1. www.guycarp.com Cat Ratemaking 22 nd May 2008 Jillian Williams CAE, Spring 2008

2. 1 Guy Carpenter Overview  Price and Events  What is a Cat Model?  Why use a Cat Model?  Commercial Cat Models  Data Cat Models Need  Uncertainty  Output and Uses

3. Delete this text box to display the color square; you may also insert an image or client logo in this space. To delete the text box, click within text, hit the Esc key and then the Delete key Price and Events

4. 3 Guy Carpenter Comparison of Number of Events and Loss to ROL Hurricane Andrew WTC Hurricane Katrina

5. What is a Cat Model

6. 5 Guy Carpenter  Encompass algorithms and expert systems that allow clients to quantify damage and financial losses from specific perils. The models are built upon detailed databases describing highly localised variations in hazard characteristics, as well as databases capturing property inventory, building stock and insurance exposure.  Uses probability and statistics to quantify and model the randomness of catastrophic events  Uses portfolio information or market share data to quantify exposure to the events What is a Cat Model?

7. 6 Guy Carpenter Aggregate Distribution  Where are the Insured values  Geographical Distribution Hazards  Floods, Storms, Earthquakes,  What processes control their  magnitude  How often (frequency)  How bad (severity) Vulnerability  Maximum Damage ratios  Building codes/types How models are built Back

8. 7 Guy Carpenter Basic Components of CAT Models Hazard Module Engineering Module Actuarial Module (Hurricane: Meteorological Info) Portfolio (Damagability of assets at risk) (Financial implications )

9. 8 Guy Carpenter Hazard Module  Estimates location, characteristics & likelihood of a natural catastrophe  Estimates site intensity – For Earthquake: Ground Motion – For Hurricane: Windspeed – For Tornado/Hail: Windspeed & Hail Impact Energy – For Flood:Depth

10. 9 Guy Carpenter Length of Fault Rupture Fault Earthquake (Magnitude) Earthquake-Generated Energy (Waves)  Fault/seismic source zone location  Magnitude  Focal Depth  Attenuation  Local soil conditions Hazard Parameters: Earthquake Ground Motion

11. 10 Guy Carpenter 1 d1 d3 d2 WV VA NC GA FL AL SC Radius of max. winds Frequency of hurricanes Landfall location Central pressure Radius of maximum winds Forward speed Track angle Maximum wind speed Terrain roughness Filling rate after landfall Forward speed Hazard Parameters: Hurricane Site Windspeed

12. 11 Guy Carpenter Tornado Track area Tornado intensity Hail Hailstones per minute Hailstone size Hazard Parameters: Tornado/Hail Hail Impact Energy & Windspeed

13. 12 Guy Carpenter Depth Velocity Duration Factors Seawater/Freshwater Sediment Loads Sewage and other Pollutants Impervious Area (Flash) Slope Hazard Parameters: Flood Intensity

14. 13 Guy Carpenter Engineering Module Estimates physical damage to portfolio Vulnerability Function (Damage given site intensity for structural type)

15. 14 Guy Carpenter Financial Module Net of Cat $5m Net of Per Risk $10m Net of Facultative $20m Gross (Less Deductibles) $25m Damage (Ground Up) $30m Insurance & reinsurance structures are applied to loss distribution

16. 15 Guy Carpenter  Hazard Module – Parameters similar – Distributions & relationships vary across models  Engineering Module – Classifications of structures – Functional forms of vulnerability curves  Actuarial Module – Portfolio exposure data interpreted differently Variation Among Models

17. 16 Guy Carpenter Modeled and Non-Modeled Perils Total Catastrophic Risk Risk Primary Hurricane Earthquake Tornado/Hail Non-Modeled Riot Winter Freeze Secondary/Collateral Sprinkler Leakage Fire Following Sea Surge Not including Terrorism or Worker Comp

18. Why use a Cat Model

19. 18 Guy Carpenter Historical Loss Experience  Catastrophe are by definition: – Infrequent – insufficient number of events in historical records for needed credibility – Severe – generate huge losses and unusual claim settlement conditions  Historical data available is difficult to normalise to today’s conditions – Incomplete data on number and values of insured properties – Rapid changes in recent decades  Population and distribution  Replacement values of properties  Policy conditions  Correlation

20. 19 Guy Carpenter Historical Loss Experience

21. Commercial Cat Models

22. 21 Guy Carpenter Models Vendors  EQECAT  Risk Management Solutions  Applied Insurance Research All can claim, but none can substantiate that they are “better”  Models are proprietary  None is consistently more accurate in actual events  No independent study has been definitive

23. 22 Guy Carpenter Available Models All Region and All Perils Number of Perils 1 2 3 7

