In the following section we compare the available economic capital with the required risk capital. Hannover Re calculates the economic equity as the difference between the market-consistent value of the assets and the market-consistent value of the liabilities. The corresponding measurement principles also largely apply to the Intrinsic Value Creation (IVC) (see the section “Management system”). While fair values are available for most investments, the market-consistent valuation of reinsurance treaties necessitates a specific valuation model. We establish the market-consistent value of technical items as the present value of projected payments using actuarial methods. This is adjusted by a risk loading that factors in the fluctuation in future payments. Such fluctuations result from risks that cannot be hedged by means of capital market products, such as underwriting risks. We use risk-free interest rates derived from yields on the highest-quality government bonds for discounting of our future cash flows. Market prices for options and guarantees embedded in insurance contracts are determined or approximated using option valuation models from the field of financial mathematics. The methods used are the same as those adopted in the calculation of our Market Consistent Embedded Value (MCEV) (for further remarks on the Market Consistent Embedded Value please see our comments in the section “Underwriting risks in life and health reinsurance”). The significance of these options and guarantees in our portfolio is, however, minimal. The valuation reserves for investments shown in the following table indicate the difference between fair value and book value of those investments recognised under IFRS at book values. Other valuation adjustments encompass above all deferred tax assets and liabilities that arise in connection with valuation adjustments. The available economic capital, which is available as liable capital for policyholders, is composed of the economic equity and the hybrid capital.

The available economic capital increased in the period under review from EUR 11,143.9 million to EUR 12,443.9 million. This was due principally to the successful business result in 2014, positive effects from the weakening of the euro against our major currencies and a rise in the valuation reserves for investments, principally owing to yield declines on government bonds in our main currency areas and also in some cases to reduced credit spreads. As a consequence of a decrease in the discounting effect for the loss reserves, the low interest rate environment gave rise to opposing effects in the valuation adjustments for property and casualty reinsurance. A further factor was an increase in the risk premium, which reflects the higher capital requirements in this business group. Positive effects derived from a higher assessment of the valuation reserve for the loss reserves. The valuation adjustments for life and health reinsurance increased due to the favourable development of new business and positive effects from economic changes associated with interest rates and exchange rates. This is opposed by a higher risk premium – above all for the increased longevity risks – as well as negative effects from revised assumptions and model adjustments. The item “Valuation adjustments due to tax effects and other” decreased primarily owing to higher tax effects from valuation adjustment. The available capital from subordinated bonds was reduced in the period under review owing to redemption of a hybrid bond, which was only partially replaced with a new issue.

The required risk capital of the Hannover Re Group at the target confidence level of 99.97% rose in the year under review from EUR 6,896.9  million  to EUR 7,786.6  million. The bulk of the increase resulted from a model- and volume-driven rise in market risks. The market risks rose due to the strengthening of several model parameters in the credit and spread model as well as of the dependency parameters between risk factors in conjunction with substantially higher investment volumes due to exchange rate movements and positive cash flows.

The underwriting risks in property and casualty reinsurance increased on account of the larger volume of reserves. In addition, parameters in the reserve risk model were strengthened for risks at the end of run-off. The premium risk (incl. catastrophe risk) has scarcely changed. The increase in the underwriting risks in life and health reinsurance, particularly in the area of longevity risks, was primarily due to the larger business volume. The operational risks also increased in step with the underlying business volumes.

Default risks decreased owing to the improved average credit status of our counterparties and a reduced volume of receivables due from retrocessionaires. To some extent the reduction was cancelled out by model adjustments. Due to the rise in the required capital for almost all risk categories, the diversification effect also increased.

The internal capital model is based on current methods from actuarial science and financial mathematics. In the case of underwriting risks, we are able to draw on a rich internal data history to estimate the probability distributions, e. g. for the reserve risk. For risks from natural perils we use external models, which are adjusted in the context of a detailed internal review process such that they reflect our risk profile as closely as possible. In the area of life and health reinsurance long-term payment flows are modelled under various scenarios. With respect to all the aforementioned risks we use internal data to define scenarios and probability distributions. The internal data is enhanced by way of parameters set by our internal experts. These parameters are especially significant in relation to extreme events that have not previously been observed.

When it comes to aggregating the individual risks, we make allowance for dependencies between risk factors. Dependencies arise, for example, as a consequence of market shocks, such as the financial crisis, which simultaneously impact multiple market segments. What is more, several observation periods may be interrelated on account of market phenomena such as price cycles. In dealing with these dependencies, however, it is our assumption that not all extreme events occur at the same time. The absence of complete dependency is referred to as diversification. Hannover Re’s business model is based inter alia on building up the most balanced possible portfolio so as to achieve the greatest possible diversification effects and in order to deploy capital efficiently. Diversification exists between individual reinsurance treaties, lines, business segments and risks. We define the cost of capital to be generated per business unit according to the capital required by our business segments and lines and based on their contribution to diversification.