Rolf Stölting and Kathleen Ehrlich, Munich

Solvency II for property-casualty insurers Reinsurance and the standard approach

This article addresses two main issues. First, we describe the basic principles of the standard approach to calculating the risk capital requirement for underwriting risk to be followed by property-casualty insurers and second, we explain how reinsurance reduces the solvency capital requirement in the standard approach.

We have used as a basis the European Commission’s July 2007 proposed framework directive and its interpretation in the third Quantitative Impact Study (QIS 3), carried out from April to June 2007 with the assistance of insurance companies. This interpretation is only provisional and consists primarily of a large Excel file. However, it provides an important indication of how the standard approach will look in the future. QIS 3 will in all probability form the basis for any changes, so that we can consider it as representing the current status of the standard approach.

Solvency I has made calculation of solvency requirements for non-life business relatively easy for insurers. They need two figures – the premium index (18% of premiums up to €50m and 16% of premiums in excess of €50m) and the claims index (26% of claims expenditure up to €35m and 23% of claims expenditure in excess of €35m). Amounts after reinsurance must be used . The required risk capital (solvency margin) is the higher of these two figures, with the proviso that it amount to a minimum of 50% of the relevant gross figures. Thus, only limited account is taken of reinsurance under Solvency I.

Solvency I’s simple methodology does not meet the need to determine solvency capital requirements on a risk basis taking account of modern risk management. For example, catastrophe risk and investment risk are disregarded. Solvency I also has undesirable side-effects. If, for example, a company increases the premium payable by an insured while the risk remains unchanged, the supervisory authority will require more risk capital, despite the fact that the company will have made its business safer by so doing. The reverse also applies, i.e. a reduction in premium saves the company risk capital, in spite of the increased probability of ruin.

Furthermore, it is difficult for insurers and reinsurers to understand how the apparently arbitrary limited recognition of reinsurance ever came about. To determine the risk capital requirement under Solvency II, all of the quantifiable risks incurred by an insurance company are identified and added together, taking account of diversification effects at various levels. Comprehensive "internal models" provide the most accurate results and for that reason, they are explicitly provided for in Solvency II. Internal models used to calculate the solvency capital requirement (SCR – the equivalent of Solvency I’s solvency margin) must be approved by the competent supervisory authority. Key prerequisites for approval are the proper quantification of all risks and the use of the model for internal corporate management purposes. Since internal models are likely to involve relatively high costs, probably only larger companies will submit internal models for approval, at least in the early days of Solvency II.

next page »

1. Standard approach

We consider below only Solvency II’s "standard approach" for property-casualty insurers according to the current status as per QIS 3. It takes the form of a extensive Excel file to be completed by the companies that performs practically all the SCR calculations. Though all of the results of the calculations can be clearly seen, some can be onerous to comprehend given the large size of the file and the numerous links. CEIOPS (and the BaFin in Germany) have published extensive technical information on the subject.

How is the SCR calculated for a property-casualty insurance company? We will begin with a general overview, followed by a more detailed description of how underwriting risk is taken into account.

a) Overview

As shown in Fig. 1, the SCR is calculated in several steps. First, the capital requirement is calculated for the following risk categories:

• —
  Underwriting risk
• —
  Market risk on investments
• —
  Investment and reinsurance credit risk

These capital requirements are then aggregated allowing for diversification effects (using a correlation matrix) and a further amount is added for operational risk. The total represents the solvency capital requirement (SCR) for a property-casualty insurer according to the standard approach.

The underwriting risk capital requirement comprises two components:

• —
  Premium and reserve risk
• —
  Catastrophe risk

As the two components are considered to be totally independent of each other, the underwriting risk is defined as the square root of the sum of their squares. Amounts net of reinsurance are used for the calculations.

b) Premium and reserve risk

"Premium risk" refers to the risk of premiums for the following year being insufficient to cover claims and other costs (excluding the risk of catastrophes).

"Reserve risk" is the risk of existing technical provisions being insufficient to cover claims. As for the premium risk, a one-year time horizon is applied. It therefore relates to the risk of the technical provisions (in the Solvency II balance sheet) for existing claims needing to be increased.

The technical provisions in the Solvency II balance sheet should be calculated using actuarial methodology and current market values. They consist of the sum of the fair values of future payments ("best estimate") plus a risk margin intended to cover the risk over the entire run-off period and calculated in such a way that, together with the best estimate, it equates to the price another market player would be willing to pay for the liability. This is the "cost of capital" approach to calculating the risk margin.

The calculations of the premium and reserve risks are performed first for each of the company’s classes of business (risk groups) and then aggregated. In property-casualty, there are a total of 15 class-of-business groups for underwriting, of which one relates to health insurance (subject to additional treatment under Solvency II) and three to (active) non-proportional reinsurance business.

The capital requirement resulting from the premium and reserve risks is then calculated for each class of business.

(1) Risk capital = Risk factor * Risk volume

Different amounts and methodologies for determining the risk factors are used for the premium risk and the reserve risk.

Premium risk by class of business
(excluding catastrophe risk)

In the formula (1) above, the volume figure taken for the premium risk is the estimated net premium after reinsurance for the year in question for the relevant class of business. The risk factor is dependent primarily (up to 80%) on fluctuations in the net loss ratio (standard deviation) for the class of business over the last 15 years, and at least 20% on the market fluctuations in the class. Thus, the calculation of the premium risk incorporates data specific to the company, so that, for example, a well-balanced business over a period of years or the smoothing of net loss ratios through reinsurance will result in a reduction of the SCR for the class of business in question.