24. Data Cat Models Need

25. 24 Guy Carpenter Data Requirements  Hazard Module – Cresta Zone, FSA, postal code, street address, latitude/longitude  Engineering Module – Construction & occupancy – Age, height, roof shape, etc.  Financial Module – TIV – Limits and values by coverage – Deductibles – Reinsurance

26. 25 Guy Carpenter Data Resolution Aggregated Data Detailed Data

27. 26 Guy Carpenter Data needs Insurable value Limit Deductible Total sum insured LOCATION They will only work well with good data

28. Delete this text box to display the color square; you may also insert an image or client logo in this space. To delete the text box, click within text, hit the Esc key and then the Delete key Uncertainty

29. 28 Guy Carpenter Types of Uncertainty  Primary (Aleatory) Uncertainty – Uncertainty of which, if any, event will occur  Secondary (Epistemic) Uncertainty – Given that an event has occurred, the uncertainty in the amount of loss – Distribution of possible outcomes, rather than expected outcome

30. 29 Guy Carpenter Major Sources of Uncertainty HAZARD Module  Limited historical data on hurricane – 220 hurricanes in past 100 years – Only 2 SSI 5 events  Unreliable data quality for old records  Lack of understanding of physical chaotic phenomena underlying hurricane behavior  Unknown elements may not be recognized e.g. El Nino & La Nina, ENGINEERING Module  Limited data on claims for catastrophic events  Unreliable data quality for old records – New types of losses - eg computers  Lack of understanding of structural behavior under severe loads FINANCIAL Module  Estimates loss after application of financial structures.  Portfolio exposure data is interpreted differently - limits versus values-at-risk  Insurance and reinsurance structures are applied to loss distribution differently: – Site-level loss – Policy-level loss

31. 30 Guy Carpenter Uncertainty Associated with Client  Risks that are in the pipeline  Miscoding of exposure details – including unknown locations – type of construction – how deductible applies  Post event regulatory environment

32. 31 Guy Carpenter Results will vary Back

33. 32 Guy Carpenter Quantifying Cat Model Uncertainty  Depending upon point on EP curve, model could be off by a factor of 2.0 to 3.5 times

34. 33 Guy Carpenter You need to recognize uncertainty…. 250 year PML with 2.0x Model 1Model 2Model 3 $20m $10m $40m $30m $15m $60m $50m $25m $100m $25m $40m

35. 34 Guy Carpenter Comparing Model Results  New Versions – All models constantly being “tweaked” – Changes are not uniform across regions, perils, construction codes, etc.  Sensitivity – Slight changes and shifts in exposure can produce dramatic changes in loss estimates – Change in loss may not be equal to exposure change

36. Output and Uses

37. 36 Guy Carpenter  Definition – Annual probability of exceeding a certain level of loss at least once.  Occurrence Exceeding Probability (OEP) – Maximum loss in a year – Drives reinsurance limit  Aggregate Exceeding Probability (AEP) – Sum of losses in a year – Mulitple net retentions Exceeding Probability (EP) Curve

38. 37 Guy Carpenter Other Results  Average Annual Losses – By line of business – By geographic area  Deterministic Losses – User defined event – Historical event  Such as Hurricane Katrina Loss $1m to $2m Loss $2m to $5m Loss $5m to $10m Loss $10m to $15m Loss greater that $15m

39. 38 Guy Carpenter How Are Models Used? Macro  Insurance firms – Loss potential – Business strategies  Reinsurance – Design and evaluation – Program pricing  Regulatory – Ability to respond  Claims – Early warning Micro  Insurance firms – Underwriting process – Rate development – Loss drivers – Portfolio management  Reinsurance – Decompose account  Claims – High priority loss drivers

40. 39 Guy Carpenter Model Applications – Product Line Management Average Annual Loss – Top Ten Zip Codes Does the premium earned support the risk assumed ?

41. 40 Guy Carpenter Model Applications – Individual Risk Underwriting Average Annual Loss – Top Ten Annual Property Premium% of Premium $65,00016.1% $15,00057.1% $24,00033.1% $45,00014.3% $49,00012.5% $9,00059.4% $75,0006.8% $17,00030.0% $90,0005.4% $19,00016.3% Policy NumberAverage Annual Loss CLP 2965$10,480 CLP 3967$8,566 CLP 5111$7,938 BOP 2905$6,450 CLP 7786$6,109 BOP 2890$5,345 EDP 2789$5,103 CLP 2121$5,099 BOP 3088$4,890 CLP 8634$3,094 Potential Red Flag Catastrophe Load

42. 41 Guy Carpenter Model Applications Reinsurance 101 – Standard Deviation Load Pricing Standard Deviation Load = 1,700,000 – 1,200,000 1,250,000 = 40% Rate on Line = Premium / Limit

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