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## Catastrophe Modeling from the Reinsurance Perspective

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**Catastrophe Modeling from the Reinsurance Perspective**Jim Maher, FCAS MAAA Platinum Re CAS Ratemaking Seminar: REI-2 JMM 3/7/05**Catastrophe Models**• Strengths • Weaknesses • Potential for misuse • Cat Models and Portfolio Management CAS Ratemaking Seminar: REI-2 JMM 3/7/05**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**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**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**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**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**Event Sets**CAS Ratemaking Seminar: REI-2 JMM 3/7/05**Create a set of Simulation Years**CAS Ratemaking Seminar: REI-2 JMM 3/7/05**Check against Poisson**CAS Ratemaking Seminar: REI-2 JMM 3/7/05**Contracts**Consider that the following contracts are available in the open market: CAS Ratemaking Seminar: REI-2 JMM 3/7/05**Calc. Contract Losses by year**CAS Ratemaking Seminar: REI-2 JMM 3/7/05**Compute AAL and expected profit for each contract**CAS Ratemaking Seminar: REI-2 JMM 3/7/05**Distribution of profit/(loss)**CAS Ratemaking Seminar: REI-2 JMM 3/7/05**Calculate return on capital**CAS Ratemaking Seminar: REI-2 JMM 3/7/05**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**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**Portfolio ctd.**CAS Ratemaking Seminar: REI-2 JMM 3/7/05**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**Return on Allocated Capital**CAS Ratemaking Seminar: REI-2 JMM 3/7/05**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**Tail oriented ROAC**CAS Ratemaking Seminar: REI-2 JMM 3/7/05**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**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