New Risk-based Capital Standards in the European Union: a Proposal Based on Empirical Data

In response to criticism concerning the current solvency system, the European Commission is developing new rules for insurance companies operating in the member states of the European Union (EU). Under this so-called Solvency II concept, an insurer is allowed to verify its solvency by using an internal risk management model previously approved by the regulatory authority. In this article we develop such an internal risk management approach for propertyliability insurers that is based on dynamic financial analysis (DFA). The proposed concept uses a simulation technique and models the central risk factors from the investment and underwriting areas of an insurance company. On the basis of the data provided by a German insurer, the ruin probabilities under different scenarios and varying planning horizons are calculated. INTRODUCTION The current European Union (EU) rules governing the solvency of insurance companies essentially base the required minimum equity capital on the volume of insurance business the companies write (Farny, 1997). Thus, no attempt is made to identify or quantify the central risks borne by insurance companies.1 In response to criticism of this approach, the European Commission is currently drafting the “Solvency II” project, which develops Hato Schmeiser is Chair for Insurance Management, West fälische Wilhelms–Universität Münster, Germany; phone: ++49-251-83-22840; fax: ++49-251-83-22840; e-mail: hato.schmeiser@ wiwi.uni-muenster.de. The author would like to thank Michael R. Powers for helpful comments on an earlier draft of this article. In addition the author would like to thank the Gesamtverband der Deutschen Versicherungswirtschaft (German Insurance Association), Berlin, for its help in collecting the data used in this article and for its financial support. 1 This can be demonstrated by means of a simplified example. Let us take two nonlife insurance companies. Company 1 generates premium income totaling €450 million and faces normal distributed claims with a mean of €400 million and a standard deviation of €40 million; none of the claims have been reinsured, and the equity capital totals €100 million. Company 2 shows the same figures, albeit with a standard deviation for the claims of €80 million. Under the current EU rules, both companies are considered solvent (equity capital (=€100 million)> required solvency margin (≈€93 million)), even though the differences measured, e.g., by the underwriting ruin probability (company 1 ≈ 0.01 percent; company 2 ≈ 3.04 percent) are considerable. 41 42 RISK MANAGEMENT AND INSURANCE REVIEW a totally new approach to solvency regulation (European Commission, 2002). In analogy to the ideas discussed, and in part implemented in the European banking sector (Basle Committee on Banking Supervision, 2001), a two-stage approach is being considered: An evaluation model used by an internationally recognized rating agency serves as the basic concept (Stage I). Instead of the Stage I basic concept, insurance companies can opt to use internal risk management models (Stage II). Such internal risk management models use quantification approaches whose validity is generally recognized and that are used regularly by insurers already in the context of in-house risk management. Before an internal model can be used as the external measure of a company’s solvency, regulator approval is required. Should the proposed two-stage model in fact be implemented, insurance companies will be able to use a single, well-developed model for solving a number of different tasks all at the same time. Apart from providing external proof of solvency and, in Germany, meeting the demands of the KonTraG,2 such models could be used for in-house risk and performance management. In the following, we focus on the Stage II concept from the viewpoint of insurance regulators. In this context arise two important questions: What would a consistent and feasible Stage II model of an insurance company look like? How could certain scenarios (e.g., reduction of premium income, “dangerous” correlations) be defined to test the insurer’s solvency? The primary goal of this article is not to discuss these questions theoretically, but to show a practical implementation of the Stage II concept by using empirical data from a German property-liability insurance company. The approach originates in dynamic financial analysis (DFA) (Lowe and Stanard, 1997; Hodes, Feldblum, and Neghaiwi, 1999; Kaufmann, Gadmer, and Klett, 2001). RUIN PROBABILITY VERSUS EXPECTED POLICYHOLDER DEFICIT An insurance company’s solvency is typically measured by using one of two approaches: the probability of ruin approach or the expected policyholder deficit (EPD) ratio approach (Butsic, 1994; Barth, 2000). The ruin probability approach, which is founded in actuarial risk theory, quantifies the probability of an insurer’s liabilities exceeding its assets in any given period.3 If U1 denotes the insurer’s equity capital at the end of the period, then the ruin probability ψ(1) in a one-period context can be written as: ψ(1) = Pr{U1 < 0}. (1) 2 “Gesetz zur Kontrolle und Transparenz im Unternehmensbereich” (Law on Control and Transparency in Business). 