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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 - PowerPoint PPT Presentation
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CAS Ratemaking Seminar: REI-2 JMM 3/7/05
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 SetsOceania Industry Excedence Freq Curve Eurasia Industry Excedence Freq Curve
Event RateExced.
Freq.Industry
LossRet.
Period Event RateExced.
Freq.Industry
LossRet.
Period
O_1 2.5% 2.5% 10,000 40 E_1 5.0% 5.0% 20,000 20
O_2 5.0% 7.5% 8,000 13 E_2 2.5% 7.5% 12,000 13
O_3 2.5% 10.0% 5,000 10 E_3 2.5% 10.0% 6,000 10
O_4 10.0% 20.0% 4,000 5 E_4 5.0% 15.0% 3,000 7
O_5 2.5% 22.5% 2,000 4 E_5 10.0% 25.0% 1,500 4
CAS Ratemaking Seminar: REI-2 JMM 3/7/05
Create a set of Simulation YearsYear 1st Event 2nd Event 3rd Event
1 O_45 E_16 O_47 O_18 O_2 E_5
13 E_514 O_217 E_418 E_419 O_3 E_521 E_222 O_425 E_132 O_539 O_4 E_3 E_5
CAS Ratemaking Seminar: REI-2 JMM 3/7/05
Check against Poisson
Combined annual mean frequencyfor the 10 events= 47.5%
# events Prob.
Expected number in
40 years
From Simulation
Set0 62.2% 24.9 251 29.5% 11.8 122 7.0% 2.8 2
3+ 1.3% 0.5 1
CAS Ratemaking Seminar: REI-2 JMM 3/7/05
ContractsConsider that the following contracts are available in the open market:
Contract Territory Limit x RetentionReinstate
ments PremiumA Oceania 1,250 x 1,000 None 500 B Eurasia 1,250 x 750 None 300 C Both 5,000 x 1,000 None 2,000
CAS Ratemaking Seminar: REI-2 JMM 3/7/05
Calc. Contract Losses by yearYear
Contract A Loss
Contract B Loss
Contract C Loss
1 1,250 - 3,000 5 - 1,250 5,000 6 1,250 - 3,000 7 1,250 - 5,000 8 1,250 750 5,000
13 - 750 500 14 1,250 - 5,000 17 - 1,250 2,000 18 - 1,250 2,000 19 1,250 750 4,500 21 - 1,250 5,000 22 1,250 - 3,000 25 - 1,250 5,000 32 1,000 - 1,000 39 1,250 1,250 5,000
CAS Ratemaking Seminar: REI-2 JMM 3/7/05
Compute AAL and expected profit for each contract
Contract A B CTerritory Oceania Eurasia BothLimit 1,250 1,250 5,000 x x x xRetention 1,000 750 1,000 Premium 500 300 2,000 AAL 275 244 1,350 LR 55% 81% 68%E[Profit] 225 56 650 sd profit 518 472 2,017
CAS Ratemaking Seminar: REI-2 JMM 3/7/05
Distribution of profit/(loss)Year A B C Year A B C
1 (750) 300 (1,000) 21 500 (950) (3,000) 2 500 300 2,000 22 (750) 300 (1,000) 3 500 300 2,000 23 500 300 2,000 4 500 300 2,000 24 500 300 2,000 5 500 (950) (3,000) 25 500 (950) (3,000) 6 (750) 300 (1,000) 26 500 300 2,000 7 (750) 300 (3,000) 27 500 300 2,000 8 (750) (450) (3,000) 28 500 300 2,000 9 500 300 2,000 29 500 300 2,000
10 500 300 2,000 30 500 300 2,000 11 500 300 2,000 31 500 300 2,000 12 500 300 2,000 32 (500) 300 1,000 13 500 (450) 1,500 33 500 300 2,000 14 (750) 300 (3,000) 34 500 300 2,000 15 500 300 2,000 35 500 300 2,000 16 500 300 2,000 36 500 300 2,000 17 500 (950) - 37 500 300 2,000 18 500 (950) - 38 500 300 2,000 19 (750) (450) (2,500) 39 (750) (950) (3,000) 20 500 300 2,000 40 500 300 2,000
Distribution of Profit by year
CAS Ratemaking Seminar: REI-2 JMM 3/7/05
Calculate return on capitalContract A B CTerritory Oceania Eurasia BothLimit 1,250 1,250 5,000 x x x xRetention 1,000 750 1,000 Premium 500 300 2,000 AAL 275 244 1,350 LR 55% 81% 68%E[Profit] 225 56 650 sd profit 518 472 2,017 Capital 1,037 944 4,033 ROC 21.7% 6.0% 16.1%
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 portfoliosP+0.1% A
P+0.1% B
P+0.1% C
CAS Ratemaking Seminar: REI-2 JMM 3/7/05
Portfolio ctd.
Contract Portfolio P+.1%A P+.1%*B P+.1%*CPremium 230.0 230.5 230.3 232.0 AAL 146.9 147.2 147.1 148.2 E[Profit] 83.1 83.4 83.2 83.8 sd profit 211.0 211.4 211.3 213.0 Capital 422.0 422.9 422.6 425.9 ROC 19.7% 19.7% 19.7% 19.7%
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
Contract 20%A 10%B 5%C PortfolioNet Premium 100 30 100 230 AAL 55 24 68 147 E[Profit] 45 6 33 83 Allocated Cap 174 54 194 422 ROAC 25.9% 10.3% 16.7% 19.7%Stand-alone ROC 21.7% 6.0% 16.1%
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
%TILE Portfolio P+.1%A P+.1%B P+.1%C2.5% (395.00) (395.75) (395.95) (398.00) 5.0% (345.00) (345.75) (345.45) (348.00) 7.5% (320.00) (320.75) (320.45) (322.50)
10.0% (270.00) (270.75) (269.70) (273.00) 12.5% (270.00) (270.75) (269.70) (273.00) 15.0% (170.00) (170.75) (169.70) (171.00) 17.5% (170.00) (170.75) (169.70) (171.00) 20.0% (170.00) (170.75) (169.70) (171.00)
TVAR (263.75) (264.50) (263.79) (265.94) Capital 791.25 793.50 791.38 797.81
P 20%A 10%B 5%CAllocated Cap 791.25 450.00 13.12 328.13
ROAC 10.5% 10.0% 42.9% 9.9%
Distribution of Profit/(Loss)
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
