methods for measuring risk which are at the center of this thesis. The second pillar focuses on qualita- tive requirements such as a supervisory review process. Pillar III focuses on greater market transparency and discloser requirements. The following sections will give a short examina- tion of the three pillars.

Abbildung in dieser Leseprobe nicht enthalten

Figure 1: The Three Pillars of Solvency II (According to Rühlicke (2013, p. 22))

2.2.1 Pillar I: Quantitative Requirements

The first pillar describes two financial requirements which an insurer must meet: the Solvency capital Requirement (SCR) and the Minimum Capital Requirements (MCR).

The SCR reflects the capital an insurer must have available to cover its risk. It can be calculated using either the European Standard Formula or an internal model, which will be shown in section 3 in detail. Developing internal models by the companies improve their own risk management and may cause a decrease of the capital requirements. But it might also lead to higher requirements than suggested by the standard formula.

The MCR is a part of the SCR and is the absolute minimum of the capital level. If the capital level fell below the MCR an ultimate supervisory action will be triggered, which would lead to closure to new business or withdrawal with authorities.

For the sake of completeness the second and the third pillar are briefly described in the following.

2.2.2 Pillar II: Qualitative Requirements

The second pillar specifies requirements on corporate governance and adequate internal risk management processes. The insurer should have internal assessment processes, showing that they understand the financial instruments their assets are invested in.

The system of governance is described in Article 41 of the SII Directive. One important block of the system is the “Own Risk and Solvency Assessment”11 (ORSA), which will serve as an internal assessment of overall solvency needs of an insurer. It is a unique characteristic of Solvency II since there are no other regulations with comparable requirements. It should help the insurer itself and the supervisory units understand better a firm’s risk situation. All insurers are obliged to produce an ORSA system, no matter whether they use the standard or the internal model. Since the regulator is able to impose capital add-ons, companies have an incentive to develop a robust self-analysis.

Another block of governance is the risk management system which is described in Article 43 of SII Directive. The components are strategies, policies, processes and internal reporting procedures. Insurers are obliged to document the objectives of risk management and risk management principles and internal risk and demonstrate daily implementation of risk prevention. These procedures and processes must enable the firm to identify, manage, monitor and report the current and future risks.

2.2.3 Pillar III: Transparency Requirements

Pillar III focuses on transparency requirements. As stated by CEIOPS’12: “Supervisory reporting requirements in the Solvency II framework should support the risk-oriented approach to insurance supervision while public disclosure requirements should reinforce market mechanisms and market discipline.” So there are two reports required:

The Regular Supervisory Report (RSR) between an insurer and its national supervisory organization, which contains narrative and quantitative information and kept confidential by the supervisory authority. It also includes business performance, governance, risk profile and capital management.

The Solvency and Financial Condition Report (SFCR), which is publicly available. It contains information about business performance, governance, risk profile, capital management as well as asset and liability valuation.

By disclosing this key information, supervisory is enabled to evaluate the information and make adjustments where necessary. Also they can identify insurers who might be heading difficulties. In this case the supervisory authorities should “have the power to take preventive and corrective measures to ensure that the insurance and reinsurance undertakings comply with” the requirement of the directive13.

3 Solvency Capital Requirements

As mentioned in section 2.2.1 the first pillar sets out quantitative requirements an insurer must satisfy to demonstrate to have sufficient financial resources. These requirements are in particular the SCR and the MCR. Because of being at the centre of this thesis only the SCR will be elaborated.

A starting point of the SCR calculation is the solvency balance sheet that will be discussed in section 3.1. Later on in section 3.2 a definition of SCR is provided. The methods of calculating the SCR (standard and internal models) are described in sections 3.3 and 3.4. Finally section 3.5 sums up the benefits and drawbacks of the two approaches.

3.1 The Solvency Balance Sheet

The determination of the SII economic capital should be in such a manner, that the insurer can avoid financial bankruptcy with a one year horizon and a confidence level of 99.5%. A starting point for the calculation is the Solvency Balance Sheet as from date [Abbildung in dieser Leseprobe nicht enthalten] and as of date [Abbildung in dieser Leseprobe nicht enthalten] The calculation also takes into account both the valuation of assets and the lia- bilities. Figure 2 shows the main elements of the Solvency Balance Sheet:

Abbildung in dieser Leseprobe nicht enthalten

Figure 2: The Solvency Balance Sheet

(According to CEIOPS Consultation Paper 20 (2006, p. 14))

As of date [Abbildung in dieser Leseprobe nicht enthalten] the values of the elements are deterministic, whereas at [Abbildung in dieser Leseprobe nicht enthalten] they are sto- chastic and depend on random factors (e.g. financial, demographics) that occur during the first year.

