Energy Pricing Techniques in the
Electricity Market
Part 4
Application of Weather Derivatives
Dr Harvey Stern,
Bureau of Meteorology, Australia
Outline of Presentation
• Background.
• An Historical Note.
• Weather-related Risk.
• The Growing Interest.
• Asia-Pacific Region.
• Some Statistics.
• Weather Derivatives Explained.
• Examples of Applications.
• Concluding Remarks.
Background
• Weather risk is one of the biggest uncertainties facing
business.
• We get droughts, floods, fire, cyclones (hurricanes), snow
& ice.
• Nevertheless, economic adversity is not restricted to
disaster conditions.
• A mild winter ruins a skiing season, dry weather reduces
crop yields, & rain shuts-down entertainment &
construction.
Background (cont.)
The increasing interest may be explained in terms of:
• A desire to meet client needs.
• A need to reduce the cost of capital.
• Cross-fertilization between various fields.
• Entry of new participants.
• Growing responsibilities of Company Directors.
Source: Prof. John Hewson’s presentation to the Weather Risk Management Association
An Historical Note:
An Early Example
• In 1992, the present author explored a methodology to
assess the risk of climate change.
• Option pricing theory was used to value instruments that
might apply to temperature fluctuations and long-term
trends.
• The methodology provided a tool to cost the risk faced
(both risk on a global scale, and risk on a company specific
scale).
• Such securities could be used to help firms hedge against
risk related to climate change.
Foundation of the Weather Market
“The foundation of today’s financial weather contracts is in
the US power market …
For the weather-sensitive end-user, not to hedge is to
gamble on the weather.”
Robert S. Dischell
Weather-related Industry Risk
"Shares in Harvey Norman fell almost 4 per cent yesterday
as a cool summer and a warm start to winter cut into sales
growth at the furniture and electrical retailer's outlets…
Investors were expecting better and marked the shares
down 3.8 per cent to a low of $3.55…
Sales at Harvey Norman were hit on two fronts. Firstly, air
conditioning sales were weak because of the cool summer,
and a warmer than usual start to winter had dampened
demand for heating appliances”.
Source: The Australian of 18 April, 2002
Weather-related Agricultural Risk
“The Australian sugar industry is facing its fifth difficult
year in a row with a drought dashing hopes of an improved
crop in Queensland, where 95% of Australia's sugar is
grown...
Whilst dry weather during the May-December harvest
period is ideal for cane, wet weather during this time
causes the mature cane to produce more shoots and
leaves, reducing its overall sugar content”.
(Australian Financial Review of 8 May, 2002)
Channels for Weather Risk Transfer
ART (Alternative Risk Transfer) is a generic phrase used to
denote various non-traditional forms of re/insurance and
techniques where risk is transferred to the capital markets.
Source: http://www.artemis.bm
The Growing Interest.
• 3,937 contracts transacted in last 12 months (up 43%
compared to previous year).
• Notional value of over $4.3 billion dollars (up 72%).
• Market dominated by US (2,712 contracts), but growth in
the past year is especially so in Europe and Asia.
• Australian market accounts for 15 contracts worth over $25
million (6 contracts worth over $2 million, previously).
Source: Weather Risk Management Association Annual Survey (2002)
The Diversification.
• Another significant development is the diversification of
the types of contracts that were transacted.
• Temperature-related protection (for heat and cold)
continues to be the most prevalent, making up over 82
percent of all contracts (92% last year)
• Rain-related contracts account for 6.9% (1.6% last year),
snow for 2.2% (0.6% last year) and wind for 0.4% (0.3% last
year).
Source: Weather Risk Management Association Annual Survey (2002)
Why has ART grown?
• Risk management moving up the agenda
• A need to manage uninsurable liabilities
• A need to protect against irregular income “spikes”
Source: Modern ART practice (Gerling Global Financial Products)
What is the future of ART?
“The term Alternative Risk Transfer (ART) will soon be a
misnomer. ART is fast becoming an essential risk
management tool for primary insurers, reinsurers and non-
insurance corporations”.
Source: Modern ART practice (Gerling Global Financial Products)
The Asia-Pacific Region
Interest in weather risk management has grown in the
Asia-Pacific Region (covering electricity, gas, &
agriculture). Countries involved include:
- Japan;
- Korea; and,
- Australia/New Zealand.
Source: Weather Risk Management Association.
Weather-linked Securities
• Weather-linked securities have prices which are linked to
the historical weather in a region.
• They provide returns related to weather observed in the
region subsequent to their purchase.
