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Catastrophe Modeling from the Reinsurance Perspective

Catastrophe Modeling from the Reinsurance Perspective. Jim Maher, FCAS MAAA Platinum Re. Catastrophe Models. Strengths Weaknesses Potential for misuse Cat Models and Portfolio Management. Cat Model Strengths. Event Set Framework Powerful tool for portfolio management Detailed models

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Catastrophe Modeling from the Reinsurance Perspective

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  1. Catastrophe Modeling from the Reinsurance Perspective Jim Maher, FCAS MAAA Platinum Re CAS Ratemaking Seminar: REI-2 JMM 3/7/05

  2. Catastrophe Models • Strengths • Weaknesses • Potential for misuse • Cat Models and Portfolio Management CAS Ratemaking Seminar: REI-2 JMM 3/7/05

  3. Cat Model Strengths • Event Set Framework • Powerful tool for portfolio management • Detailed models • Good exposure tracking tool, even if don’t like loss results • Ability to handle (re)insurance structures • Not perfect but getting better CAS Ratemaking Seminar: REI-2 JMM 3/7/05

  4. Cat Model Weaknesses • Non-modeled perils • Brushfire, winter storm, meteor strike • Missing elements of modeled perils • Hurricane: inland flooding • Earthquake: tsunami • Non-modeled coverages • Marine: yachts, cargo CAS Ratemaking Seminar: REI-2 JMM 3/7/05

  5. Potential for misuse of cat models • Abuse of secondary modifiers- e.g. roof tie-downs • Potential for anti-selection- run all the models and provide lowest • More anti-selection- run detailed and aggregate models and provide lowest CAS Ratemaking Seminar: REI-2 JMM 3/7/05

  6. Cat Models and Portfolio Management • Event Set framework is a powerful tool for portfolio management • Ability to model portfolio’s risk vs. return • Determine portfolio capital and allocate to individual deals CAS Ratemaking Seminar: REI-2 JMM 3/7/05

  7. Portfolio Framework Example • Consider two countries • Oceania and Eurasia • 5 possible events for each country • Industry losses specified • Goal-determine risk vs. return for various reinsurance portfolios CAS Ratemaking Seminar: REI-2 JMM 3/7/05

  8. Event Sets CAS Ratemaking Seminar: REI-2 JMM 3/7/05

  9. Create a set of Simulation Years CAS Ratemaking Seminar: REI-2 JMM 3/7/05

  10. Check against Poisson CAS Ratemaking Seminar: REI-2 JMM 3/7/05

  11. Contracts Consider that the following contracts are available in the open market: CAS Ratemaking Seminar: REI-2 JMM 3/7/05

  12. Calc. Contract Losses by year CAS Ratemaking Seminar: REI-2 JMM 3/7/05

  13. Compute AAL and expected profit for each contract CAS Ratemaking Seminar: REI-2 JMM 3/7/05

  14. Distribution of profit/(loss) CAS Ratemaking Seminar: REI-2 JMM 3/7/05

  15. Calculate return on capital CAS Ratemaking Seminar: REI-2 JMM 3/7/05

  16. Portfolio Effects • Now assume that the reinsurer’s portfolio consists of certain shares of these 3 contracts • Want to calculate the overall portfolio capital and • Each contract’s share of this portfolio capital CAS Ratemaking Seminar: REI-2 JMM 3/7/05

  17. Portfolio • Consider the following portfolio: P = 20% A + 10% B + 5% C • Then consider 3 other portfolios P+0.1% A P+0.1% B P+0.1% C CAS Ratemaking Seminar: REI-2 JMM 3/7/05

  18. Portfolio ctd. CAS Ratemaking Seminar: REI-2 JMM 3/7/05

  19. Allocating Portfolio Capital • The portfolio capital can be allocated as follows: Cap[20%A]= 20%/0.1% * (422.89-422.02)=174 Cap[10%B]= 10%/0.1% * (422.56-422.02)= 54 Cap[5%C] = 5%/0.1% * (425.90-422.02)=194 -------------- -------- Cap[Portfolio] = 422 CAS Ratemaking Seminar: REI-2 JMM 3/7/05

  20. Return on Allocated Capital CAS Ratemaking Seminar: REI-2 JMM 3/7/05

  21. Tail oriented Capital Metrics • Approach also works for tail oriented capital metrics- e.g. TVAR • Define capital = 3 x TVAR (80%) CAS Ratemaking Seminar: REI-2 JMM 3/7/05

  22. Tail oriented ROAC CAS Ratemaking Seminar: REI-2 JMM 3/7/05

  23. Allocated Capital Calcs • As before, alloc. capital based on marginal • For example, for the 20%A contract: 450 = (793.5-791.25)/0.1% * 20% • Portfolio Cap = Sum of Alloc. Capitals • N.B. according to this capital metric, 10%B has the highest ROAC in the portfolio CAS Ratemaking Seminar: REI-2 JMM 3/7/05

  24. Summary • CAT Models provide a powerful tool for portfolio management • Can be used to derive capital for a contract within a portfolio and ROC • There is no “contract order” issue as is sometimes thought • Portfolio can then be optimized to maximize ROC CAS Ratemaking Seminar: REI-2 JMM 3/7/05

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