Sydney December 11, 2006 Page 1 Lessons from implementations of Basel II and for Solvency II - Supervision of Internal Models in the Insurance Industry (Solvency II) Gerhard Stahl & Stefan Jaschke, BaFin

Sydney December 11, 2006 | Page 2 BaFin White Paper – The guiding principle twin problems of traditional, prescriptive rule-based regulation: 1.complexity & variety: there is no “world-formula” 2.speed of innovation: international mediation of rule-based standard methods is regularly outpaced by markets (Basel II) Basel Committee of Banking Supervision (BCBS), 1995: „The guiding principle of such an approach is the preservation of banks’ incentives to measure market risks as accurately as possible and to continue to upgrade their internal models as financial markets and technology evolve.“ “as accurately as possible” -> “as accurately as necessary” Ashby’s law: “Only variety can destroy variety.” internal models = higher degrees of freedom

Sydney December 11, 2006 | Page 3 The incentive structure (“win-win”) more relevant and adequate supervision (e.g. for derivatives) supervisors and senior management speak the same language continual development is in the firm’s own interest supervisors get access to more relevant risk exposure data common calibration target: comparability of risks deal between supervisors and firms: “lower regulatory capital in exchange for more timely and more detailed information” similar to rating agencies, except for: odepth of examination oin the case of “gambling for resurrection”

Sydney December 11, 2006 | Page 4 Role of Internal Models under Solvency II Three topics: 1.to give a short overview of the conceptual framework for the regulation of internal models in Solvency II, as published by CEIOPS in its Consultative Paper 16; 2.to explain the practical consequences of this framework and propose practical solutions to the specific challenges of the supervision of the insurance industry, as compared to the supervision of internal models for the market risk of the trading books of banks; 3.to explain how to achieve harmonization of the supervision of internal models across the EU, without restricting the freedom of insurance undertakings to build internal models that are most useful for their risk management.

Sydney December 11, 2006 | Page 5 Objectives supervisory objectives (CfA 11.64): better risk management, which also improves policyholder protection (CfA 11.4), continual upgrading and encouragement of innovation in risk management methodology (CfA 11.2, 11.4) and improved risk sensitivity of the SCR, especially for undertakings with non-standard risk profiles (CfA ). but: potentially higher costs of supervision

Sydney December 11, 2006 | Page 6 Benefits benefits to supervisors, undertakings and, ultimately, policyholders (CfA 11.7 and 11.65): higher competitiveness through better risk management and hence lower costs of capital, more adequate modelling of non-standard, especially non- linear, contracts, more effective pillar 2 discussion and familiarity of the supervisor with more detailed exposure data than is generally available in accounting records, realization of cost efficiencies through re-use of risk modelling infrastructure for discussion with supervisors, rating agencies, analysts and shareholders.

Sydney December 11, 2006 | Page 7 CEIOPS’ answer to CfA11 Common goal and target criterion (CfA10) goal: absorb unforeseen losses reasonable assurance to policyholders that payments will be made target criterion: 1-year TailVaR (VaR as approximation) 99.5% VaR  99% TailVaR Standard formula (CfA10)Internal models (CfA11) low-cost inputs one-size-fits-all formulaic computation of a risk number targeted at top level of aggregation more detailed risk exposure data tailor-made to the business/processes provides distributions used for subportfolios as well

Sydney December 11, 2006 | Page 8 The 3-component framework myth1: main use is regulatory  internal use more important myth2: main goal is computation of SCR  SCR & EC = “airbag”: just one aspect of car safety myth3: one risk measure  distributions & several risk measures/metrics for reporting SCR (regulatory capital) internal model (in wider risk management sense) actuarial model (i.m. in the narrow sense) risk exposure data risk driver data internal risk control functions forecasts for P&L distributions SCR estimate adjusted SCR Pillar-2 adjustment use test calibration test statistical quality test actions/ steering reporting/ monitoring

Sydney December 11, 2006 | Page 9 The 3-component framework 2. Internal risk management3. SCR estimate use test: Is the actuarial model genuinely relevant for and used within risk management? calibration test: Is the SCR computed by the undertaking a fair, unbiased estimate of the risk as measured by the common SCR target criterion? 1. Base methodology (“actuarial model”) statistical quality test: Is the data and methodology that underlies both internal use and regulatory SCR computation sound and reliable enough to support both of them satisfactorily?

Sydney December 11, 2006 | Page 10 Three Challenges Differences between sectors:  how to achieve comparability of the SCR in a sector that uses a multitude of risk measures for risk management purposes,  how to assess the bias of an SCR estimate that is defined in terms of events well beyond normal experiences (the 200-year- event loss in the case of 99.5%-VaR and the average of the losses beyond the 100-year-event in the case of 99%-TaiIVaR),  how to minimize the resources needed for the validation of internal models by both supervisors and undertakings.

