1 / 46

Reserve Variability Modeling: Correlation

Reserve Variability Modeling: Correlation. Mark R. Shapland, FCAS, ASA, MAAA Consulting Actuary. 2007 Casualty Loss Reserve Seminar San Diego, California September 10-11, 2007. A “Range” is not the same as a “Distribution”

jebediah
Download Presentation

Reserve Variability Modeling: Correlation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Reserve Variability Modeling:Correlation Mark R. Shapland, FCAS, ASA, MAAA Consulting Actuary 2007 Casualty Loss Reserve SeminarSan Diego, CaliforniaSeptember 10-11, 2007

  2. A “Range” is not the same as a “Distribution” A Range of Reasonable Estimates is a range of estimates that could be produced by appropriate actuarial methods or alternative sets of assumptions that the actuary judges to be reasonable. A Distribution is a statistical function that attempts to quantify probabilities of all possible outcomes. Ranges vs. Distributions

  3. How do we: • correlate multiple ranges? • correlate multiple distributions? • incorporate different types of correlation? • use correlation for ERM? Ranges vs. Distributions

  4. A Distribution can be used for: • Risk-Based / Economic Capital • Reserve Risk • Pricing Risk • ALM Risk • Pricing / ROE • Reinsurance Analysis • Quota Share • Aggregate Excess • Stop Loss • Loss Portfolio Transfer • Dynamic Risk Modeling (DFA) • Strategic Planning / ERM Allocated Capital Ranges vs. Distributions Risk Transfer

  5. Model Assumptions Incremental Changes Price Adequacy Model Correlation

  6. Development Period … 0 1 d Past Correlation of Model Assumptions Future 1997 1998 Payment Period t = w+d 2006 w Accident Period

  7. Are the Incremental Payments Correlated? LOB B LOB A Correlation of Incremental Changes Are the Model Assumptions Correlated?

  8. Are the Residuals Correlated? LOB B LOB A Correlation of Incremental Changes Correlation: 26.3% P-Value: 5.7%

  9. Are the Ultimate Loss Ratios Correlated? LOB B LOB A Correlation of Premium Adequacy Is Premium Adequacy Correlated?

  10. Protection Against “Adverse Outcomes” Ruin Theory: “Risk of Bankruptcy < X%” Statutory Valuation / Stockholder Perspective Types of Risk Related to Bankruptcy: Insurance Risks Financial Risks Operational Risks Strategic Risks Risk Based Capital

  11. Insurance Risks: Reserving Risk: Protect against “Adverse Development” Reserves Not Sufficient to Cover “All” Possibilities Pricing Risk: Protect against “Future Losses” Will Combined Ratios Exceed Breakeven? Financial Risks: Asset / Liability Matching Risk: Protect Against “Cash Flow Deficiencies” Will Timing of Investment Cash Match Claim Payments? Risk Based Capital

  12. Reserving Risk: Will Capital Cover 99% of Possible Outcomes? Risk Based Capital 99th Percentile Required Capital

  13. Reserving Risk: Capital is a “Shared Asset” LOB “A” Aggregate Distribution with 100% Correlation (Added) Risk Based Capital LOB “B” Aggregate Distribution with 0% Correlation (Independent) LOB “C”

  14. Expected Value Expected Value 99th Percentile 99th Percentile Reserving Risk: Capital is a “Shared Asset” Aggregate Distribution with 0% Correlation (Independent) Aggregate Distribution with 100% Correlation (Added) Risk Based Capital Capital = 1,000M Capital = 600M

  15. Reserving Risk: Capital is a “Shared Asset” Risk Based Capital

  16. Protection Against “Adverse Outcomes” How Bad if we Exceed Ruin Threshold? Market Valuation / Policyholder Perspective Discounting / Tail Value at Risk Same Types of Risk Related to Bankruptcy Capital is a Shared Asset Economic Capital

  17. ... Reserving Risk: Is Capital Sufficient If We Exceed 99th Percentile? Economic Capital 99% TVaR Required Capital

  18. Reserving Risk: Capital is a “Shared Asset” Economic Capital

  19. Protection Against “Adverse Outcomes” Focus on Future Losses How Many Years into Future? Breakeven Loss Ratio With or Without Investment Income? Assume Constant Expense Ratio Some Expenses Vary with Loss Ratio Capital is a Shared Asset Stronger Correlation than Reserve Risk? Pricing Risk

  20. ... Pricing Risk: Capital Sufficient If We Exceed 99th Percentile? Risk Based / Economic Capital 99% TVaR Required Capital

  21. Pricing Risk: Multi-Year Approach Future Years Risk Based / Economic Capital

  22. Protection Against “Cash Flow Deficiencies” Focus on Future Cash Flow How Many Years into Future? Timing of Current Liability Payments Timing of Future Liability Payments Assume Constant Expense Ratio Some Expenses Vary with Loss Ratio Capital is a Shared Asset Blend Reserving & Pricing Correlation? Asset / Liability Matching Risk

