Internal Model Industry Forum (IMIF) Workstream G: Dependencies and Diversification. 2 February Jonathan Bilbul Russell Ward

Transcription

1 Internal Model Industry Forum (IMIF) Workstream G: Dependencies and Diversification Jonathan Bilbul Russell Ward 2 February

2 Background Within all of our companies internal models, diversification benefit is likely to be the largest single component of capital Within and between classes of business Within and between investment categories Between risk types Unfortunately outside of investment data, there is very limited information to assess or validate these assumptions, particularly when you incorporate tail correlations

3 Objectives of the Workstream Our aim is to: Report back on various approaches to assessing dependencies Use live examples to illustrate how they can be validated Look at how they can be communicated Note the limitations of their usage Bring together a set of supporting external benchmarks available to all We are not going to address the mathematical assessment of dependencies as this is already covered elsewhere in academic literature This presentation covers approaches to assessing and validating dependencies using two live modelling approaches

4 Uses of the internal model IMV Cycle: Alignment to IMIF Workstreams Workstream D: IM Flexibility and alternative uses of IM Workstream B: IMV Governance and operating model a. Potential triggers for Internal Model Validation b. Model Risk Impact Assessment c. IMV scope, plan development & prioritisation Workstream E: Validation tools and Model Change Policy Internal Model f. Validation cycle lessons learned & improvement h. Governance d. Validation execution g. Communication of, and actions on, Validation findings e. Validation assessment, conclusion & reporting Draft: Current working draft Workstream C: Board s understanding and challenge of IM and IMV Process / Board s IMV MI and reporting Workstream F: IMV for Operational Risk Workstream G: IMV for Dependencies and Diversification

5 Biggest Shared Learning About Validation There is usually limited or no data that can be used to mathematically assess dependencies Therefore validating them becomes very difficult It is better to place the emphasis on having a clear modelling methodology and framework that facilitates granular expert judgments because the clarity makes understanding the dependencies easier because the size of the problem can be reduced and better understood and therefore easier to validate However, this needs to be supplemented by validation on the outcomes of applying the dependencies

6 Case Study Causal Analysis Supported by Royal London and Milliman

7 7 Background The challenge = assessing dependencies: Frequentist approach 1 st port of call, but most dependency relationships of interest have insufficient data for a fully robust assessment Expert judgement valuable, but how to capture this in a consistent structured way that facilitates modelling Causal modelling - causal modelling using Bayesian networks can provide an alternative approach to both the setting and validation of correlation assumptions, leveraging both data and business knowledge

8 Process Overview Interrogate Correlation From Cause Information Capture Calibrate Picture Your Thoughts Bring It To Life Get To The Point

9 Picturing Your Thoughts If the data was lost by a partner there would be contractual issues to resolve which would strain the relationship and there would be damages to claim. This could cause a loss of confidence in the partner themselves.. Produced by Milliman using

10 Cognitive Mapping Full Map View Lapse Drivers Equity Drivers

11 Getting To The Point Identify unfinished explanations more clearly Produce a minimally complex summary Find the most important elements of the system Produced by Milliman using

12 Bringing It To Life Causal modelling techniques can be used to demonstrate highly non-linear dynamics using relatively simple-looking models, which can be widely understood and easily explained

13 Validation Correlation From Cause To the extent that two or more variables share underlying drivers, they will exhibit some degree of correlation. This can be calculated directly from the causal model and explained. Importantly, the degree of co-variation under different starting assumptions can be tested and explained. Derivation Source: Milliman, using AgenaRisk r =

14 Next Steps Complete Progress & Next Steps Risk discussion workshops (x2) held with business experts to determine and validate the cognitive map Trial causal model developed Full calibration session (x1) with business experts Further calibration sessions & model validation Determine implied correlation Explore correlation results: Compare to ex-ante assumption Reverse stress tests Impact of alternative scenarios correlation variability

15 Case Study Statistical Dependencies Supported by AIG

16 Risk Types and Modelling Approach Correlations within a capital model are typically: Reserve variability and premium risk variability within and between class Rate movements between classes Catastrophe claims between classes, both natural and man made Overall reinsurance default and overall level catastrophe risk Default risk between reinsurers / brokers Asset returns, inflation and exchange rates Claims experience and market risk Operational risk and claims or macro events Validation of the model is assisted by a modelling methodology and framework that facilitates granular expert judgments: Calibrated dependencies, e.g. rates tend to move in all classes at the same time. These are judgementally selected parameters. Structural dependencies, e.g. consistent use of inflation on both attritional and large claims. These are selected associations through the model design Where possible tail dependencies are used to reflect the potential for things to go wrong in the tails at the same time.

