Weather Derivatives Dr Harvey Stern, Victorian Regional Office Dr Harvey Stern, Victorian Regional Office Weather Services Planning Conference Friday 19 April 10.15am-10.45am Weather Services Planning Conference Friday 19 April 10.15am-10.45am

The Noah Rule “Predicting rain doesn’t count; Building arks does”. Warren Buffett, Australian Financial Review,11 March “Predicting rain doesn’t count; Building arks does”. Warren Buffett, Australian Financial Review,11 March 2002.

Outline of Presentation Some recent developments in weather risk. Applications of weather derivatives. Utilising forecast accuracy and other databases. Role of ensemble weather forecasting. Recommendations to enable the BoM to keep abreast of devlopments in this growing sector of weather services. Some recent developments in weather risk. Applications of weather derivatives. Utilising forecast accuracy and other databases. Role of ensemble weather forecasting. Recommendations to enable the BoM to keep abreast of devlopments in this growing sector of weather services.

IntroductionIntroduction The meteorological community is becoming increasingly skilled at applying weather-related risk management products. Most of these products originate from the financial markets. It is the energy sector (in the USA) that has, so far, taken best advantage of the growing weather-risk market. The meteorological community is becoming increasingly skilled at applying weather-related risk management products. Most of these products originate from the financial markets. It is the energy sector (in the USA) that has, so far, taken best advantage of the growing weather-risk market.

The words of O. G. Sutton “The analogy between meteorology and astronomy is often made … There is a closer resemblance, to my mind, between meteorology and economics. Both deals fundamentally with the problem of energy transformations and distribution - in economics, the transformation of labour into goods and their subsequent exchange and distribution; - in meteorology, transformation and distribution of the energy received from the sun. Both are subject to extremely capricious external influences.” (from “Mathematics and the future of meteorology”, Weather, October, 1951) “The analogy between meteorology and astronomy is often made … There is a closer resemblance, to my mind, between meteorology and economics. Both deals fundamentally with the problem of energy transformations and distribution - in economics, the transformation of labour into goods and their subsequent exchange and distribution; - in meteorology, transformation and distribution of the energy received from the sun. Both are subject to extremely capricious external influences.” (from “Mathematics and the future of meteorology”, Weather, October, 1951)

BackgroundBackground The property and casualty reinsurance industry experienced several major 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. A third party issues these securities. The securities provide a return structured in a manner related to the occurrence (or otherwise) of an adverse event. The property and casualty reinsurance industry experienced several major 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. A third party issues these securities. The securities provide a return structured in a manner related to the occurrence (or otherwise) of an adverse event.

Weather Risk Weather risk is one of the biggest uncertainties facing Australian business. - We get droughts, floods, fire, and cyclones. Economic adversity is not restricted to disaster conditions. - A mild winter ruins a ski season, dry weather reduces crop yields, & rain shuts-down entertainment & construction. - Recently, a brewer blamed an earnings decrease on a cool summer. Weather risk is one of the biggest uncertainties facing Australian business. - We get droughts, floods, fire, and cyclones. Economic adversity is not restricted to disaster conditions. - A mild winter ruins a ski season, dry weather reduces crop yields, & rain shuts-down entertainment & construction. - Recently, a brewer blamed an earnings decrease on a cool summer.

Securitisation of Weather Risk Weather securitisation may be defined as the conversion of the abstract concept of weather risk into packages of securities. These may then be sold as income-yielding structured products. Weather securitisation may be defined as the conversion of the abstract concept of weather risk into packages of securities. These may then be sold as income-yielding structured products.

ForecastsForecasts Weather forecasts may be used to manage risk associated with short-term activities (e.g. pouring concrete). Climate forecasts may be used to manage risk associated with long-term activities (e.g. sowing crops). With the focus upon managing risk, the forecasts are increasingly being couched in probabilistic terms. Weather forecasts may be used to manage risk associated with short-term activities (e.g. pouring concrete). Climate forecasts may be used to manage risk associated with long-term activities (e.g. sowing crops). With the focus upon managing risk, the forecasts are increasingly being couched in probabilistic terms.

The Road to Weather Risk Management. The era of (mostly) categorical forecasts. The rapid increase in the application of probability forecasts. The provision of forecast verification 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 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).

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 two years ago. A number of businesses have now moved into the trading of weather risk products, almost all “over the counter”. Partnerships 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 two years ago. A number of businesses have now moved into the trading of weather risk products, almost all “over the counter”. Partnerships between merchant banks and weather forecasting companies.

Weather-risk & the Financial Markets 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.

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.

What is a Derivative? A Derivative is a financial instrument whose value is derived from the value of some other financial variable. A Derivative is a financial instrument whose value is derived from the value of some other financial variable.

A Familiar Example of a Derivative. A familiar example of Derivatives were the TELSTRA Instalment Receipts. Their value fluctuated in accordance with fluctuations in the value of TELSTRA shares. A familiar example of Derivatives were the TELSTRA Instalment Receipts. Their value fluctuated in accordance with fluctuations in the value of TELSTRA shares.

What is a Weather Derivative? A Weather Derivative is a financial instrument whose value is derived from the magnitude of some weather variable. A Weather Derivative is a financial instrument whose value is derived from the magnitude of some weather variable.

Expanding the Definition Weather derivatives are financial instruments that are utilised to manage weather (& climate) related risk. They 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 financial instruments that are utilised to manage weather (& climate) related risk. They 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? 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.

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. 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.

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. 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.

Another Example A common example is the Cooling Degree Day (CDD) Call Option. Total CDDs in a season 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”, then the seller pays the buyer a certain amount for each CDD above “the strike”. A common example is the Cooling Degree Day (CDD) Call Option. Total CDDs in a season 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”, then the seller pays the buyer a certain amount for each CDD above “the strike”.