  23. Asset / Liability Matching Risk: Multi-Year Approach (Current Liabilities) Future Years Risk Based / Economic Capital

  24. Total Capital is Based on Total Risks How Do We Allocate to LOB, SBU, etc.? In Proportion to VaR or TVaR: Independent / “First In” Approach In Proportion to Increase in VaR or TVaR: Marginal / “Last In” Approach Average of All Possible Combinations: Game Theory (Shapley Values), Myers-Read, Covariance Share (Mango-Brehm-Kreps) Can Result in Negative Capital Not Intended to Completely Equalize ROE DRM Approach to Equalize ROE Capital Allocation

  25. In Proportion to VaR / “First In” LOB “A” Allocated Capital Aggregate Distribution with Model Correlation Capital Allocation LOB “B” Allocated Capital LOB “C” Total Capital Allocated Capital

  26. In Proportion to Increase in VaR / “Last In” LOB “A” Allocated Capital Aggregate Distribution with Model Correlation Capital Allocation LOB “B” Allocated Capital LOB “C” Total Capital Allocated Capital

  27. Average of Possible Combinations / Game Theory LOB “A” Allocated Capital Aggregate Distribution with Model Correlation Capital Allocation LOB “B” Allocated Capital LOB “C” Total Capital Allocated Capital

  28. Average of Possible Combinations / Game Theory Capital Allocation

  29. Allocate Capital “Equally” / In Proportion to Exposure Strongest “Risk-Adjusted” Target ROE Allocate Capital Using “First In” or “Last In” Approach Stong “Risk-Adjustment” for Target ROE Allocate Capital Using Covariance Share Approach Some “Risk-Adjustment” for Target ROE DRM Approach to Allocate Capital / Equalize ROE Constant Target ROE by LOB Pricing / ROE

  30. Game Theory Allocation / Some Risk Adjusted ROE Pricing / ROE

  31. Reinsurer Assumes Constant Percentage of Both Premiums & Losses Ceding Commission Varies with Loss Ratio With Maximum and Minimum Bounds Impact on Net and Ceded Results Expected Average Ceding Commission Future / Pricing Analysis Quota Share Reinsurance

  32. Variable Ceding Commission: Gross / Ceded / Net All Different Gross Distribution Ceded Distribution Net Distribution Quota Share Reinsurance Ceding Commission

  33. Variable Ceding Commission: Gross / Ceded / Net All Different Quota Share Reinsurance

  34. Reinsurer Assumes Losses if Aggregate Exceeds Company Retention Aggregate Excess Layer Includes Maximum Limit Aggregate Layer Can Include Co-Insurance Percent Multiple Layers / Reinsurers Future / Pricing Analysis Aggregate Excess Reinsurance

  35. No Co-Insurance: Small Ceded Expected Value, Large Risk Gross Distribution Net Distribution Ceded Distribution Aggregate Excess Reinsurance Agg XS Layer

  36. No Co-Insurance: Small Ceded Expected Value, Large Risk Aggregate Excess Reinsurance

  37. Reinsurer Assumes Losses if Aggregate Loss Ratio Exceeds Company Retention Stop Loss Layer Includes Maximum Limit Stop Loss Layer Can Include Co-Insurance Percent Multiple Layers / Reinsurers Does Other Reinsurance Inure to Benefit of Stop Loss? Future / Pricing Analysis Include Correlation Stop Loss Reinsurance

  38. Aggregate Excess Does Not Benefit Stop Loss LOB “A” Aggregate Distribution with Model Correlation Stop Loss Layer Stop Loss Reinsurance LOB “B” LOB “C”

  39. Aggregate Excess Does Benefit Stop Loss LOB “A” Aggregate Distribution with Model Correlation Stop Loss Layer Stop Loss Reinsurance LOB “B” LOB “C”

  40. Aggregate Excess Does Not Benefit Stop Loss Stop Loss Reinsurance

  41. Aggregate Excess Does Benefit Stop Loss Stop Loss Reinsurance

  42. Reinsurer Assumes All Losses for Specific LOBs and Years LPT Could Include Maximum Limit Multiple Layers / Reinsurers Are Liabilities Discounted? Historical Analysis Include Correlations Similar to Commutations Loss Portfolio Transfer

  43. Only Selected LOBs & Years LOB “A” Aggregate Distribution with Model Correlation Loss Portfolio Transfer LOB “C”

  44. Only Selected LOBs & Years Loss Portfolio Transfer

  45. DRM is the Quantifying Risk Portion of ERM Start Small to Build a Complete Management System Capital Management Strategic Financial Planning Performance Management Reinsurance Optimization Enterprise Risk Management

  46. Questions?

More Related