C _ Group Management Report the local risk management systems, and the adherence to the risk Diversification and correlation assumptions policy framework. Key results of the qualitative risk assessments are Our internal model considers concentration, accumulation, and reported to the Group on a regular basis. Unlike the insurance correlation effects when aggregating results at the Group level. The business, which is balance sheet sensitive, our Asset Management is resulting diversification reflects the fact that all potential worst-case mainly a cash flow business. Therefore, the solvency position of the losses are not likely to materialize at the same time. As we are an Asset Management business segment is also analyzed through the integrated financial services provider offering a variety of products impact of pre-defined material stress scenarios on the operating profit. across different business segments and geographic regions, These are one component in a system of key risk indicators, which are diversification is key to our business model. regularly monitored and benchmarked to risk limits as far as possible Diversification typically occurs when looking at combined risks and reasonable. that are not, or only partly, interdependent. Important diversification In view of the above, Allianz’s risk capital framework covers all factors include regions (for example, windstorm in Australia vs. material and quantifiable risks. Risks not specifically covered by the windstorm in Germany), risk categories (for example, market risk vs. internal model include strategic, liquidity, and reputational risks. underwriting risk), and subcategories within the same risk category (for example, commercial vs. personal lines of property and casualty risk). Ultimately, diversification is driven by the specific features of the investment or insurance products in question and their respective risk Risk-free rate and volatility adjustment exposures. For example, an operational risk event at an Australian When calculating the fair values of assets and liabilities, the entity can be considered to be highly independent of a change in assumptions regarding the underlying risk-free yield curve are crucial credit spreads for a French government bond held by a German entity. in determining and discounting future cash flows. For liability Where possible, we derive correlation parameters for each pair of valuation, we apply the methodology provided by the European market risks through statistical analysis of historical data, considering Insurance and Occupational Pensions Authority (EIOPA) as part of its observations over more than a decade. In cases where historical data technical documentation (EIOPA-BoS-20/109) to extrapolate the risk- or other portfolio-specific observations are insufficient or unavailable, free interest rate curves beyond the last liquid tenor.1 correlations are set by the Correlation Settings Committee, which In addition, we adjust the risk-free yield curves by a volatility combines the expertise of risk and business experts in a well-defined adjustment (VA) in most markets where a volatility adjustment is and controlled process. In general, when using expert judgment we set defined by EIOPA and approved by the local regulator. This is done to the correlation parameters to represent the joint movement of risks better reflect the underlying economics of our business, as the cash under adverse conditions. Based on these correlations, we use an flows of our insurance liabilities are largely predictable. The industry-standard approach, the Gaussian copula, to determine the advantage of being a long-term investor is the opportunity to invest in dependency structure of quantifiable sources of risk within the applied bonds yielding spreads over the risk-free return and earning this Monte Carlo simulation. additional yield component over the duration of the bonds. Being a long-term investor mitigates much of the risk of having to sell debt Actuarial assumptions instruments at a loss prior to maturity. Our internal model also includes assumptions on claims trends, liability We take account of this by applying the volatility adjustment to inflation, mortality, longevity, morbidity, policyholder behavior, mitigate the credit spread risk, which we consider to be less meaningful expenses, etc. We use our own internal historical data for actuarial for long-term investors than the default risk. Allianz also models the assumptions wherever possible, additionally considering volatility adjustment dynamically within our approved internal model, recommendations from the insurance industry, supervisory authorities, which differs from the static EIOPA VA concept applied in the standard and actuarial associations. The derivation of our actuarial formula. For risk capital calculations, we assume a dynamic movement assumptions is based on generally accepted actuarial methods. of the volatility adjustment broadly consistent with the way the VA Within our internal risk capital and financial reporting framework, would react in practice; however, we base the movement on our own comprehensive processes and controls exist for ensuring the reliability portfolio rather than the EIOPA portfolio. To account for this deviation, of these assumptions. Allianz applies a more conservative, reduced application ratio for the dynamic volatility adjustment. Validation is performed regularly to verify the appropriateness and prudency of the approach. As the internal model is based on a 99.5 % confidence level, there is a low statistical probability of 0.5 % that actual losses could exceed this Valuation assumptions: replicating portfolios threshold at the Group level in the course of one year. We replicate the liabilities of our Life/Health insurance business. This We use model and scenario parameters derived from historical technique enables us to represent all product-related options and data, where available, to characterize future possible risk events. If guarantees, both contractual and discretionary, by means of standard future market conditions were to differ substantially from the past, for financial instruments. In the risk calculation, we use the replicating example, in an unprecedented crisis or as a possible result of severe portfolio − together with a Least Square Monte Carlo approach for structural breaks resulting from climate change, our VaR approach risks that are not covered by the replication − to determine and revalue might be too conservative or too liberal in ways that are difficult to these liabilities under all potentially adverse Monte Carlo scenarios. predict. In order to mitigate reliance on historical data, we complement our VaR analysis with stress testing. 1_Due to late availability of EIOPA’s publication, the risk-free interest rate term structure used may differ slightly from the one published by EIOPA. 106 Annual Report 2021 − Allianz Group