CATASTROPHE MODELING,
PORTFOLIO BUILDING AND
OPTIMIZATION
Why Use Multiple Models ?
 Natural Bias
 Any model encompasses inherent biases

Input data and methodology

Technical biases of the developer

Simple errors and inconsistencies
 Single model users nearly always “optimise into the model”
 Single model users are very susceptible to model change
Assessing/Normalising Model Bias
 Independent hazard/vulnerability tests


No-one knows the “right” answer – some reasonability should apply
Complexities of wind speed vs loss makes comparison difficult
 Internal consistency


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Many simple tests for this e.g. compare expected loss costs by Country and sub region
Information easily obtainable within the model
European Windstorm
Number of Countries with losses in Recent Events
 Taking major events of last 30
years how many countries had
meaningful losses in each event
(>$50m)?
Capella
87J
Daria
Herta
Vivian
Wiebke
Anatol
Lothar
Martin
Jeanette
Erwin
Avg
3
Vendors Reinsurer A Reinsurer B
5
4
4
5
4
3
6
7
6
5
5
3
5
8
5
5
7
3
4
3
4
4
3
3
4
2
2
4
4
4
4
4
4
4.64
4.64
3.73
European Windstorm
Model Diversity
Pan European Events
0.35
0.3
Model A (2.754)
Model B (5.922)
0.25
Model C (6.335)
Ratio of 0.2
the event
0.15
set
0.1
0.05
0
1
2
3
4
5
6
7
8
Number of countries hit
4
9
10
11
12
European wind
% Events hitting each country
MODEL A raw
MODEL B raw
MODEL C raw
2.7554
5.92286
6.335775
Europe
100.0%
100.0%
100.0%
Belgium
33.5%
9.0%
40.6%
Denmark
39.4%
15.9%
37.4%
France
69.4%
21.7%
48.4%
Germany
51.3%
14.9%
55.0%
Netherlands
40.4%
45.7%
49.8%
Switzerland
52.8%
-
-
UK
86.6%
87.0%
72.4%
Austria
44.1%
-
0.0%
Sweden
63.6%
22.4%
37.8%
Ireland
76.7%
22.8%
59.0%
Europe Frequency
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European windstorm
Internal Consistency
 Looking at expected loss cost and at the 99th percentile - the
spread is large
 Check Denmark for internal consistency comparing Res/Com
for models A and C – Which relationship makes most sense ?
M odel
A
B
C
Zone
Belgium
Belgium
Belgium
Com m ercial
M ean
99
0.0023%
0.0355%
0.0116%
0.1189%
0.0050%
0.1065%
Residential
M ean
99
0.0097%
0.1394%
0.0094%
0.0948%
0.0054%
0.1166%
A
B
C
Denm ark
Denm ark
Denm ark
0.0055%
0.0219%
0.0128%
0.1027%
0.2976%
0.2137%
0.0179%
0.0123%
0.0072%
0.2857%
0.1865%
0.1386%
A
B
C
Netherlands
Netherlands
Netherlands
0.0059%
0.0141%
0.0041%
0.1173%
0.0974%
0.0755%
0.0160%
0.0122%
0.0081%
0.2417%
0.0913%
0.1429%
*Loss cost is calculated by Industry loss/Industry exposure
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Are commercially available Property Cat models a
comprehensive view of risk?
 Additional perils captured in REMS© increase loss estimates relative to vendor models (e.g. winter freeze, eastern
European flood, Australian Hail and others)
 Secondary factors like post-event inflation (demand surge) and fire following earthquake need to examined specifically
to determine if they are adequately increasing loss estimates
 Secondary factors are important differentiators of risk.
REMS vs. AIR - US Perils
REMS vs. RMS - US Perils
1.00 = REMS Max. Loss
1.00 = REMS Max. Loss
1.00
1.00
0.80
0.80
0.60
0.60
0.40
0.40
0.20
0.20
-
95.00%
96.00%
97.00%
REMS
98.00%
AIR - I
99.00%
95.00%
100.00%
96.00%
AIR - II
97.00%
98.00%
REMS
RMS-I
vs. I
vs. II
1/250 PML for US Perils
Basic vendor model
REMS w/o add'l perils
REMS
AIR
0.47
0.57
0.69
vs. I
22.2%
47.9%
vs. II
21.0%
RMS
0.56
0.57
0.69
1.8%
23.3%
Vendor I = Basic vendor model for major perils with no add'l loss costs for post-event inflation or fire following EQ
Vendor II = REMS model including secondary factors but excluding perils not in vendor model
REMS = REMS model including secondary factors and capturing all perils
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21.2%
99.00%
RMS-II
100.00%
Modeling Malpractice
 Poor model or incomplete model
 Pilot error – model is used incorrectly or with incorrect ‘dial settings’
 Good model used for the wrong purpose
 Too much or too little trust in the models; results = estimates not “facts”
 Unstable model where small changes in assumptions drive large changes in results
 Black box model where users are unable to link which assumptions are driving results
 Too much output – leaves users lost in piles of data
 Cumbersome model – takes too much time to run or does not provide the info needed
to make decisions in a timely way
 Separation of modeling from underwriting – All our modellers are underwriters and all
our underwriters are modellers.
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All lines of business should be incorporated into the same risk
management framework to effectively manage entity risk
 Cat Model needs to integrate with other Risk Models:
 Flexible framework to add other lines
 A tool for underwriters to make risk decisions
 An exposure management system to track and control risk aggregations.
 Do not rely on commercially available models; each book of business must be
captured stochastically
 Not every line of business can be modeled with the same level of sophistication and
refinement as Property Cat
 At Renaissance, we built proprietary models for terrorism and workers comp cat that are
built off of the analytics and ‘engineering’ of the REMS© Property Cat models; capture
correlation with Cat
 Other lines of business modeled using stand-alone stochastic distributions; more judgment
involved but approach needs to be compatible
 Facilitates a complete aggregation of risk no gaps in the model or risk analysis
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Calculation of marginal ROE by contract
New Deal
Beginning
Portfolio
Capital
Rules:
10
Probability
Distribution
Portfolio &
Contract “A”
Probability
Distribution
Expected
Profit
Expected
Profit
 Expected
Profit
Required
Capital
Required
Capital
 Required
Capital
Portfolio Construction Matters
 Portfolios:
 Opt Universe: Reinsurance CAT Market - equal share
 Opt Port x OLW: Optimal Portfolio no retro
 Opt Port: Optimal Portfolio with retro
 Optimization:
 Maximize Expected Profit for a given level of capital
 No more than 50% of any placement
 Deals taken from Reinsurance CAT Market
 Results:
Opt Universe
Exp Profit
99.60%
Zero Profit
Prob
Return Period
Default Prob
Return Period
11
Opt Port x OLW
Opt Port
35%
59%
45%
-355%
-233%
-82%
20%
11%
9%
5.0
8.7
11.4
7.77%
3.21%
0.24%
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31
417
Portfolio Construction Matters
Profit (Loss) as Percent of Premium
200%
100%
0%
-100%
-200%
-300%
-400%
-500%
-600%
O pt U niv
O pt Port
O pt x O LW
-700%
-800%
0%
10%
20%
30%
40%
50%
60%
Exceeden ce Probability
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70%
80%
90%
100%
Be Very Afraid:
 Allison
 Sydney Hail
 Tiawan Earthquake
 World Trade Center
 Four Storms in Florida
 Anatol
 Tsunami
 Turkey Earthquake
 Bushfires (California & Australia)
 Canadian Freeze
 1999 Storms
 The List goes on…..
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