Cutting-edge Weather Risk Management (WRM) Harvey Stern & Shoni Dawkins Bureau of Meteorology, Melbourne Harvey Stern & Shoni Dawkins Bureau of Meteorology,

Cutting-edgeCutting-edgeWeather Risk ManagementWeather Risk Management

(WRM) (WRM)

Cutting-edgeCutting-edgeWeather Risk ManagementWeather Risk Management

(WRM) (WRM)

Harvey Stern & Shoni DawkinsHarvey Stern & Shoni Dawkins

Bureau of Meteorology, MelbourneBureau of Meteorology, Melbourne

Harvey Stern & Shoni DawkinsHarvey Stern & Shoni Dawkins

Bureau of Meteorology, MelbourneBureau of Meteorology, Melbourne

Important WEB SitesImportant WEB SitesImportant WEB SitesImportant WEB Sites

• http://www.bom.gov.au

• http://www.artemis.bm/artemis.htm

• http://www.wrma.org

http://www.bom.gov.au/

http://www.artemis.bm/artemis.htm

Outline of PresentationOutline of PresentationOutline of PresentationOutline of Presentation

• Current state of the global WRM market.• Types of WRM products.• Weather Derivatives.• Hedging Applications.

• Current state of the global WRM market.• Types of WRM products.• Weather Derivatives.• Hedging Applications.

The Noah RuleThe Noah RuleThe Noah RuleThe Noah Rule

“Predicting rain doesn’t count;

Building arks does”.

Warren Buffett,Australian Financial Review,11 March 2002.

“Predicting rain doesn’t count;

Building arks does”.

Warren Buffett,Australian Financial Review,11 March 2002.

Some Recent NewsSome Recent NewsSome Recent NewsSome Recent News

• The next few slides illustrate some recent news.• The next few slides illustrate some recent news.

Foundation of the Weather MarketFoundation of the Weather MarketFoundation of the Weather MarketFoundation 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

“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

Views prior to the release of the Views prior to the release of the WRMA 2003 Survey ResultsWRMA 2003 Survey Results

Views prior to the release of the Views prior to the release of the WRMA 2003 Survey ResultsWRMA 2003 Survey Results

“Most market participants … are predicting an increase in total notional volumes”

“The general malaise that has clouded the weather risk market in the past year may be on the wane”

“…we will see a sizeable decrease in volumes … as Enron, Aquila … have left the market”

“The effect of market departures was clearly felt …[but]… big players more than compensated for the loss, providing liquidity and execution of service”

“…weather forecasting improvements could pose a threat to market development”

Energy Power Risk ManagementMay2003

“Most market participants … are predicting an increase in total notional volumes”

“The general malaise that has clouded the weather risk market in the past year may be on the wane”

“…we will see a sizeable decrease in volumes … as Enron, Aquila … have left the market”

“The effect of market departures was clearly felt …[but]… big players more than compensated for the loss, providing liquidity and execution of service”

“…weather forecasting improvements could pose a threat to market development”

Energy Power Risk ManagementMay2003

WRMA 2002 Survey Results.WRMA 2002 Survey Results.The Growing Interest.The Growing Interest.

WRMA 2002 Survey Results.WRMA 2002 Survey Results.The Growing Interest.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)

• 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).


WRMA 2002 Survey Results. WRMA 2002 Survey Results. The Diversification.The Diversification.

WRMA 2002 Survey Results. WRMA 2002 Survey Results. The Diversification.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).


• 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).


The Asia-Pacific RegionThe Asia-Pacific RegionThe Asia-Pacific RegionThe 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.

• 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.

Australian Developments Australian Developments Australian Developments Australian Developments • For many years, the power industry has received detailed

weather forecasts from the Bureau.

• Now, Australia has joined the global trend towards an increased focus on the management of weather-related risk.

• The first instance of an (Australian) weather derivative trade occurred about three years ago.

• A number of businesses have now moved into the trading of weather risk products, almost all “over the counter”.

• Partnerships are emerging between merchant banks and weather forecasting companies.

• For many years, the power industry has received detailed weather forecasts from the Bureau.

• Now, Australia has joined the global trend towards an increased focus on the management of weather-related risk.

• The first instance of an (Australian) weather derivative trade occurred about three years ago.

• A number of businesses have now moved into the trading of weather risk products, almost all “over the counter”.

• Partnerships are emerging between merchant banks and weather forecasting companies.

