# internal model concepts at scor

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Internal Model Concepts at SCOR. Tel Aviv, November 23, 2010. Presented by Ulrich Mller, SCOR SE. Initial remarks. The emerging European supervisory framework Solvency II not only has a Standard Model (successor of QIS5) but offers the possibility of employing an Internal Model . - PowerPoint PPT PresentationTRANSCRIPT

Internal Model Concepts at SCOR Tel Aviv, November 23, 2010Presented by Ulrich Mller, SCOR SE

Internal Model Concepts at SCORTel Aviv, November 23, 2010Ulrich Mller

Initial remarksThe emerging European supervisory framework Solvency II not only has a Standard Model (successor of QIS5) but offers the possibility of employing an Internal Model.Motivation: an Internal Model assesses the risks of large insurers and reinsurers more accurately than the Standard Model.The internal modeling methods presented here reflect the requirements of the reinsurer SCOR. They are based on the work of the FinMod team and other departments at SCORSCOR developed its Internal Model for internal use, before Solvency II, in the sense of Own Risk and Solvency Assessment (ORSA).Now the enhanced model is in the Solvency II pre-approval processAs a large reinsurer, SCOR has a more diversified business portfolio than most primary insurance companies of similar sizeTherefore the scope of modeling challenges is huge: modeling of P&C and Life business, dependencies, retrocession, asset and credit risk etc

Internal Model Concepts at SCORTel Aviv, November 23, 2010Ulrich Mller

Agenda

1Internal Models and regulation: SST and Solvency II2Economic profit distribution, risk-adjusted capital, market risk, credit risk3Risks in life (re)insurance4P&C liabilities: underwriting, reserving, dependencies, retrocession

5Integrated company model: aggregation, additional dependencies

6Conclusions

Internal Model Concepts at SCORTel Aviv, November 23, 2010Ulrich Mller

The Internal Model as a stochastic simulation engineThe Internal Model is comprehensive: All risks of the company are stochastically simulated (Monte-Carlo simulation)Stress scenarios are fully contained in the normal stochastic simulation: the simulation scenarios with the most extreme outcomes behave like stress scenariosThen there is no need to add some artificial extra stress scenariosThe main result is required Risk-Adjusted (or Risk-Based) Capital (RAC) for the whole company and for individual parts and risk typesCapital is required to cover extreme outcomes. These arise from extreme events (heavy tails of distributions) and dependencies between risks.Therefore the modeling of distributions including realistic (often heavy) tails and dependencies is key

Internal Model Concepts at SCORTel Aviv, November 23, 2010Ulrich Mller

*Risk factors affecting the Risk-Adjusted Capital ( Risk-Based Capital Required Capital)RACUnderwriting Riske.g. Default of Retrocessionairese.g. Financial CrisisOperational Riskse.g. Reputational, Fraud, System Failures, Misconceived Processes(Liability Risk)Life and P&C, e.g. Natural CatastrophesWhat kind of risks are covered by the Risk-Adjusted Capital (RAC)?Reserving RiskLife and P&C, e.g. Reserve StrengtheningCredit RisksMarket RisksCorrelation (more general: dependence) has a primary importance in determining the RAC.

Internal Model Concepts at SCORTel Aviv, November 23, 2010Ulrich Mller

Internal models: evolutionMarket RiskCredit RiskInsurance RiskOperational RiskFinancial InstrumentsPortfolio DataIGRTotal RiskMarket RiskCredit RiskInsurance RiskFinancial InstrumentsPortfolio DataDistributional and Dependency AssumptionsValuation Model 1Valuation Model 2Risk Model 1Risk Model 2Valuation Model 3Collection of sub models quantifying parts of the risksQuantification of different risk typesRisk types are combined to arrive at the companys total riskModelling of underlying risk driversValue ProtectionValue SustainmentValue CreationManagement Strategy

Internal Model Concepts at SCORTel Aviv, November 23, 2010Ulrich Mller

Applications of the Internal Model: internal use, Swiss Solvency Test (SST), Solvency IIInternal use of the Group Internal Model:Risk assessment, capital allocation, planning, basis for new business pricing, asset allocation, retrocession optimization etc.Report on results to the Executive Committee and the Risk Committee of the Board of DirectorsEuropean regulators encourage the internal use under the heading Own Risk and Solvency Assessment (ORSA)Swiss Solvency Test (SST):SCOR Switzerland (a legal entity of the SCOR Group) produces SST reports based on the Internal Model since 3 years.The Swiss regulator (FINMA) has reviewed the Internal Model, with a focus on some parts of special interestSolvency II: The Internal Model (with some adaptations to Solvency II guidelines) is in the pre-approval process

