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. 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. For the discounting of future cash flows we use the risk-free basic yield curves without volatility adjustment or matching adjustment calculated in accordance with Solvency II rules. 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 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 adjustments encompass above all the deferred taxes as well as the deduction of foreseeable dividends as required by Solvency II. The available economic capital, which is available as liable capital for policyholders, is composed of the economic equity and the hybrid capital. Hybrid capital is recognised at market-consistent value as required by Solvency II, with changes in own credit risk not being included in the valuation.

The available economic capital increased to EUR 12,614.7 million as at 30 September 2015 compared to EUR 12,443.9 million as at 31 December 2014. This was due principally to the good business performance in the first three quarters as well as positive effects from the weakening of the euro against our major foreign currencies and from economic adjustments for underwriting reserves. The value adjustments increased primarily as a consequence of the good development of new business in life and health reinsurance and due to a more favourable assessment of future cash flows in property and casualty reinsurance. This is opposed by a decrease in the available capital from subordinated bonds owing to redemption of a hybrid bond.

The required risk capital of the Hannover Re Group at the target confidence level of 99.97% rose to EUR 9,593.0 million as at 30 September 2015, compared to EUR 7,786.6 million as at 31 December 2014. The bulk of the increase was due to the weaker euro against our major foreign currencies and the associated higher foreign-currency volumes underlying the risks, such as the volume of investments or loss reserves. These increases in volume driven by exchange rate movements caused the risk capital to climb in all risk categories. A further factor was the diminished diversification effect as a consequence of dependencies between, in particular, US-dollar-dominated risks. The decline in the tax effect resulted from the fact that with the currently higher risk capital the loss-minimising effect of taxes is subject to greater limitations.

The elevated risk in relation to market risks was not only volume-driven but also reflected the building of an equity allocation in the investment portfolio.

The underwriting risks in property and casualty reinsurance increased primarily on account of the larger volume of reserves and the higher catastrophe risks, which could be attributed above all to the stronger US dollar. The increase in the underwriting risks in life and health reinsurance was driven not only by exchange rate movements but also by larger business volumes in the area of longevity risks.

Counterparty default risks increased principally as a result of a larger volume of cash and short-term deposits. Operational risks developed in step with the underlying business volumes.

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.