Reserve risk by class of business

In the formula (1) above, the volume figure taken for the reserve risk is the amount of the technical provisions after reinsurance (from the Solvency II balance sheet). The risk factor reflects the annual fluctuations in the net loss ratios for the market as a whole. The procedure thus differs from that used for the premium risk in that only the provisions, but not the fluctuation data, relate to the company itself.

Aggregation of the premium and reserve risks across all classes of business

The separately calculated capital requirement figures are then aggregated taking account of the weighted fluctuations of the premium and reserve risks. Two factors should be borne in mind as regards the calculation of the SCRpre/res for underwriting risk (excluding catastrophe risk).

First, when performing the above aggregation, various diversification effects must be taken into account, both between classes for the premium and reserve risks and between the premium and reserve risks within each class (using a correlation matrix with 30 lines and columns).

Second, the principle in the proposed Solvency II framework directive that the calculation of the solvency capital requirement should incorporate a probability of ruin of 0.5% (99.5% value at risk) must be taken into account. Of course, this is not possible in a standard approach, but the solvency capital requirement is defined as the 99.5% quantile of a pre-selected probability distribution (lognormal) for the premium and reserve risks.

c) Risk of catastrophe losses

The catastrophe risk is defined for each country individually and for all significant natural catastrophe hazards and other catastrophe losses. In QIS 3 for Germany, the natural catastrophe risks of windstorm/hail, earthquake and flooding were taken into consideration for property insurance and treated as natural hazards for motor own damage insurance. It is also possible in Germany to estimate a company’s share of a natural catastrophe loss in property-casualty on the basis of insurance premiums or the number of insured properties. This figure is then multiplied by the 200-year natural-catastrophe loss. The calculation of the 200-year loss was based on extensive market statistics and probability theory and then compared with other geophysical calculations. The windstorm risk is further adjusted using a factor that takes account of the regional concentration and spread of the company’s windstorm liabilities. A broad spread reduces the solvency capital requirement.

In QIS 3, companies were also asked to evaluate a further scenario for other catastrophes with a return period of 200 years.

The capital requirement figures for these catastrophe risks are treated separately and aggregated to obtain the SCRCat allowing for the applicable diversification effects.

« previous page  |  next page »

2. Reinsurance

Whilst Solvency I recognises, subject to certain restrictions, that reinsurance reduces risk, Solvency II does so without limitation. As mentioned above, precise quantification of a company’s risk situation is only possible with an internal risk model. This is also basically true of the risk-mitigating effects of reinsurance and a considerable amount of work is involved.

Nonetheless, the standard approach in its current form as represented by QIS 3 ought to depict the savings in risk capital achieved by purchasing reinsurance adequately, and in any event much better than under Solvency I. In principle, it will always be difficult to depict all types of risk transfer in detail in a standard approach to calculating solvency capital because of the many ways of transferring risk to a reinsurer.

There are several ways in which reinsurance reduces the solvency capital requirement in the standard approach. Proportional and non-proportional reinsurance have different effects, both on natural catastrophe risk and on the premium and reserve risks.

The effects of proportional reinsurance (using a quota share as an example) and non-proportional reinsurance are described below. Surplus treaty reinsurance produces both effects, though to a lesser degree.

a) Proportional reinsurance

The effect of a quota share reinsurance treaty on the solvency capital requirement can be easily demonstrated. As regards the premium and reserve risks by class of insurance, the quota share affects the net premium and the net provisions in proportion to the retention (see (1)), as the risk is shared proportionally by the insurer and the reinsurer, whilst the annual fluctuations in the loss ratio relevant to the premium risk are specific to the company and remain unchanged. Thus, the proportional effect on the solvency capital requirement is dependent on the retention under the quota share treaty.

A quota share treaty reduces catastrophe risk in the same proportion.

b) Non-proportional reinsurance

The limits of catastrophe covers (CatCovers) are taken into account directly in the calculation of the SCRCat in that the risk capital required for natural catastrophes is reduced by the amount of the limits (in any event in so far as the treaty covers events with a return period of under 200 years with a value at risk of 99.5%).

XL covers have a completely different effect from that of quota share treaties on the risk capital calculation for premium risk. They generally have less effect on the volume figure – the net premium in (1) – than a quota share for a comparable risk transfer. However, the annual loss ratios, which do not change at all with quota shares, fluctuate with XL covers. Thus, in the case of a non-proportional reinsurance programme lasting 15 years, the fluctuations in a company’s loss ratios are much lower with the result that the risk factor for (1), which is closely linked to the fluctuations, is reduced considerably, with a consequent fall in the premium risk and the related capital requirement.

As there are (at present) no plans to take account of fluctuations in companies’ loss ratios in the reserve risk calculation, non-proportional reinsurance affects only the net treatment of technical provisions.

« previous page  |  next page »

3. Summary

Since the aim will always be to make a standard approach to calculating the solvency capital requirement as uncomplicated as possible, it will of necessity be based on compromises on the accurate depiction and quantification of insurance companies’ risk situations. Solvency II needs to find the right balance between simplicity and adequate consideration of the overall risk.

In our opinion, the proposed treatment of the underwriting risks incurred by property-casualty insurers represents a reasonable compromise. Clarification is required in some cases to enable relief through reinsurance to be better recognised (e.g. fluctuations in the net loss ratio in past years resulting from a change in the reinsurance programme).

There is no doubt that Solvency II will further increase the risk awareness of insurance companies, including those using the standard approach to calculate their solvency capital requirement, as, whatever the company, the risks incurred on the underlying business are of primary importance.

« previous page