1. Dealing With the Differences in Hurricane Models Catastrophe Risk Management Seminar October 2002 Will Gardner FIAA

2. Agenda  Modeling Based on Historic LossesSection 1  Quantification of Model UncertaintySection 2  Variations in Licensed Model ResultsSection 3 DISCLAIMER: Any ideas and/or opinions given in this presentation are those of the speaker and not of his employer or any of the sponsors of this program. The employer and such sponsors will accept no responsibility for any liability arising as a result of this presentation.

3. Models Based on Historic Losses Section 1

4. Catastrophic Events Definition –Low Frequency (<100 per year) –High Severity (>$100m) Models –Vary in levels of complexity –One star Based on historic data; or –More stars Based on science/engineering, validated against historic data –High end of five star range impossible to achieve Theory –That more complicated models produce more accurate results (with less error)

5. Historic Loss Model Data –99 years of data –Losses inflated to current value (inflation) –Losses inflated by population and property growth Calculations –Losses ranked in descending order –Return period calculated = (n+1) / (rank * time period) = 100 / rank –50 year PML=$13.8bn

6. Fit to Extreme Value Distribution 50 years

7. Estimation of Model Uncertainty Coefficient of Variation of PML at 50 year return period = 56%

8. Components of Model Uncertainty Section 2

9. Scenario Analysis Sample hurricane exposed portfolio –Industry weighted age/construction –Exposure = $12 trillion –County level exposure Average Annual Loss = $1.572bn 50 Year PML = $13.8bn

10. Sensitivity Tests (Assumed to be) Independent Scenarios –Damage function uncertainty –Central pressure versus ambient pressure –Filling rate of central pressure over land –Improved geo-coding –Radius of hurricane eye –Terrain and topography adjustments –Forward velocity of eye –Wind-field variability

11. Hurricane Wind Speed Uncertainty Site versus Source site source Distance from center of eye Wind speed Local variabilityEvent variability

12. Allowing for Event Variability Central pressure differential f(x)

13. Landfall “Filling”  p(t) =  p 0 exp(-at) where a = a 0 + a 1  p 0 +  Source : Vickery, “Windfield and Filling Models for Hurricane Wind Speed Predictions”, ASCE 1995

14. Scenario Results

15. Model Error versus Model Complexity Greater complexity = Increased degrees of freedom

16. Need for “More Complex” Scientific Models Lack of mathematical credibility of loss data –Event frequency low Hurricane, Earthquake in smaller regions –Company or region history of few years Dynamic nature of risk profiles –Construction standards –Exposure growth –Value growth Determination of further metrics –Risk premium calculation –Reinsurance cost allocation –Growth management

17. Variations in Licensed Model Results Section 3

18. FCHLPM Damage Estimates (Form C)

19. FCHLPM PML Results (Form E)

20. Differences between FCHLPM Results from Same Companies from 1999-2001 (Form E)

21. Pricing of Catastrophe Reinsurance using Severity Curves Derived from FCHLPM Form E Data

22. Implications of Pricing Differences Different layer prices leads to –Differing reinsurance purchase decisions –Opportunities to shop around using model output Beneficial to use a multi-model approach to appreciate the range of potential pricing outcomes

23. Summary / Conclusions Increased model complexity does not always guarantee a reduction in model error Multiple high quality models based on equivalent data may produce widely ranging model results It is important to understand the causes of and extent of uncertainty in model results A multi-model philosophy is beneficial