Sydney December 11, 2006 | Page 11 Similarities and differences  goals for internal models in Solvency II are similar to the goals and principles of the regulatory approval of internal models for the market risk in the trading books of banks  but: there are significant differences in the risk management practices: ◊Very similar models used in banking ◊In contrast a variety of risk measures is used by insurance undertakings: -TailVaR (beyond the 100-year-event) -VaR (1400-year-event) -2 x VaR (100-year-event)

Sydney December 11, 2006 | Page 12 The variety challenge BankingInsurance similar models, similar risk measures diversity in modelling methodology and very different risk measures Solution allow individual risk measures, potentially several, in the internal reporting and risk management throughout all hierarchical levels, subject to the general use test requirements, but require the computation of the regulatory capital requirement calibrated to the Solvency II SCR standard at the legal entity level for solo supervision and at group level for group supervision, subject to calibration test requirements.  make the difference between the economic risk capital (EC) and regulatory risk capital (SCR) explicit

Sydney December 11, 2006 | Page 13 The “back-testing” challenge BankingInsurance Profits and losses are computed daily for the trading book VaR models for market risk can easily be 'back-tested' Using modern statistical techniques, the quality of 99%-VaR models, which predict the 100-day-event, can be assessed using about 100 daily data points. A completely different solution to back-testing needs to be found for Solvency II. Quarterly or, more commonly yearly profit and loss data 200 years are needed to assess the quality of a model that predicts the 200-year-event.

Sydney December 11, 2006 | Page 14 The “back-testing” challenge Solution is to decouple the 'back-testing' from the risk measure that defines the SCR calibration standard.  Assessment of the methodological basis in the 'statistical quality test' needs to be based on actually observed losses Example: The worst-ever NatCat event (Katrina) is now considered to be roughly a 35-year-event ->‘back-testing‘ needs to be based on the 5 - to 25-year-events. (Corresponds to the 80%- to 96%-VaR, if expressed as a risk measure.) The gap between observable losses and the extreme events defining the SCR is bridged by assumptions on the shape of the probability distribution of (gross) losses:  pooled industry data / constrained calibration / peer review

Sydney December 11, 2006 | Page 15 The complexity challenge funds hedge funds banks derivates houses insurers re-insurers complexity of products complexity of risk drivers market risk + credit risk + exotic derivatives (e.g. wheather) +insurance risks +longer time horizons more uncertainty

Sydney December 11, 2006 | Page 16 The complexity challenge Pillar 1Pillar 2 Bottom-up approach to risk measurement Important and quantifiable risks like interest rate risk in the banking book are not treated by pillar 1 Pillar 2 requirements on the internal capital adequacy assessment process have significant quantitative aspects. banking All quantifiable risks covered by pillar 1 in Solvency II Qualitative and use test requirements on internal models in pillar 2 insurance

Sydney December 11, 2006 | Page 17 The complexity challenge Solution to the problem:  there is virtually no difference between the general pillar 2 requirements on the internal risk and capital assessment on the one hand and the internal model use test on the other hand in the case of undertakings that apply for regulatory approval of their internal model.  little extra effort for the internal model use test on top of the pillar II SRP, which will be performed regardless of whether the undertaking applies for regulatory capital of its internal model.

Sydney December 11, 2006 | Page 18 What kind of comparability can and should be achieved? Qualitative aspects:  Comparability across EU member states will be achieved more by the intensive dialogue between national supervisors in the context of group supervision (CfA 20) and the general peer review between supervisors (CfA11.67, CfA17), than by very detailed, prescriptive rules on how to manage risk and capital or how to build actuarial models. Quantitative aspects:  can be further broken down into the question of the proper ranking of risks versus the proper calibration of the SCR

Sydney December 11, 2006 | Page 19 Freedom for risk ranking Risk ranking:  important for the internal risk management  the fact that diverse risk measures are used in the insurance sector means that different risk-rankings are used Systemic risk:  If all undertakings use the same ranking of risks, then all undertakings will shun the same types of risk at the same time and exacerbate market disruptions Diversity in risk-rankings - related to diversity in the risk measures used for internal risk management - should be encouraged.

Sydney December 11, 2006 | Page 20 Comparability …is achieved by requiring undertakings to calibrate their estimate of the SCR to the Solvency II calibration standard. In summary, a possible solution to achieving the twin goals of flexibility and comparability is  to carefully distinguish the more principle-based requirements on the internal use of the model ('use test' and the risk-ranking aspects of statistical quality) and the more prescriptive requirements on the regulatory use of the model ('calibration test').

Sydney December 11, 2006 | Page 21 Comparability BankingInsurance one extreme: OpRisk AMA = utmost modeling flexibility, little comparability other extreme: credit risk IRBA = minimal modeling flexibility, high comparability (almost like a standard formula) achieve comparability without abandoning modeling flexibility Solution supervisory control over key parameters: require stability analyses require the usage of (pooled) industry data require constrained calibration of models use peer review of models

Sydney December 11, 2006 | Page 22 Partial Use of Internal Models Aims and benefits are to ease transition to 'full' internal models; to encourage innovation and specialization to certain business areas; to deal with exceptional cases, like the merger of two undertakings (one with an approved model, the other using the standard formula) in a pragmatic way. (CfA 11.85) Requirements: 5-year transition plan -> full flexibility for “ transitional partial use ” 80% coverage required for “non-transitional partial use” further requirements regarding interplay with standard formula components (-> P&L attribution)