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Cat Ratemaking

22 nd May 2008. Cat Ratemaking. Jillian Williams CAE, Spring 2008. 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.

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Cat Ratemaking

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

  2. 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. Comparison of Number of Events and Loss to ROL Hurricane Andrew Hurricane Katrina WTC

  5. What is a Cat Model

  6. What is a Cat Model? • 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

  7. $ How models are built 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 Back

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

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

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

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

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

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

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

  16. Variation Among Models • 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

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

  18. Why use a Cat Model

  19. 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. Historical Loss Experience

  21. Commercial Cat Models

  22. 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. N u m b e r o f P e r i l s 1 2 3 7 Available Models All Region and All Perils

  24. Data Cat Models Need

  25. 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. Detailed Data Aggregated Data Data Resolution

  27. Insurable value Total sum insured Limit Deductible Data needs 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. 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. 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, Major Sources of Uncertainty 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 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

  31. 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. Results will vary Back

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

  35. 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. Exceeding Probability (EP) Curve • 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

  38. 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. 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 How Are Models Used?

  40. Model Applications – Product Line ManagementAverage Annual Loss – Top Ten Zip Codes Does the premium earned support the risk assumed ?

  41. Model Applications – Individual Risk UnderwritingAverage Annual Loss – Top Ten Catastrophe Load Potential Red Flag Potential Red Flag Potential Red Flag

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

  43. www.guycarp.com

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