1. Catastrophe Models December 2, 2010 Richard Bill, FCAS, MAAA R. A. Bill Consulting Bill.consulting@frontier.com

2. Overview Use of Cat Models in: Exposure Management Ratemaking Note: will use Hurricane as example

3. 3 Cat Models

4. RABill Consulting4 Exposure Management - In old days, pins were used to identify concentration of risk

5. Exposure Management – Pins in Map Cumbersome practice was eliminated due to expense considerations Billions of Dollars of Exposure is on or near the coast of the US subject to severe hurricanes Likewise, for earthquake, the insurance industry exposure is tremendous, particularly in California and the New Madrid Area ----------------------------------------------------------------------- How do insurance companies judge how much business to write in catastrophe prone areas such as on the coast of Florida without exposing the company to bankruptcy????

6. Catastrophe Ratemaking Problem A Hurricane is an unlikely event for a particular location on the coast The experience period for making rates would need to be very long to reflect the probability of a Hurricane at a particular location Even if past history were available, it would not reflect the increase in new construction on the coast -------------------------------------------------------------------- How do Insurers decide how much to charge for catastrophe prone areas????

7. Catastrophe Models evolved as a solution to the problem AIR founded the catastrophe modeling industry in 1987 Models were not used much in the beginning Hurricane Hugo in 1989 and particularly Hurricane Andrew in 1992 were wakeup calls Many insurance companies had not realized the extent of their exposure concentrations.

8. Cat Model Definition Catastrophe modeling is the process of using computer-assisted calculations to estimate the losses that could be sustained by a portfolio of properties due to a catastrophic event such as a hurricane or earthquake

9. Property Casualty Insurance Industry Major Risk Factors Hurricanes Earthquakes Terrorism Losses Insufficient Reserves Asbestos/Pollution or similar Exposure Poor underwriting and/or Inadequate Rates Collectibility of Reinsurance High Expenses Bad Investments

10. TYPES OF MODELS Earthquake Fire Following EQ Hurricane Storm Surge Tornado/Hail Winter Storm Terrorism

11. Catastrophe Models Catastrophe events are simulated for many years (for example 10,000) Company submits detailed information on their book of business Losses are calculated based on the company’s book of business Losses are stated in terms of return time, i.e. 100 year event

12. Construction of Hurricane Model The annual number of occurrences is generated from the frequency distribution Landfall Location of each Hurricane is determined Simulation of Storm track after landfall Hurricane severity simulation Wind Speed Size of Hurricane The movement of the event across the affected area is simulated, and dollar damages are calculated based on insured value, type of building, deductible, etc.

13. Simplified Example

14. Simulation of Frequency Assume average of 3 Hurricane Landfalls per year Assume Poisson Distribution

25. Model Output

29. Return Period Perspective 250 Years-20 years before the Declaration of Independence - 1756 500 Years- 14 years after Christopher Columbus discovers America - 1506 1,000 Years-Leif Erickson discovers “Vinland” (possibly New England - 1006?) 10,000 Years – 8000 B.C. - ??????

31. Industry % of Insured Value in Coastal Counties 79% in Florida 63% in Connecticut 61% in New York 54% in Massachusetts 16% Nationwide

32. Top 10 Most Costly Hurricanes in US History, (Insured Losses, $2005) From III Presentation on Hurricanes Sources: ISO/PCS; Insurance Information Institute. Seven of the 10 most expensive hurricanes in US history occurred in the 14 months from Aug. 2004 – Oct. 2005: Katrina, Rita, Wilma, Charley, Ivan, Frances & Jeanne

33. Exposure Management Component of Insurance Company’s Enterprise Risk Management (ERM) Make sure that a catastrophe does not wipe out the company Maintain financial strength after an event Maintain financial ratings Smooth earnings (publicly held companies)

34. Accumulation Management Manage accumulation during underwriting process Limit new business Non renewals Increase business in lower risk areas

35. Exposure Management (cont.) Rating Agencies are placing a lot more reliance on cat management since the hurricanes of 2004 and 2005 A Company can either purchase more reinsurance or reduce exposure or raise prices or a combination

36. Industry Reaction More demand for reinsurance Many companies are pulling back from coastal areas particularly, the gulf states Insurance Rates for coastal properties have skyrocketed

37. Ratemaking

38. Pricing for Hurricane “When hurricane rating analyses were first expanded from five to 30 years of storm experience, the technique was applauded as a vast improvement, which is was. The 30 years were replaced by 100,000 years and real life events were replaced by silcon-prompted simulations. “

40. Average Annual Loss Indicates what needs to be charged each year to cover hurricane losses over the long run Can be calculated for each individual building- useful for pricing large commercial buildings Can be calculated at a zip code level or even finer to be used in pricing – example, all dwellings within 1 mile of the coast Risk charge can be calculated as an additional charge

41. How Models Are Used Underwriting Establish guidelines Differentiate risks Develop pricing Portfolio Management Determine risk drivers Evaluate capital adequacy Allocate capital Estimate post-event losses Accumulation Management Risk Transfer Determine reinsurance needs Structure and price of reinsurance