Internal Model Concepts at SCORTel Aviv, November 23, 2010Ulrich Mller

Methodology: Solvency II and Swiss Solvency Test (SST)Both use the same underlying mathematical methodology:Solvency Capital Requirement should buffer risks emanating during a 1-year time horizonRisk is defined on the basis of the change in economic value (available capital) over a 1-year time horizonA risk margin is assessed to cover the cost of the capital necessary to buffer non-hedgeable risks during the entire run-off of the liabilities.There are differences between Solvency II and SST: Treatment of group solvency, standard model vs standard formula, VaR at 0.5% vs tVaR at 1% as a risk measure, treatment of operational risk,

Internal Model Concepts at SCORTel Aviv, November 23, 2010Ulrich Mller

Dependency modeling in the Internal Model and the Solvency II Standard Model (or QIS 5)Comparing two approaches:QIS 5 / possible Solvency II Standard Model: Loss distributions with thin tails (normal or log-normal) low capital requirement per single risk or line of business flat, uniform correlation of risk factors also in the tail. This is compensated by of high, prescribed correlation coefficients between risks low diversification benefit.Internal Model of SCOR: Loss distributions with heavy tails wherever appropriate in realistic modeling; increased correlation of risk factors in the tails (case of stress, extreme behavior) higher capital requirement. But: The correlation of average events / risks factors is often quite moderate larger diversification effect between risks for a well-diversified company.Main problem: QIS 5 tends to underestimating risks of single risk factors, single lines of business and monoliners and to overestimating risks of strongly diversified companiesApproval process: pre-approval of the Internal Model and its dependence model by national regulator(s). Essential for a globally well-diversified reinsurer such as SCOR and for any insurance business based on strong diversification between different risks.

Internal Model Concepts at SCORTel Aviv, November 23, 2010Ulrich Mller

Agenda

1Internal Models and regulation: SST and Solvency II2Economic profit distribution, risk-adjusted capital, market risk, credit risk3Risks in life (re)insurance4P&C liabilities: underwriting, reserving, dependencies, retrocession

5Integrated company model: aggregation, additional dependencies

6Conclusions

Internal Model Concepts at SCORTel Aviv, November 23, 2010Ulrich Mller

Measuring risk: Risk-Based Capital and economic profit distributionA (re)insurance company is assessing the risk of existing or new business for several purposes: regulatory solvency tests, rating agency models, capital allocation in planning and pricing, The risk of a certain business is usually measured in terms of the capital required to carry it: Risk-Adjusted Capital (RAC) = Risk-Based Capital Required CapitalThe RAC has to be compared to the available capital of a company in order to assess its solvency. Both capital measures rely on the economic valuation of businessHere we focus on risk-adjusted capital and its computationRisk implies uncertainty. The economic profit (= change in economic value) is not certain; we model its distribution as a basis for RAC calculations.

Internal Model Concepts at SCORTel Aviv, November 23, 2010Ulrich Mller

Balance Sheet accounting and economic viewReservesHybrid debtShareholdersequityInvested AssetsAccounting viewReinsurance assetsOther assetsIntangiblesOther liabilitiesDiscounted ReservesEconomic CapitalMarket Value of Invested AssetsEconomic viewDiscounted Reinsurance assetsOther assetsOther liabilitiesMain adjustments to the accounting view balance sheet: Discounting reserves and Reinsurance assets Considering loss value of Unearned Premium Reserves Hybrid debt can be considered as capital Intangibles has economic value of zero

Internal Model Concepts at SCORTel Aviv, November 23, 2010Ulrich Mller

Profit distribution as a centerpiece of risk modelingThere are different definitions of risk and risk-based capital (Internal Model, Solvency II, Swiss Solvency Test, rating agency models, models for capital allocation in pricing and planning, )Some (traditional) models are simple factor models: short-cuts that directly aim at results using fixed parameters and formulas.For large multi-line companies, factor models are of little use as they are too coarse and underestimate diversificationFor state-of-the-art models, we need full profit distributions of all parts of the businessProfit distributions can be used for the stochastic simulation of the future behavior (Monte-Carlo simulation)A set of simulated scenarios can serve as a substitute of profit distributions (e.g. in Property Cat modeling)

Internal Model Concepts at SCORTel Aviv, November 23, 2010Ulrich Mller

Economic profit distributions and model granularityEconomic profit distribution = distribution of the future change in economic value. This profit is uncertain, stochasticTime horizon: usually one year. What will be the value of the business at the end of this period?We take economic values as best estimates at the end of the stochastically simulated period. This implies discounting of all projected cash flows, for all simulated scenariosWe

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