Weather-linked SecuritiesWeather-linked SecuritiesWeather-linked SecuritiesWeather-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.

• 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.

SecuritisationSecuritisationSecuritisationSecuritisation

• 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.

• 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 BondsCatastrophe BondsCatastrophe BondsCatastrophe 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

• 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.


Catastrophe SwapsCatastrophe SwapsCatastrophe SwapsCatastrophe 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.


• 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.


Weather DerivativesWeather DerivativesWeather DerivativesWeather Derivatives

• Weather derivatives are similar to conventional financial derivatives.

• The basic difference lies in the underlying variables that determine the pay-offs.

• These underlying variables include temperature, precipitation, wind, and heating (& cooling) degree days.

• Weather derivatives are similar to conventional financial derivatives.

• The basic difference lies in the underlying variables that determine the pay-offs.

• These underlying variables include temperature, precipitation, wind, and heating (& cooling) degree days.

Derivative or Insurance?Derivative or Insurance?Derivative or Insurance?Derivative or Insurance?

• A Derivative:

-has ongoing economic value,

-is treated like any other commodity,

-is accounted for daily, &

-may therefore affect a company’s credit rating.• An Insurance Contract:

-is not regarded as having economic value, &

-therefore does not affect a company’s credit rating.

• A Derivative:

-has ongoing economic value,

-is treated like any other commodity,

-is accounted for daily, &

-may therefore affect a company’s credit rating.• An Insurance Contract:

-is not regarded as having economic value, &

-therefore does not affect a company’s credit rating.

A Weather-linked OptionA Weather-linked OptionA Weather-linked OptionA Weather-linked Option

• An 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”.

• An 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”.

Specifying the CDD Call OptionSpecifying the CDD Call OptionSpecifying the CDD Call OptionSpecifying the CDD Call Option

• Strike: 400 CDDs.

• Notional: $100 per CDD (> 400 CDDs).

• If, at expiry, the accumulated CDDs > 400, the seller of the option pays the buyer $100 for each CDD > 400.

• Strike: 400 CDDs.

• Notional: $100 per CDD (> 400 CDDs).

• If, at expiry, the accumulated CDDs > 400, the seller of the option pays the buyer $100 for each CDD > 400.

Pay-off Chart for the CDDPay-off Chart for the CDDCall OptionCall Option

Pay-off Chart for the CDDPay-off Chart for the CDDCall OptionCall Option

An Historical Note: An Historical Note: An Early ExampleAn Early Example

An Historical Note: An Historical Note: An Early ExampleAn 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.

• 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.

Carbon Disclosure Project (2003)Carbon Disclosure Project (2003)Carbon Disclosure Project (2003)Carbon Disclosure Project (2003)

• "Investors failing to take account of climate change and carbon finance issues in the asset allocation and equity valuations may be exposed to significant risks which, if left unattended, will have serious investment repercussions over the course of time."

• "Investors failing to take account of climate change and carbon finance issues in the asset allocation and equity valuations may be exposed to significant risks which, if left unattended, will have serious investment repercussions over the course of time."

Cooling Degree Days (1855-2000)Cooling Degree Days (1855-2000)(and climate change)(and climate change)

Cooling Degree Days (1855-2000)Cooling Degree Days (1855-2000)(and climate change)(and climate change)

• Frequency distribution of annual Cooling Degree Days at Melbourne using all data:

• Frequency distribution of annual Cooling Degree Days at Melbourne using all data:

Cooling Degree Days (1971-2000)Cooling Degree Days (1971-2000) (and climate change)(and climate change)

Cooling Degree Days (1971-2000)Cooling Degree Days (1971-2000) (and climate change)(and climate change)

• Frequency distribution of annual Cooling Degree Days at Melbourne using only recent data:

• Frequency distribution of annual Cooling Degree Days at Melbourne using only recent data:

Should Companies Worry? Should Companies Worry? Should Companies Worry? 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.

• 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.

Weather-related Industry RiskWeather-related Industry RiskWeather-related Industry RiskWeather-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

"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 RiskWeather-related Agricultural RiskWeather-related Agricultural RiskWeather-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)

“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)

The Road toThe Road toWeather Risk Management. Weather Risk Management.

The Road toThe Road toWeather Risk Management. Weather Risk Management.

• The era of (mostly) categorical forecasts.

• The rapid increase in the application of probability forecasts.

• The provision of forecast verification (i.e. accuracy) data.

