is why we have defined it with an index n in equation 4 In Table 1 we give an

# Is why we have defined it with an index n in equation

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is why we have defined it with an index, n , in equation (4). In Table 1, we give an example of the diversification benefit as reported by SCOR during its Investor Day in July 2009 (SCOR 2009). Even if they are a little dated, these figures are a good illustration of the advantage to be gained by examining the diversification benefit obtained by a company when the calculation of its capital is based on all the risks involved. It can be seen, for example, that in the case of a reinsurer, investments only represent a small portion of the risk in comparison with the portfolio, although their individual capital corresponds to more than half the individual capital of the company’s life insurance business. In the end run, when its main business lines are considered, the company achieves a diversification benefit of 47%, which is considerable. The figures published by other reinsurers are similar. The diversification benefit is essential for this type of business to operate smoothly (Boller and Dacorogna, 2004). Reinsurers therefore take particular care when modelling their portfolios. To complete this brief incursion into the world of internal models, we would like to mention that at least three types of quantitative model exist for insurance risks: 1. Stochastic-type models based on probability distributions and more or less sophisticated modelling of risk interdependence. Generally speaking, the internal models of companies belong to this category. 2. Deterministic-type models, or factor models. The capital is calculated by multiplying the volume of business by a specific factor (often called the capital intensity). These models are typically used by rating agencies to estimate the capital requirements of the companies they are rating. 3. Scenario-based models. Several scenarios are applied to the economic balance sheet to examine the value of the company in relation to different states of the world. These models, also called stress tests, were applied by the FED to American banks in March 2009. The positive results restored market confidence in the financial system. Table caption: Internal Model Results for SCOR as published in 2009 Risk capital (RC) of group (net of reinsurance) Individual RC Diversified RC Total portion of RC Diversification benefit New P&C business 1200 820 24% 32% P&C reserves 1600 1240 36% 23% Life business 1800 900 26% 50% Investments 970 130 4% 87% Counterparty and credit risks 280 40 1% 86% Risks due to exchange rate and other positions on the economic balance sheet 330 60 2% 82% Operational risks 210 210 6% 0% Total 6720 3400 100% 47% (4)
SCOR paper n°34 - A Change of Paradigm for the Insurance Industry 9 Most companies use a combination of these approaches. While deterministic models are preferred because they are simple to use and give almost instantaneous answers to the questions posed, they are not very flexible. Factors that have been determined in certain situations may be less influential in other circumstances or if there is a substantial change in the insurer’s portfolio. The other two types are basically the same. Stochastic models

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