• They therefore may be used to help firms hedge against
weather related risk.
• They also may be used to help speculators monetise their
view of likely weather patterns.
Securitisation
• The reinsurance industry experienced several catastrophic
events during the late 1980s & early 1990s.
• The ensuing industry restructuring saw the creation of new
risk-management tools.
• These tools included securitisation of insurance risks
(including weather-related risks).
• Weather securitisation may be defined as the conversion of
the abstract concept of weather risk into packages of
securities.
• These may be sold as income-yielding structured products.
Catastrophe Bonds
• A catastrophe (cat) bond is an exchange of principal for
periodic coupon payments wherein the payment of the
coupon and/or the return of the principal of the bond is
linked to the occurrence of a specified catastrophic event.
• The coupon is given to the investor upfront, who posts the
notional amount of the bond in an account.
• If there is an event, investors may lose a portion of (or their
entire) principal.
• If there is no event, investors preserve their principal and
earn the coupon.
Source: Canter & Cole at http://www.cnare.com
Catastrophe Swaps
• A catastrophe (cat) swap is an alternative structure, but
returns are still linked to the occurrence of an event.
• However, with swaps, there is no exchange of principal.
• The coupon is still given to the investor upfront, but the
structure enables investors to invest the notional amount
of the bond in a manner of his own choosing.
Source: Canter & Cole at http://www.cnare.com
Weather Derivatives Explained
Clewlow et al. (2000) describe a derivative as "a financial
product that derives its value from other more basic
variables".
These products include futures, forwards, call options, put
options, and swaps.
They describe weather derivatives as being similar "to
conventional financial derivatives, the basic difference
coming from the underlying variables that determine the
payoffs", such as temperature, precipitation, wind, Heating
Degree Days (HDDs), and Cooling Degree Days (CDDs).
Pricing Derivatives
There are three approaches that may be applied to the pricing
of derivatives.
These are:
•Historical simulation (applying "burn analysis");
•Direct modelling of the underlying variable’s distribution
(assuming, for example, that the variable's distribution is
normal); and,
•Indirect modelling of the underlying variable’s distribution
(via a Monte Carlo technique).
Direct modelling is chosen for the current exercise, the
distribution of forecast errors being assumed to be normal.
Returning to the Cane Grower
• Suppose that our cane grower has experienced an
extended period of drought.
• Suppose that if rain doesn't fall next month, a substantial
financial loss will be suffered.
• How might our cane grower protect against exceptionally
dry weather during the coming month?
One Approach
• One approach could be to purchase a Monthly Rainfall
Decile 4 Put Option.
• Assume that our cane grower decides only to take this
action when there is already a risk of a dry month.
• That is, when the current month's Southern Oscillation
Index (SOI) is substantially negative.
• So, the example is applied only to the cases when the
current month's Southern Oscillation Index (SOI) is in the
lowest 5% of possible values, that is, below -16.4.
Specifying the Decile 4 Put Option
• Strike: Decile 4.
• Notional: $100 per Decile (< Decile 4).
• If, at expiry, the Decile is < Decile 4, the seller of the option
pays the buyer $100 for each Decile < Decile 4.
Pricing Methodologies
• Historical simulation.
• Direct modeling of the underlying variable’s distribution.
• Indirect modeling of the underlying variable’s distribution
(via a Monte Carlo technique).
Payoff Chart for Decile 4 Put Option
Outcomes for Decile 4 Put Option
Evaluating the Decile 4 Put Option
• 14.2% cases of Decile 1 yields $(.142)x(4-1)x100=$42.60
• 13.2% cases of Decile 2 yields $(.132)x(4-2)x100=$26.40
• 8.4% cases of Decile 3 yields $(.084)x(4-3)x100=$8.40
• The other 25 cases (Decile 4 or above) yield nothing.
…leading to a total of $77.40, which is the price of our put
option.
Should Companies Worry?
• In the good years, companies make big profits.
• In the bad years, companies make losses.
- Doesn’t it all balance out?
- No. it doesn’t.
• Companies whose earnings fluctuate wildly receive
unsympathetic hearings from banks and potential
investors.
Another Example
• Another example of a weather linked option is the Cooling
Degree Day (CDD) Call Option.
• Total CDDs is defined as the accumulated number of
degrees the daily mean temperature is above a base figure.
• This is a measure of the requirement for cooling.
• If accumulated CDDs exceed “the strike”, the seller pays
the buyer a certain amount for each CDD above “the
strike”.