17 Calibrating Dependencies The following tools are at our disposal to calibrate correlations between lines of business and risk types: Categorisation of correlations as High/Medium/Low based on expert judgment Risk drivers analysis looking at the sources of common claims occurrence (example on next slide) Historical data both at a company and industry level Sensitivity testing helps to prioritise areas of importance But it s important to focus not only on sources of correlation in the body but also in the tail Significant industry events and news articles Scenario tests This then acts as a framework for robust discussion process with key stakeholders across the organisation: Actuaries, Underwriters, Risk Management, Executives and the Board Ensuring consistency in assumption setting is key is any expert judgement elicitation process

18 18 Explaining Dependencies - Framework for Expert Judgement Look at drivers of common claims across lines of business by looking at the impact of macro events across lines of business. Driver Economic downturn, Unemployment Equities Frequency of claims Description Fraud increases, litigation against employers increases and claims are made that would usually be ignored by policyholders As equity prices fall, D&O become under further scrutiny for mistakes. Driver Medical Inflation Wage Inflation Property inflation Severity of claims Impact Increase in medical and care cost claims Increase in wages, which drives the increase in the loss of income, earnings claims Increase in parts and labour costs to make repairs Tort changes Legislative changes, judicial inflation, legal costs General CPI Inflation Loss or damage of goods as part of property or cargo. Premium vs. Reserve risk dependencies. In addition to claims correlations, the correlation of premium risk is affected by the volatility of premium levels and the commonality of the underwriting cycle across classes The approach above which is focused on macro drivers then lends itself to operational, credit and market risk.

19 Dependency for Non Cat Premium risk Premium Gross Premium (Millions) Accident & Health Challenge and Review on Outputs An Example Surety & Credit Financial Lines General Liability Marine & Aviation Motor - Commercial Motor - Personal Property - Commercial Property - Personal Accident & Health 1, % 5% 5% 10% 5% 5% 10% 5% 10% 10% Surety & Credit 100 5% 100% 40% 10% 10% 10% 2% 5% 5% 5% Financial Lines 700 5% 40% 100% 20% 10% 20% 2% 10% 5% 10% General Liability % 10% 20% 100% 10% 40% 5% 30% 5% 50% Marine & Aviation 300 5% 10% 10% 10% 100% 10% 2% 10% 5% 5% Motor - Commercial 200 5% 10% 20% 40% 10% 100% 2% 30% 5% 50% Motor - Personal % 2% 2% 5% 2% 2% 100% 3% 30% 2% Property - Commercial 1,000 5% 5% 10% 30% 10% 30% 3% 100% 5% 10% Property - Personal % 5% 5% 5% 5% 5% 30% 5% 100% 5% Workers Comp % 5% 10% 50% 5% 50% 2% 10% 5% 100% Workers Comp 19 Weighted Average Life / Duration Premium Risk Accident & Health 2.0 Credit 2.0 Fidelity & Surety 3.0 Financial Lines 4.0 General Liability 5.0 Marine, Aviation & Transit 2.0 Motor - Commercial 3.0 Motor - Personal 2.0 Property - Commercial 1.5 Property - Personal 1.5 Specialty 5.0 Workers Compensation Expect this to be higher: Shared experience in road conditions. Even with geographical diversification expect motor parts and labour to be relative. Inflation is not currently explicitly modelled and instead is modelled through parameterisation and correlation. Inflation should have some correlation impact for long-tail lines. Expect this to be higher: Shared raw material costs and labour Shared events such as subsidence, heave. Un-modelled Cat events are also captured within non-cat premium risk and so should expect more correlation Also check for consistency between these.

20 Validation of Dependencies Independent assessment Stress and scenario testing Back-testing and aggregation testing using company s own data Line of business level data is likely too noisy for granular analysis, combining lines may result in a level at which meaningful analysis can be performed Benchmarking - compare to the market Benchmarks may focus at line of business correlations and not include geographic diversification Input / Output checks Focus on appropriate metrics don t use linear correlation in the tail Useful to test positive semi-definiteness (by comparing the simulated output correlation matrix vs the input correlation matrix) Challenges in checking cascading structures Conditional probability testing and risk ranking Analysis of change

21 Summary Assessing dependencies is challenging, validating them is even more so It is better to place focus on having a clear and coherent framework within which to apply expert judgement to assess the dependencies - and then to apply validation on the expert judgements being made There are some commonly adopted validation tools across the work-stream members that we will elaborate on in our final report

22 Tel: +44(0) Fax: +44(0) Institute of Risk Management 6 Lloyd s Avenue London EC3N 3AX United Kingdom