3 Conversely, by setting a maximum permitted ruin probability, it is possible to determine the minimum amount of equity capital that is needed at the beginning of the planning horizon. NEW RISK-BASED CAPITAL STANDARDS IN THE EUROPEAN UNION 43 The ruin probability approach suffers from several shortcomings (Butsic, 1994; Powers, 1995). In particular, it has been criticized for not considering the severity of an insolvency. Thus, an EPD approach has been recommended (Butsic, 1994; Wang, 1998). The EPD approach calculates the expected costs of the ruin, i.e., the probability of ruin is multiplied by the expected cost of that ruin should it actually occur. Hence, we get in a one-period context: EPD = E[Max{0 − U1, 0}] = Pr{U1 < 0} · E[0 − U1 | U1 < 0]. (2) Given a fixed value for EPD, Equation (2) illustrates that there is a substitutional relationship between the ruin probability and the expected cost of ruin, assuming that a ruin occurs. As can be seen from a simple example, this is not entirely without problems.4 To set comparable standards for insurance companies of different sizes, the EPD is not considered directly; instead, an EPD ratio is formed. An EPD ratio is typically defined as the EPD divided by the expected value of the liabilities (Butsic, 1994; Barth, 2000). As Barth (2000) has shown on the basis of an empirical study, setting an EPD ratio in this way typically means that a relatively higher probability of ruin is sufficient for large insurance companies.5 This might be problematic because large insurers pose a greater threat to market stability as the collapse of a single large insurer results in significant indirect costs (Barth, 2000). The problems associated with the two approaches to measuring risk do not, in our opinion, make it possible for one particular method to be considered fundamentally superior to the other. It is more important to clarify what conclusions can or cannot be drawn with the use of any particular risk measure. In this article, we use the ruin probability approach. Although the ruin probability is, in general, a useful tool for regulators, it ignores the time value of money (Powers, 1995). In other words, the ruin probability concept does not take into account that—ceteris paribus—insolvencies occurring in the near future generally cause much higher concern than insolvencies occurring in the distant future. If the regulators want to address this point, the expected discounted cost of insolvency (EDCI) concept, a generalization of the ruin probability approach, should be used (Powers, 1995; see also Gerber and Shiu, 1998). RUIN PROBABILITY: SOME THEORETICAL REMARKS Let us assume that U denotes the equity capital and G represents the insurance company’s gains. From this the following basic relation can be obtained: Ut = Ut−1 + Gt (3) for some time period t ∈ T. 4 For example, an insurance company with a ruin probability of 1 percent and an expected cost of €1,000,000 assuming that a ruin occurs has approximately the same EPD as an insurance company with a ruin probability of 99 percent and an expected cost of €10,101 should the ruin actually occur (see Barth, 2000, pp. 410-11). 5 Fixing a certain EPD ratio for a large insurer (i.e., one with high expected liabilities) results in a high EPD value being set. Compared with a small company, this typically results in relatively greater values for Pr{U1 < 0} and E[ 0 − U1 | U1 < 0] being permitted (see Equation (2)). 44 RISK MANAGEMENT AND INSURANCE REVIEW If N stands for the first occurrence of ruin, we can write: N = inf {t : Ut < 0} . (4) Hence in the multi-period case, the probability of ruin can generally be defined as (Heilmann, 1988, p. 247): ψT = Pr {N < ∞} . (5) Depending on the chosen set T of time point t, one can distinguish the following four cases (Bühlmann, 1996, p. 134; Straub, 1997, p. 36): Case T1: Finite planning horizon and discrete time parameter (only a countable number of time points in the planning interval are of interest). Case T2: Infinite planning horizon and discrete time parameter. Case T3: Finite planning horizon and continuous time parameter (all points of time in the planning interval are of interest). Case T4: Infinite planning horizon and continuous time parameter. For the different versions T1, T2, T3, and T4, the following inequalities hold for the probability of ruin (Bühlmann, 1996, p. 134): ψT1 ≤ ψT2 ≤ ψT4 , (6)