The valuation in both points of time is done in a market-consistent manner, meaning that market values of assets and liabilities should be used where available14. In other words, whenever it is possible, the valuation shall use the fair value, called the mark-to-market method.

Determining the market-value of the assets is not that complicated, valuing the liabilities is more sophisticated. Here the expected cash flows of the liabilities are decomposed into units and linked to financial instruments. In this way the current arbitrage free market price for the instrument can be used to calculate the liability cash flow.

However this replicating strategy is not always possible. This can occur in incomplete markets, where no replicating strategies for liabilities exist. Therefore a mark-to-model approach should be used. In this case the value consists of a best estimate and a risk mar- gin15. According to article 77 of the SII Directive the best estimate is a “probability- weighted average” of discounted future cash flow of claims and expenses, “using the rele- vant risk-free interest rate term structure”. The risk margin can be described as the extra capital which ensures that the technical provisions are equivalent to the capital another insurer would require on order to take over all of the undertaking’s obligations16. It is cal- culated by determining the “cost of providing an amount of eligible own funds equal to the SCR necessary to support the (re)insurance obligations over the lifetime”17. To calculate the cost of holding that amount of capital a so called Cost-of-Capital rate is used18.

Technical provisions, which are defined to be capital needed to meet obligations the company has towards the policyholder, are the sum of best estimate and the risk margin.

3.2 Definition of SCR

The solvency of an insurer is in particular exposed through risks of the assets and technical provisions (see Figure 2). In a simplified representation the own fund can be calculated as follows:

Abbildung in dieser Leseprobe nicht enthalten

If the own funds are equal or fell below zero the solvency of an insurer is exposed. This may happen if the assets lose in value (investment risk), the technical provisions increase (underwriting risks) or if claims have to be paid immediately (underwriting risks).

According to the (simplified) formula 1 the risk of getting insolvent can be covered by holding enough solvency capital. This cushion is described in the Solvency II Directive as the Solvency Capital Requirement (SCR). The purpose of the SCR is to “deliver a level of capital that enables an insurance undertaking to absorb significant unforeseen losses over a specified time horizon and gives reasonable assurance to policyholders that payments will be made as they fall due”19. Further the SCR should be as high enough that the probability of getting insolvent is less or equal 0.5%20. The calculation of the capital requirement in Solvency II is based on the Value-at-Risk (VaR) method, given a certain time horizon and a confidence level of 99.5%. Figure 3 shows the concept of the value-at-risk approach:

Abbildung in dieser Leseprobe nicht enthalten

Figure 3: SCR regarding Value-at-Risk Approach (According to Gründl/Schlütter/Post (2014, p.45))

The SCR follows a dynamic approach looking at the balance sheets at two points in time: [Abbildung in dieser Leseprobe nicht enthalten] (i.e. at beginning of the year) and [Abbildung in dieser Leseprobe nicht enthalten](i.e. at the end of the year). The graph in Figure 3 shows the density function of the own funds at [Abbildung in dieser Leseprobe nicht enthalten]. In other words the graph shows probable values of the own funds (x-axis) at the end of the year. Because of being exposed to different risk the value of the own funds at the end of the year is uncertain. Therefore the higher the graph the higher the likelihood that the own funds fluctuate at this range.

The area under the curve represent the probability of different values of the own funds. If the probability of getting insolvent should be less or equal 0.5% the area left of the position, at which the own funds are equal zero, must be less or equal 0.5%.

So the SCR is calculated at a certain level of prudence with the value-at-risk approach and its level should be

Abbildung in dieser Leseprobe nicht enthalten

If insurance cannot fulfil the SCR requirements, then this will trigger supervisory review and corrective actions21.

According to articles 100 and 110 of the Solvency II Directive insurance companies are allowed to calculate their SCR using either the described standard approach or internal model, as approved by the supervisory authorities. They may use their own data to cali- brate some of the parameters in the underwriting risk modules. Furthermore insurance undertakings may use a simplified model22 or a partial model23 consistent of both internal and standard model.

While the standard formula is defined by the European Commission in a more general (and simplified) manner the internal is developed by the insurance company and is more de- tailed.

At the centre of this thesis is a comparison of two models for calculating the SCR: standard model and fully internal model. The following sections will describe these two different approaches in detail.

