Weather Derivatives

Sean Devlin ACAS, MAAACAS Annual Meeting

November 1999

1AMERICAN RE4

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

Product

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

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

Customers Energy Suppliers

Utilities

Municipalities

Individual Corporations

Agricultural Products

Airlines

Clothing Manufacturers and Retailers

Resorts

Beverage Companies

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

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.

Transformed Deals

Electric Company Bermuda Re

Bermuda ReAmerican Re

ISDA Agreement

Insurance Policy

Reinsurance Treaty

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

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:

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

No Loss Loss

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.

AttachmentPoint

Limit

Pricing: Loss Distribution and PremiumStep 3:

Step 4:

Risk LoadMean

Premium

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

•No

•No

•No

Actuarial Pricing Method is Most Appropriate

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.

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

1AMERICAN RE4

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

1AMERICAN RE4

Portfolio Management

LogNormalDistribution@2,0.85D

LOSS DISTRIBUTION

Loss Size

Pro

babi

lity

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

Portfolio’s Risk & RewardScenario 1 2 3 4Net Premium ('000 USD) 5,000 10,000 20,000 33,000Limit ('000 USD) 34,000 63,000 125,000 230,00050 Yr PML ('000 USD) 10,860 16,540 30,068 45,829100 Yr PML ('000 USD) 12,147 17,786 33,253 49,711Std Dev ('000 USD) 2,857 4,676 7,219 10,678Mean Loss ('000 USD) 3,000 6,000 12,000 19,800CV = St Dev / Mean 95% 78% 60% 54%Tech. Gain ('000 USD) 2,000 4,000 8,000 13,200

Analyzed four portfolios, varying in spread of risk

Quantified the risk and reward parameters:

Capacity Consumption

Portfolio Uncertainty

Technical Gain

Reward to Risk Ratio

Portfolio Reward - Premium less the expected loss

Portfolio Risk - Probable loss at a return period of 100 years

Reward/Risk

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

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

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.

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