Transcript Handout 2

1AMERICAN RE4
Weather Derivatives
Sean Devlin ACAS, MAAA
CAS Annual Meeting
November 1999
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
ISDA Agreement
Bermuda Re
Electric Company
Insurance
Policy
American Re
Reinsurance Treaty
Bermuda Re
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
1949-98 Phoenix (WBAN # 23183)
Apr-Oct Cooling Degree Days
Step 1:
Collect and adjust data.
Coverage is based on
measured temperatures at
fixed locations.
Degree Days
4900
4400
3900
CDD Days
Trended
Attachment
Limit
3400
2900
1997
1993
1989
1985
1981
1977
1973
1969
1965
1961
1957
1953
1949
Time series needs to be
adjusted due to biases
Years
Phoe nix , WBAN 23183, CDD (Apr-Oct)
Step 2:
8
7
Fit a distribution. Use
adjusted measurements to
determine the probability
distribution of temperature
index per season
6
# of Events
5
4
3
2
1
0
3900
4000
4100
4200
4300
4400
4500
4600
4700
4800
4900
5000
5100
CDD(F)
The Key to Pricing is Understanding the Data
Pricing: Underlying Data
1949-99 Phoenix (WBAN # 23183)
Apr-Oct Cooling Degree Days
Degree Days
4900
Time series needs to be
adjusted due to bias in:
4400
3900
CDD Days
Trended
Strike
Exhaust
3400
2900

Surrounding
environment

Measuring instrument

Climate change
1997
1993
1989
1985
1981
1977
1973
1969
1965
1961
1957
1953
1949
Years
The Key to Pricing is Understanding the Data
Pricing: Loss Distribution and Premium
Step 3: Apply Contract Structure.
Phoe nix, WBAN 23183, CDD (Apr-Oct)
12,000
Payout Structure
8
No Loss
7
Loss
Limit
10,000
6
8,000
Loss (000)
# of Events
5
4
6,000
4,000
Attachment
Point
3
2,000
2
0
1
-2,000
0
3900
4000
4100 4200
4300
4400
4500 4600
4700
4800 4900
5000
5100
3800
4200
4600
5000
5400
CDD (F)
CDD(F)
Step 4:
Determine Loss Distribution and
Premium.
Loss Distribution Phoenix CDD Put
40
Obtain the loss distribution using
transformed data obtained in Step 3
# of Events
30
Premium
20
Mean
10
Determine mean and standard deviation of
loss distribution
Risk Load
0
0
1,000
2,000
3,000
4,000
5,000
6,000
Loss ($000)
7,000
8,000
9,000
10,000
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.
Pricing: Methodology
 Black-Scholes Versus Actuarial-Based Pricing
“Do the Black-Scholes Pricing Assumptions Apply to
Weather Covers?”
Assumptions
Applicable
• Is the market liquid?
• No (?)
• Are the mean and standard deviation timeindependent?
• No
• Do arbitrage conditions exist (Put-Call parity)?
• No
• Is the underlying asset traded?
• No
• Does a lognormal distribution of the underlying
asset exist?
• No
Actuarial Pricing Method is Most Appropriate
Puts and Calls
 Call Cover: Covers for
accumulated index (CDD or
HDD) being Above a level.
 Put Cover: Covers for
accumulated index (CDD or
HDD) being below a level.
12,000
12,000
Payout Structure
10,000
8,000
8,000
6,000
Loss (000)
Loss (000)
Payout Structure
10,000
4,000
6,000
4,000
2,000
2,000
0
0
-2,000
-2,000
3800
4200
4600
CDD (F)
5000
5400
3400
3800
4200
CDD (F)
4600
5000
1AMERICAN RE4
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
Portfolio Management
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
@D
LogNormalDistribution 2, 0.85
Probability
LOSS DISTRIBUTION
1.0% of area to right of PML
Median
Mean
Loss Size
PML
Portfolio’s Risk & Reward
Scenario
Net Premium ('000 USD)
Limit ('000 USD)
50 Yr PML ('000 USD)
100 Yr PML ('000 USD)
Std Dev ('000 USD)
Mean Loss ('000 USD)
CV = St Dev / Mean
Tech. Gain ('000 USD)
1
2
3
4
5,000 10,000 20,000 33,000
34,000 63,000 125,000 230,000
10,860 16,540 30,068 45,829
12,147 17,786 33,253
49,711
2,857
4,676
7,219
10,678
3,000
6,000
12,000
19,800
95%
78%
60%
54%
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 to Risk Ratio
30%
28%
26%
Reward to Risk Ratio
24%
22%
Reward/Risk
20%
18%
16%
14%
12%
10%
0
5,000
10,000
15,000
20,000
25,000
Premium ('000 USD)
30,000
35,000
Coefficient of Variation
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
Portfolio Coefficient of Variation
100%
93%
90%
80%
Coefficient ofVariation
Coefficient of Variation
(CV) - Ratio between
portfolio’s standard
deviation and its expected
loss
77%
70%
60%
59%
53%
50%
40%
30%
20%
10%
0%
0
5,000
10,000
15,000
20,000
Premium ('000 USD)
25,000
30,000
35,000
End Users
Power
Distributors
Natural Gas
Distributors
Energy
Consumers
Heating Oil
Distributors
Energy
Producers
BROKER or DIRECT
Investment
Banks
Trading
Companies
Commercial
Banks
Energy
Marketers
Reinsurance
Companies
Providers
WEATHER MARKET PLAYERS
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