3.3 Standard Model

The idea behind the standard formula is to construct the different types of the insurance undertakings in a simplified manner, to measure these risks and determine the SCR. The structure is module-based24. The overall structure of the standard formula is illustrated in the following figure:

Abbildung in dieser Leseprobe nicht enthalten

Figure 4: The overall Structure of the Standard Formula (Source: EIOPA (2014, p. 6))

According to Article 103 of the Solvency II Directive the SCR is determined as

Abbildung in dieser Leseprobe nicht enthalten25 26 27

Based on the findings of the final quantitative impact studies (QIS5) in the section below the relevant module from figure 4 are briefly described.

3.3.1 Basic Solvency Capital Requirements

BSCR which is the SCR before any adjustments shall comprise individual risk modules28. It needs the following input information:

Abbildung in dieser Leseprobe nicht enthalten

where[Abbildung in dieser Leseprobe nicht enthalten] is the entry of the correlation table [Abbildung in dieser Leseprobe nicht enthalten]capital requirements for the risk categories according to rows and columns of the correlation table.

A discussion on dependence structure is done by CEIOPS29. Therefore the capital require- ments are quantiles of probability distributions. Linear correlations would not fully reflect the dependence between distributions and result in over- or underestimated capital re- quirements.

Thus CEIOPS suggested dependence parameters as choice of the correlation factors to avoid misestimating. This dependence structure is shown in table 1 (the matrix is symmet- rical).

Abbildung in dieser Leseprobe nicht enthalten

Table 1: BSCR Correlation Table

For this thesis the risk category health is not relevant. All other will be described in the following sections.

3.3.2 Market Risk Module

According to the findings of QIS5 this module has with a share of 67.4%30 the most important impact on the calculation of BSCR in life undertakings.

Market risk arises from “the level or volatility of market prices of financial instruments, which have an impact upon the value of the assets and liabilities”31. The market risk module consists of seven risk submodules: interest rate, equity, property, currency, spread and concentration, illiquidity premium.

The calculation of the market risk module is given by a square function which includes two correlation matrices for two scenarios (interest rate up and interest rate down):

Abbildung in dieser Leseprobe nicht enthalten

where [Abbildung in dieser Leseprobe nicht enthalten] represent the entries of the correlation matrix, [Abbildung in dieser Leseprobe nicht enthalten]are the capital requirements for the individual market risk under the stress up/down according the rows and columns of the correlation matrix.

All the submodule capital requirements are calculated in such a manner that the aggregation of[Abbildung in dieser Leseprobe nicht enthalten]results from a stress test consistent with all the worst case scenarios happening in one point of time. If one of the submodules leads to a negative SCR, the respective SCR will set to 0. Interest Rate Risk

Interest rate risk is defined as “the sensitivity of the values of assets, liabilities and finan- cial instruments to changes in the term structure of interest rates or in the volatility of in- terest rates”32. The assets include fixed income securities, loans and interest rate deriva- tives. The liabilities include in particular technical provisions and pension provisions.

It is calculated as a change of the own funds, if the zero-swap-rate changes in a specified way. Therefore an upward[Abbildung in dieser Leseprobe nicht enthalten] and a downwards [Abbildung in dieser Leseprobe nicht enthalten] stress factor are defined. The new term structure is determined by multiplying the current zero-swap-rate by[Abbildung in dieser Leseprobe nicht enthalten] where both factors are specified for individual maturities33. For example the downward shocked interest rate with the maturity of 10 years[Abbildung in dieser Leseprobe nicht enthalten]would be calculated with[Abbildung in dieser Leseprobe nicht enthalten]

The shock factors are then related to the risk-neutral market value. In this way the change in net asset value[Abbildung in dieser Leseprobe nicht enthalten] (net value of assets minus liabilities) is determined for both shocks. The unfavourable result from both scenarios has to be chosen.

The basis zero-rate curve and shock factors are published on the EIOPA website on a monthly basis34. Equity Risk

“Equity risk arises from the level or volatility of market prices for equities. Exposure to equity risk refers to all assets and liabilities whose value is sensitive to changes in equity prices"35. In terms of calculation the equity risk module indices are used as risk proxies, to derive volatility and correlation information. First a separation of the assets is made be- tween “Global” and “Other”. Shares which are listed on regulated markets in countries of the EEA (European Economic Area) and OECD (Organization for Economic Co-operation and Development) are categorized as “Global”. Emerging market equity, non-listed and private equity, hedge funds and any other assets which are not considered in other modules are categorized as “Other”36. In a second step, for each category a capital requirement is determined as the result of a pre-defined stress scenario, where the equity shock for the “Global”-category is 30% and “Other”-category 40%. Finally the two capital requirements are aggregated using a correlation matrix.