Pay-off Chart for a CDD
Call Option
Cooling Degree Days (1855-2000)
(and climate change)
• The chart shows frequency distribution of annual Cooling
Degree Days at Melbourne using all data:
Cooling Degree Days (1971-2000)
• The chart shows frequency distribution of annual Cooling
Degree Days at Melbourne using only recent data:
Weather & Climate Forecasts
• Daily weather forecasts may be used to manage short-term
risk (e.g. pouring concrete).
• Seasonal climate forecasts may be used to manage risk
associated with long-term activities (e.g. sowing crops).
• Forecasts are based on a combination of solutions to the
equations of physics, and some statistical techniques.
• With the focus upon managing risk, the forecasts are
increasingly being couched in probabilistic terms.
An Illustration of the
Impact of Forecasts
• When very high temperatures are forecast, there may be a
rise in electricity prices.
• The electricity retailer then needs to purchase electricity
(albeit at a high price).
• This is because, if the forecast proves to be correct, prices
may “spike” to extremely high (almost unaffordable) levels.
Impact of Forecast Accuracy
• If the forecast proves to be an “over-estimate”, however,
prices will fall back.
• For this reason, it is important to take into account forecast
accuracy data in determining the risk.
Forecast Accuracy Data
The Australian Bureau of Meteorology's Melbourne office
possesses data about the accuracy of its temperature
forecasts stretching back over 40 years.
Customers receiving weather forecasts have, recently,
become increasingly interested in the quality of the service
provided.
This reflects an overall trend in business towards
implementing risk management strategies. These strategies
include managing weather related risk.
Indeed, the US Company Aquila developed a web site that
presents several illustrations of the concept:
http://www.guaranteedweather.com
Using Forecast Accuracy Data
• Suppose we define a 38 deg C call option (assuming a
temperature of at least 38 deg C has been forecast).
• Location: Melbourne.
• Strike: 38 deg C.
• Notional: $100 per deg C (above 38 deg C).
• If, at expiry (tomorrow), the maximum temperature is
greater than 38 deg C, the seller of the option pays the
buyer $100 for each 1 deg C above 38 deg C.
Pay-off Chart: 38 deg C Call Option
Determining the Price of the
38 deg C Call Option
• Between 1960 and 2000, there were 114 forecasts of at
least 38 deg C.
• The historical distribution of the outcomes are examined.
Historical Distribution of Outcomes
Evaluating the 38 deg C
Call Option (Part 1)
• 1 case of 44 deg C yields $(44-38)x1x100=$600
• 2 cases of 43 deg C yields $(43-38)x2x100=$1000
• 6 cases of 42 deg C yields $(42-38)x6x100=$2400
• 13 cases of 41 deg C yields $(41-38)x13x100=$3900
• 15 cases of 40 deg C yields $(40-38)x15x100=$3000
• 16 cases of 39 deg C yields $(39-38)x16x100=$1600
cont….
Evaluating the 38 deg C
Call Option (Part 2)
• The other 61 cases, associated with a temperature of 38
deg C or below, yield nothing.
• So, the total is $12500.
• This represents an average contribution of $110 per case,
which is the price of our option.
A Financial Guarantee
The guarantee described is that the forecast will be in error
by no more than 3°C.
The terms of the guarantee are that the seller of the
guarantee will pay the buyer $100.00 for each 0.1°C greater
than 3°C that the forecast is in error.
It is the purpose of the paper to develop an approach to
pricing such a financial guarantee, and to provide it as a
technique that is available on the web.
(after Stern & Dawkins, 2003)
The Instrument
The instrument is made up of a combination of a call option
and a put option about the next day's maximum temperature
at Melbourne, the "strikes" being set respectively 3°C above
and below the forecast temperature.
The taker of this option combination receives $100 for each
0.1°C that the observed temperature is above or below the
respective strikes.
(after Stern & Dawkins, 2003)
Forecast Errors
Dawkins and Stern (2003) show that the magnitude of the
forecast errors is largely a function of season and synoptic
pattern.
Dahni (2003) describes an automated technique for "typing"
synoptic patterns.
(after Stern & Dawkins, 2003)
Forecast Errors as a Function of Season
(after Dawkins & Stern, 2003)
Forecast Errors as a Function of Synoptic
Pattern
(after Dawkins & Stern, 2003)
The Approach Used
The approach used is as follows:
•The forecast verification data is stratified according to
month, and also according to the nature of the prevailing
atmospheric circulation - cyclonicity, direction and strength
of the surface flow.
