CONFIDENTIAL MATERIALS
CATASTROPHE MODELING, PORTFOLIO BUILDING AND
OPTIMIZATION
2
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 Many simple tests for this e.g. compare expected loss costs by Country and sub region Information easily obtainable within the model
3
European WindstormNumber of Countries with losses in Recent Events
Taking major events of last 30 years how many countries had meaningful losses in each event (>$50m)?
Vendors Reinsurer A Reinsurer BCapella 5 4 487J 5 4 3Daria 6 7 6Herta 5 5 3Vivian 5 8 5Wiebke 5 7 3Anatol 4 3 4Lothar 4 3 3Martin 4 2 2Jeanette 4 4 4Erwin 4 4 4
Avg 4.64 4.64 3.73
4
European WindstormModel Diversity
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Ratio of the event
set
1 2 3 4 5 6 7 8 9 10 11 12
Number of countries hit
Pan European Events
Model A (2.754)
Model B (5.922)
Model C (6.335)
5
European wind% Events hitting each country
MODEL A raw MODEL B raw MODEL C raw
Europe Frequency 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%
6
European windstormInternal 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 ?
Model Zone Mean 99 Mean 99
A Belgium 0.0023% 0.0355% 0.0097% 0.1394%B Belgium 0.0116% 0.1189% 0.0094% 0.0948%C Belgium 0.0050% 0.1065% 0.0054% 0.1166%
A Denmark 0.0055% 0.1027% 0.0179% 0.2857%B Denmark 0.0219% 0.2976% 0.0123% 0.1865%C Denmark 0.0128% 0.2137% 0.0072% 0.1386%
A Netherlands 0.0059% 0.1173% 0.0160% 0.2417%B Netherlands 0.0141% 0.0974% 0.0122% 0.0913%C Netherlands 0.0041% 0.0755% 0.0081% 0.1429%
*Loss cost is calculated by Industry loss/Industry exposure
Commercial Residential
7
Are commercially available Property Cat models a comprehensive view of risk?
REMS vs. AIR - US Perils1.00 = REMS Max. Loss
-
0.20
0.40
0.60
0.80
1.00
95.00% 96.00% 97.00% 98.00% 99.00% 100.00%
REMS AIR - I AIR - II
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. RMS - US Perils1.00 = REMS Max. Loss
-
0.20
0.40
0.60
0.80
1.00
95.00% 96.00% 97.00% 98.00% 99.00% 100.00%
REMS RMS-I RMS-II
1/250 PML for US PerilsAIR vs. I vs. II RMS vs. I vs. II
Basic vendor model 0.47 0.56 REMS w/o add'l perils 0.57 22.2% 0.57 1.8%REMS 0.69 47.9% 21.0% 0.69 23.3% 21.2%
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
8
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.
9
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
10
ExpectedProfit
ExpectedProfit
ExpectedProfit
RequiredCapital
CapitalRules:
New DealBeginningPortfolio
ProbabilityDistribution
RequiredCapital
Portfolio &Contract “A”ProbabilityDistribution
RequiredCapital
Calculation of marginal ROE by contract
11
Portfolio Construction Matters
Opt Universe Opt Port x OLW Opt Port
Exp Profit 35% 59% 45%
99.60% -355% -233% -82%
Zero Profit Prob 20% 11% 9%
Return Period 5.0 8.7 11.4
Default Prob 7.77% 3.21% 0.24%
Return Period 13 31 417
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:
12
Portfolio Construction Matters
-800%
-700%
-600%
-500%
-400%
-300%
-200%
-100%
0%
100%
200%
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Exceedence Probability
Pro
fit
(Lo
ss
) a
s P
erc
en
t o
f P
rem
ium
Opt UnivOpt PortOpt x OLW
13
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…..