The recent field studies have shown that the equity risk is an essential component of the market risk module. According to QIS5 the share of equity risk is 64%37 in life undertak- ings. Based on the published Level 2 measures38 to the market and in particular for equity risk, this module is characterized by a very high stability with high efficiency to the capital requirements. Property Risk

The property risk arises from price fluctuations in the real estate market. The calculation does not differentiate between purpose of property (company building or investment property) and location of the property. All properties are shocked with 25%39. As a basis for determining the real estate risk, the fair value for all properties is required.

The property risk has only a small share of the capital requirements. The fact that there is no distinction in company building and investment properties led some discussion as to whether a lower approach is appropriate for corporate use properties. Currency Risk

Currency risk arises from fluctuation in exchange rates for asset and liabilities held in for- eign currencies. Again two scenarios are tested: an upward (downward) shock that is an instantaneous rise (fall) in the value of 25% of the foreign currency against the local cur- rency40. Spread Risk

A spread can be interpreted as the compensation for the investor over the risk free interest rate. It is an indicator of the fear of the market against defaults.

According to EIOPA spread risk arises from changes “in the value of assets and liabilities caused by changes in the level or the volatility of credit spreads over the risk free term structure”41. The change in credit spread results primarily from changes in creditworthiness of debtors. In principle, the same financial instruments are considered in this module as in the interest rate module with the exception of government bonds, which are considered as risk neutral regarding the spread risk.

The capital requirement for spread risk module is derived by summing up the capital requirements for spread risk of

Abbildung in dieser Leseprobe nicht enthalten

Capital requirements for credit derivatives are determined by calculating two scenarios: an upward shock and a downward shock scenario. Concentration Risk

Concentration risk arises from a higher volatility and an increased risk of default of an issuer in an investment portfolio with a low dispersion. This module covers assets, which are considered in the interest rate, equity, spread and property risk sub-modules. Assets covered by the counterparty default risk module are excluded “in order to avoid any overlap between both elements of the standard calculation of the SCR”42.

The concentration risk refers to the concentration of investment portfolios with the same business partner. Other concentration dimensions of the portfolio, such as the region or industry remain unconsidered.


1 See GDV (2014, p. 8).

2 See Börger (2009, p. 2).

3 See section 5.1 “Literature Review” on page 36.

4 Directive 2009/138/EC of the European Parliament and of the Council (11/25 2009).

5 Regulation (EU) No 575/2013 of the European Parliament and of the Council of 26 June 2013.

6 See Vaughan and Vaughan (2008, p. 34).

7 See CEA Groupe Consultatif (2007, p. 55).

8 The European Commission (1999, sect. 1.1).

9 Prudential Supervision of Insurance Undertakings (2002).

10 Wüthrich (2010, p.1).

11 See art. 44 of SII Directive.

12 Supervisory Reporting and Public Disclosure in the Framework of the Solvency II Project (2002).

13 See art. 34 of the SII Directive.

14 See art. 75 of the SII Directive.

15 See art. 77 of the SII Directive.

16 See Gründl/Kraft (2014, p. 37), also EIOPA (2013, V.2.5).

17 See CEIOPS (2009, p. 6).

18 See CEIOPS (2009, section 3.125).

19 See Sandström, (2001, p. 453).

20 See art. 101 of the SII Directive.

21 See art. 138 SII Directive.

22 See art. 109 SII Directive.

23 See art. 112 SII Directive.

24 See art. 103-108 SII Directive.

25 See QIS5 Technical Specifications (2010, p. 95).

26 See CEIOPS’ Advice for Level 2 Implementing Measures on Solvency II (2009, p. 5).

27 See CEIOPS’ Advice for Level 2 Implementing Measures on Solvency II (2009, p. 5).

28 See art. 104 SII Directive.

29 See CEIOPS‘ Advice for Level Implementing Measures on Solvency II (2010, pp. 8-10).

30 See EIOPA Report on the fifth Quantitative Impact Study (QIS5) for Solvency II (2011, p. 67).

31 See art. 105 of the SII Directive.

32 See art. 105 of the SII Directive.

33 See QIS5 Technical Specifications (2010, p. 111).

34 See (link).

35 See EIOPA (2013, p. 112).

36 See QIS5 Technical Specifications (2010, p. 113).

37 See QIS 5 - Ergebnisse der fünften quantitativen Auswirkungsstudie zu Solvency II (2011, p.17).

38 See Consultation document on the Level 2 implementing measures for SII (2011, p.14).

39 See QIS5 Technical Specifications (2010, p. 117).

40 See QIS5 Technical Specifications (2010, p. 118).

41 See EIOPA (2014, p. 23).

42 See EIOPA (2014, p. 26).

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Solvency II. A comparison of the standard model with internal models to calculate the Solvency Capital Requirements (SCR)
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