•The distribution of the magnitude of forecast errors for each
month (and also for each synoptic pattern type) is noted &
this distribution is adjusted in order to take into account a
long-term downward trend in the magnitude of the errors;
•The distribution of forecast errors is assumed to be normal
for each data subset, and a "fair value" price for the option
combination for each month and each circulation type is then
obtained.
(after Stern & Dawkins, 2003)
Example
The example we shall use to illustrate the methodology is a
forecast produced during the month of January, associated
with a synoptic type flow possessing the following
characteristics:
•weak strength;
•cyclonic (curvature);
•from the north-north-west.
Over the 40-year period (1961-2000), occurrences of such a
flow across SE Australia (over all months of the year) have
been temperature forecasts with an RMS error of 2.70°C.
(after Stern & Dawkins, 2003)
Example (cont.)
More recently (1991-2000), such a flow has been
accompanied by an RMS error of (a much reduced) 2.26°C.
It is then assumed that the forecast performance during the
period 1991-2000 better represents what one might anticipate
to be the current level of performance, than does the forecast
performance over the 1961-2000 period.
It is also assumed that the proportional improvement in
forecasting for each individual month (January, February,
March etc.) is the same, that is, a proportional decrease in
RMS error of (2.26/2.70)=(0.84) in the current case.
(after Stern & Dawkins, 2003)
Example (cont.)
The monthly RMS error calculated over the 1961-2000 period
for the current synoptic type and the current month (3.32°C in
this case) is then multiplied by the ratio (0.84) in order to
achieve an estimate of the likely RMS error for the current
forecast.
So, the case of a January cyclonic weak north-north-west
synoptic flow yields (0.84x3.32)=2.79°C for our estimated
RMS error.
It is then assumed that the errors are normally distributed
and, utilising areas under the standard normal curve, one
calculates the expected return on the guarantee to be $410.
This procedure is then repeated for all months and for all
synoptic patterns.
(after Stern & Dawkins, 2003)
The WEB Site
A web site is developed in order that :
•potential "customers" may readily obtain a price for the
instrument; and,
•researchers may test its output.
This may be viewed and tested at
http://www.weather-climate.com/guarantee.html
(after Stern & Dawkins, 2003)
A View of the WEB Site
Testing the Instrument’s Validity
It was considered that if, over a large number of cases,
writers of the option combination do not make either a
significant profit or a significant loss, the validity of the "fair
value" price would be demonstrated.
The instrument's validity was then tested by calculating the
"fair value" price on independent cases taken for the entire
year of 2001.
However, from an analysis of all of the year-2001 cases, it
was determined that writers of the option combination would
have received $75,574 over the year, while paying out only
$23,800.
(after Stern & Dawkins, 2003)
Testing (cont.)
Nevertheless, this substantial profit (over 200% return) is not
necessarily suggesting a possible flaw in the valuation
technique.
On the contrary, it may be explained in terms of the
spectacular improvement in the accuracy of forecasts
achieved during 2001 (see next slide).
One may show that had the forecasts been of similar skill to
those of previous years, the payout would have been much
closer to the monies received.
The profit achieved by the option writers can, therefore, be
explained in terms of that increased skill.
(after Stern & Dawkins, 2003)
Sharp Improvement in Forecast Accuracy in
2001 (after Dawkins & Stern, 2003)
Comments on the Financial
Guarantee
A methodology to price a financial guarantee about the
accuracy of a forecast has been described and demonstrated
with "real" data.
It has been shown that had such a guarantee been applied to
day-1 maximum temperature forecasts issued during 2001 for
Melbourne, providers of the guarantee would have made a
substantial profit
-on account of the increased skill displayed by the forecasts.
(after Stern & Dawkins, 2003)
Ensemble Forecasting
(another approach to measuring forecast uncertainty)
• Another approach to obtaining a measure of forecast
uncertainty, is to use ensemble weather forecasts.
• The past decade has seen the implementation of these
operational ensemble weather forecasts.
• Ensemble weather forecasts are derived by imposing a
range of perturbations on the initial analysis.
• Uncertainty associated with the forecasts may be derived
by analysing the probability distributions of the outcomes.
Some Important Issues
• Quality of weather and climate data.
• Changes in the characteristics of observation sites.
• Security of data collection processes.
• Privatisation of weather forecasting services.
• Value of data.
• Climate change.
Concluding Remarks
• The sophistication of weather-related risk management
products is growing.
• In evaluating weather securities one needs to use historical
weather data and forecast accuracy data, and also to take
into account climate trends.
• Ensemble forecasting is a new approach to determining
forecast uncertainty.