1. On The Cost of Financing Catastrophe Insurance Presentation to the Casualty Actuarial Society Dynamic Financial Analysis Seminar By Glenn Meyers and John Kollar Insurance Services Office, Inc. July 13 &14, 1998

2. Catastrophes and Insurer Capital Two major insurers lost more than their “capital” in Hurricane Andrew They are solvent today, because they had “rich” parents. You need a LOT of capital to cover catastrophes. Is holding sufficient capital to cover catastrophes efficient?

3. Capital Substitutes Reinsurance –Does not have the capacity to cover the really big catastrophes –Cat Limits are usually small compared to surplus Securitization –Large potential capacity –Index trading has been slow –Recent over the counter deals are insurer specific, like reinsurance

4. Potential Advantages of Catastrophe Indices Low transaction costs No counter-party risk Ease of entry for investors and insurers Liquidity

5. Problems with Catastrophe Indices Investors don’t understand the risk Insurers don’t know how much their risk will be reduced (i.e. basis risk) The insurer-specific deals have found investor support because they could quantify the risk using a catastrophe model on the insurer’s exposures.

6. ISO’s Contribution Quantify risk for investors Quantify risk for insurers Use a catastrophe model and underlying exposure for catastrophe indices and insurers. Agreements with AIR and RMS Can use GCCI or PCS options

7. A Quick Explanation of Hurricane Models Multiple Events Each Event –Affects a collection of ZIP codes –Each ZIP code has a wind speed Insurer –Has exposure for each class and ZIP code

8. A Quick Explanation of Hurricane Models For each event –For each ZIP Get wind speed For each class –Get Value of buildings –Get Damage Ratio for wind speed –Loss = Value × Damage ratio –Add up all losses for the event

9. The Guy Carpenter Catastrophe Index (GCCI) Consists of the combined experience of 39 insurers who report their data to ISO Contracts on the GCCI are traded on the Bermuda Commodities Exchange (BCOE) The underlying exposures are available, so it is possible to use a catastrophe model to quantify the risk to both investors and insurers.

10. The GCCI Index

11. Bermuda Commodities Exchange Traded GCCI Contracts Covered Events Aggregate Loss Largest Event Second Largest Event Contracts pay $5000 if Index exceeds the posted strike price Geographic Regions National Southeast Northeast Mid/West Florida Gulf Strike prices traded on BCOE - 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 20, 25, 30, 35, 40, 45, 50, 100, 150, 200, 250, 300, 350, 400, 450, 500, 550, 600, 650, 700

12. The Examples Use an Illustrative Index Similar to the GCCI Programming GCCI rules is under way Used proxy GCCI for now. –Ran cat model through 50 insurers –Set the largest event = 100 Industry Equivalent - 100 Billion + –Maximum event contracts for $1,000 –Strike prices at 5,10, …, 95,100

13. Maximum Event Catastrophe Options

14. Catastrophe Options vs Other Investments One way to compare risk and cost Moody’s - Projected 12-month default rate of speculative-grade bonds is 2.5%. Average spread of speculative-grade bonds over risk-free bonds is 3.5% Probability of exercising a catastrophe option with a strike price of 20 is 2.3%

15. Insurer Objectives Using Catastrophe Options Reduce the cost of financing insurance –Expected insurer costs –Cost of Capital –Cost of Capital Substitutes Reinsurance Contracts on a catastrophe index Find the right mix of capital and capital substitutes

16. Quantifying the Cost of Capital Depends on the variability of the insurer’s business Standards will depend on the insurer management An “easy” formula Cost of Capital = K  T   Where:  = Standard deviation of total insurer loss T = Factor reflecting risk aversion K = Rate of return needed to attract capita

17. Quantifying Basis Risk Ran hurricane model through insurers and index. Compare variability before and after Is the risk reduction worth the cost ? + about 9000 more

18. Minimize Sum of Cost Elements Insurer Capital Cost of Capital = K  T   (Net Losses) Reinsurance Transaction Cost + Expected Cost Cat index contracts Transaction Cost + Expected Cost U se cat model results to back out transaction costs.

19. Analysis of Three Insurers Insurer #1 - A medium national insurer Highly correlated with the index Insurer #2 - A large national insurer Moderately correlated with the index Insurer #3 - A small regional insurer Slightly correlated with the index

20. Search for Best Strategy to Minimize Cost of Financing Insurance Search for the combination of index and reinsurance purchases that minimizes total cost of providing insurance. Questions How many index contracts at each strike price? What layer of reinsurance?

21. Results of Search

22. Financing With Reinsurance and Catastrophe Options

23. Financing Without Reinsurance and Catastrophe Options

24. Differences in Costs

25. The Marginal Cost of Financing Catastrophe Insurance The effect of Catastrophe Options and reinsurance in rates. Calculate the cost of financing with and without catastrophe coverage.

26. Marginal Cost with Reinsurance and Catastrophe Options

27. Marginal Cost without Reinsurance and Catastrophe Options

28. The Next Steps Analyze regional and state indices Embed catastrophe options within reinsurance contracts Reinsurer hedges combined risk of its primary insurers Reinsurer covers customized indices — adverse selection is not an issue.