• The era of the “guaranteed forecast”, with user communities being compensated for an inaccurate prediction.

• The purchase of “stakes” in the industry (by multi-national companies).

• The era of (mostly) categorical forecasts.

• The rapid increase in the application of probability forecasts.

• The provision of forecast verification (i.e. accuracy) data.

• The era of the “guaranteed forecast”, with user communities being compensated for an inaccurate prediction.

• The purchase of “stakes” in the industry (by multi-national companies).

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).

Returning to the Cane GrowerReturning to the Cane GrowerReturning to the Cane GrowerReturning 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?

• 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 ApproachOne ApproachOne ApproachOne 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.

• 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 OptionSpecifying the Decile 4 Put OptionSpecifying the Decile 4 Put OptionSpecifying 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.

• 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.

Payoff Chart for Decile 4 Put OptionPayoff Chart for Decile 4 Put OptionPayoff Chart for Decile 4 Put OptionPayoff Chart for Decile 4 Put Option

Outcomes for Decile 4 Put OptionOutcomes for Decile 4 Put OptionOutcomes for Decile 4 Put OptionOutcomes for Decile 4 Put Option

Evaluating the Decile 4 Put OptionEvaluating the Decile 4 Put OptionEvaluating the Decile 4 Put OptionEvaluating 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.

• 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.

Weather & Climate ForecastsWeather & Climate ForecastsWeather & Climate ForecastsWeather & 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.

• 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 theAn Illustration of theImpact of Forecasts Impact of Forecasts An Illustration of theAn Illustration of theImpact of Forecasts 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.

• 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 Impact of Forecast Accuracy Impact of Forecast Accuracy 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.

• 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

http://www.guaranteedweather.com/



Using Forecast Accuracy DataUsing Forecast Accuracy DataUsing Forecast Accuracy DataUsing 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.

• 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 OptionPay-off Chart: 38 deg C Call OptionPay-off Chart: 38 deg C Call OptionPay-off Chart: 38 deg C Call Option

Determining the Price of theDetermining the Price of the38 deg C Call Option38 deg C Call Option

Determining the Price of theDetermining the Price of the38 deg C Call Option38 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.

• 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 OutcomesHistorical Distribution of OutcomesHistorical Distribution of OutcomesHistorical Distribution of Outcomes

Evaluating the 38 deg C Evaluating the 38 deg C Call Option (Part 1)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….

• 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….



• 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.

• 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.

Ensemble ForecastingEnsemble Forecasting(another approach to measuring forecast uncertainty)(another approach to measuring forecast uncertainty)

Ensemble ForecastingEnsemble Forecasting(another approach to measuring forecast uncertainty)(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.

• 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.

An Illustrative Example of “Cutting Edge Risk Management”.

A financial guarantee about a forecast –

This was described in a paper presented by Harvey Stern and Shoni Dawkins to the 2003 Annual Meeting of the American Meteorological Society held at Long Beach, California.

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.

(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.


Forecast Errors as a Function of Season

(after Dawkins & Stern, 2003)

Synoptic Weather Patterns

Synoptic weather patterns are maps depicting the distribution of atmospheric pressure.

They are used to describe the prevailing weather situation.

Winds blow clockwise around low pressure systems and anticlockwise around high pressure systems.

The weather is related to the origin of the air that is flowing over a particular location.

The next few slides present some synoptic weather patterns.

Consider what they mean in terms of Melbourne’s weather.

Southeast Winds over MelbourneSoutheast Winds over MelbourneSoutheast Winds over MelbourneSoutheast Winds over Melbourne

Southwest Winds over MelbourneSouthwest Winds over MelbourneSouthwest Winds over MelbourneSouthwest Winds over Melbourne

Northwest Winds over MelbourneNorthwest Winds over MelbourneNorthwest Winds over MelbourneNorthwest Winds over Melbourne

Forecast Errors and 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.


ExampleThe 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.


Synoptic Weather PatternSynoptic Weather PatternSynoptic Weather PatternSynoptic Weather Pattern

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.


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.


The WEB SiteA 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)

http://www.weather-climate.com/guarantee.html

A View of the WEB Site

Testing the Instrument’s ValidityIt 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.


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.


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.


Documents

Cutting-edge Weather Risk Management (WRM) Harvey Stern & Shoni Dawkins Bureau of Meteorology, Melbourne Harvey Stern & Shoni Dawkins Bureau of Meteorology,