2. Weather Derivatives Sean Devlin ACAS, MAAA CAS Annual Meeting November 1999 1 A MERICAN R E 4

3. Topics What is the Product Who are the Customers How is the Business Transacted How is the Deal Priced What are the Risk Management Controls Future

4. Product Weather Derivatives provide coverage for the risk that the weather is different from the historical averages for a period of time

5. Risks covered Average Temperature - HDDs/CDDs Abnormal Temperature - # Days above 90F Precipitation/Snowfall Snowpack Windspeed Riverflow Barometric Pressure Humidity Combination of two or more of the above

6. Customers Energy Suppliers Utilities Municipalities Individual Corporations Agricultural Products Airlines Clothing Manufacturers and Retailers Resorts Beverage Companies

7. How the Business is Transacted Each contract has a stated limit Risk is actively managed, traded and hedged Transacted through SEC-licensed broker-dealer on public exchanges and in private transactions

8. Why Not Use Insurance Policies? Insurers and reinsurers in the market are at a significant disadvantage due to: More cumbersome and expensive insurance transaction. Inability to hedge and manage risk efficiently. No access to complete market data and trading strategies or other players.

9. Transformed Deals Electric CompanyBermuda Re American Re ISDA Agreement Insurance Policy Reinsurance Treaty

10. Sample Deal Problem: Phoenix Energy Company knows during hotter summers, the cost of producing abnormal amounts of electricity is extremely expensive. The company estimates that it loses $25,000 for every Cooling Degree Day (CDD*) above a certain threshold. Solution: Company takes out a CDD call option with an attachment point of cumulative 4600 CDDs. For every CDD above 4600, AmRe pays $25,000 with a limit of $10M. The temperature reference station is Phoenix Sky Harbor Airport. *CDD = Average Daily Temperature - 65

11. Pricing: Underlying Data Collect and adjust data. Coverage is based on measured temperatures at fixed locations. Time series needs to be adjusted due to biases The Key to Pricing is Understanding the Data Fit a distribution. Use adjusted measurements to determine the probability distribution of temperature index per season Step 1 : Step 2:

12. Pricing: Underlying Data Time series needs to be adjusted due to bias in: Surrounding environment Measuring instrument Climate change The Key to Pricing is Understanding the Data

13. No LossLoss Apply Contract Structure. Determine Loss Distribution and Premium. Obtain the loss distribution using transformed data obtained in Step 3 Determine mean and standard deviation of loss distribution Determine coverage premium by using a risk load factor that is a function of mean payoff, standard deviation, frictional costs, long term climate forecast and marginal impact on portfolio. Attachment Point Limit Pricing: Loss Distribution and Premium Step 3 : Step 4: Risk Load Mean Premium

14. Pricing: Methodology Black-Scholes Versus Actuarial-Based Pricing “Do the Black-Scholes Pricing Assumptions Apply to Weather Covers?” Assumptions Is the market liquid? Are the mean and standard deviation time- independent? Do arbitrage conditions exist (Put-Call parity)? Is the underlying asset traded? Does a lognormal distribution of the underlying asset exist? Applicable No (?) No Actuarial Pricing Method is Most Appropriate

15. Puts and Calls Put Cover: Covers for accumulated index (CDD or HDD) being below a level. Call Cover: Covers for accumulated index (CDD or HDD) being Above a level.

16. Trading Objectives Objective is to establish a climate-neutral portfolio during a given season: profit scenarios are slightly skewed but do not depend on very warm or very cold temperatures we do not speculate on temperature We seek to realize profits through: taking advantage of the disparity of prices in geographic regions creating positions by combining two or more contracts 1 A MERICAN R E 4

17. Underwriting and Investment Guidelines The portfolio is subject to maximum trading limits based on Maximum Potential Economic Loss (MPEL) and Value at Risk (VaR). MPEL aggregates the stated limit of all contracts. VaR reduces MPEL by taking into account the offsetting nature of correlated events. The portfolio is also subject to certain other guidelines: individual transaction size counterparty exposure limits contract length minimum years of related weather data for analysis regional exposure limits 1 A MERICAN R E 4

18. Portfolio Management Mean PML 1.0% of area to right of PML Portfolio Risk Metrics Expected Loss –Measure for mean of loss distribution Expected Loss Ratio –Expected loss normalized by premiums: Mean/Total Premium Median –50% of losses will be less than this value; 50% are greater Probable Maximum Loss (PML) –Measure for the tail of the loss distribution –Loss exceeded once every 100 years: –More appropriate measure of risk than variance for skewed distributions Median

19. Portfolio’s Risk & Reward Analyzed four portfolios, varying in spread of risk Quantified the risk and reward parameters: Capacity Consumption Portfolio Uncertainty Technical Gain

20. Reward to Risk Ratio Portfolio Reward - Premium less the expected loss Portfolio Risk - Probable loss at a return period of 100 years Reward/Risk

21. Coefficient of Variation Coefficient of Variation (CV) - Ratio between portfolio’s standard deviation and its expected loss CV reflects level of uncertainty or variability of the portfolio Plot indicates that CVs decrease as capacity / volume of premiums increases, allowing for an optimal portfolio mix

22. WEATHER MARKET PLAYERS Power Distributors Natural Gas Distributors Heating Oil Distributors Energy Producers Trading Companies Investment Banks Energy Marketers Reinsurance Companies Commercial Banks Providers End Users BROKER or DIRECT Energy Consumers

23. Other Applications Combining weather risk within overall risk management program. Dual trigger or combined retention programs. Combining weather risk(volume) risk with commodity(price) risk, i.e. gas, oil, electricity. Weather-linked debt to finance power generation equipment. Offered as insurance or reinsurance contracts.

24. Weather Market Outlook Continued growth in frequency of transactions Faster deal negotiations and closings Larger sized, multi-year deals Short-term monthly/weekly markets (e.g. CME) International expansion More participation by banks, financial intermediaries and consultants More end user hedging participation Retail weather products and services