Specifying 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 CDD Call Option

Approaches to Pricing Historical simulation. Direct modeling of the underlying variable’s distribution. Indirect modeling of the underlying variable’s distribution (via a Monte Carlo technique). Historical simulation. Direct modeling of the underlying variable’s distribution. Indirect modeling of the underlying variable’s distribution (via a Monte Carlo technique).

Significant Long-term Trends Some weather elements have trended significantly. Trends need to be considered when valuing weather securities (such as CDD Call Options). The trend in the minimum temperature at Melbourne (Australia) is shown here. Some weather elements have trended significantly. Trends need to be considered when valuing weather securities (such as CDD Call Options). The trend in the minimum temperature at Melbourne (Australia) is shown here.

Cooling Degree Days ( ) The chart shows frequency distribution of annual accumulated Cooling Degree Days at Melbourne using all data:

Cooling Degree Days ( ) The chart shows frequency distribution of annual accumulated Cooling Degree Days at Melbourne using only recent data:

Pricing the CDD Call Option The two CDD frequency distributions are quite different. Utilising the different data in valuation results in different prices. Utilising data yields a price thus: $(.051x x x12500)= $ Utilising data yields a price thus: $(.238x x x12500)= $ The more recent frequency distribution should provide a more relevant result. The two CDD frequency distributions are quite different. Utilising the different data in valuation results in different prices. Utilising data yields a price thus: $(.051x x x12500)= $ Utilising data yields a price thus: $(.238x x x12500)= $ The more recent frequency distribution should provide a more relevant result.

An Option linked to a Climate Index Suppose we define a rainfall put option, to apply when the Southern Oscillation Index (SOI) is in the lowest three deciles. Location: Echuca. Strike: Decile 4. Notional: $100 per decile below Decile 4. - If, at expiry, the rainfall Decile is less than 4, then the seller of the option pays the buyer $100 for each Decile below 4. Suppose we define a rainfall put option, to apply when the Southern Oscillation Index (SOI) is in the lowest three deciles. Location: Echuca. Strike: Decile 4. Notional: $100 per decile below Decile 4. - If, at expiry, the rainfall Decile is less than 4, then the seller of the option pays the buyer $100 for each Decile below 4.

Pay-off Chart for Decile 4 Put Option

Rainfall Distribution To value the put option one uses data giving actual distribution of rainfall for cases when the SOI is in the lowest 3 deciles.

Evaluating the Decile 4 Put Option 9 cases of Decile 1 yields $(4-1)x9x100=$ cases of Decile 2 yields $(4-2)x6x100=$ cases of Decile 3 yields $(4-3)x4x100=$400 The other 25 cases (Decile 4 or above) yield nothing. …leading to a total of $4300, and an average contribution of $98, which is the price of our put option. Later, a catastrophe bond, which may be issued to provide protection in the case of drought, will be described. 9 cases of Decile 1 yields $(4-1)x9x100=$ cases of Decile 2 yields $(4-2)x6x100=$ cases of Decile 3 yields $(4-3)x4x100=$400 The other 25 cases (Decile 4 or above) yield nothing. …leading to a total of $4300, and an average contribution of $98, which is the price of our put option. Later, a catastrophe bond, which may be issued to provide protection in the case of drought, will be described.

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 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 verification 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 verification data in determining the risk.

Using Forecast Verification 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 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. 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 $(43-38)x2x100=$ cases of 42 deg C yields $(42-38)x6x100=$ cases of 41 deg C yields $(41-38)x13x100=$ cases of 40 deg C yields $(40-38)x15x100=$ 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 $(43-38)x2x100=$ cases of 42 deg C yields $(42-38)x6x100=$ cases of 41 deg C yields $(41-38)x13x100=$ cases of 40 deg C yields $(40-38)x15x100=$ 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 $ 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 $ This represents an average contribution of $110 per case, which is the price of our option.

A Forecast Error Put Option (defining error as predicted minus observed) Strike: 0 deg C. Notional: $100 per degree of forecast error below 0 deg C If the forecast underestimates the actual temperature, then the seller of the option pays the buyer $100 for each 1 deg C of underestimation. - Historical simulation yields a suggested price of $67 for our put option. Strike: 0 deg C. Notional: $100 per degree of forecast error below 0 deg C If the forecast underestimates the actual temperature, then the seller of the option pays the buyer $100 for each 1 deg C of underestimation. - Historical simulation yields a suggested price of $67 for our put option.

Particularly Australian Applications Purchase of put contracts to protect against reduced rainfall, by a generator of hydroelectricity. Purchase of call contracts to protect against a sequence of very hot days. Purchase of variable degree day contracts to protect against very high temperatures. Purchase of guaranteed yield contracts (based on relationships between wheat yield & rainfall and temperature). Purchase of put contracts to protect against reduced rainfall, by a generator of hydroelectricity. Purchase of call contracts to protect against a sequence of very hot days. Purchase of variable degree day contracts to protect against very high temperatures. Purchase of guaranteed yield contracts (based on relationships between wheat yield & rainfall and temperature).

Ensemble Forecasting In order to obtain a measure of forecast uncertainty, there is an alternative to using historical forecast verification data. This is to use 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. In order to obtain a measure of forecast uncertainty, there is an alternative to using historical forecast verification data. This is to use 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.

Concluding Remarks The sophistication of weather-related risk management products is growing. Australia has joined this new market. In evaluating weather securities, one may use a variety of data types, and take into account climate trends. Ensemble forecasting is an alternative approach to determining forecast uncertainty. The sophistication of weather-related risk management products is growing. Australia has joined this new market. In evaluating weather securities, one may use a variety of data types, and take into account climate trends. Ensemble forecasting is an alternative approach to determining forecast uncertainty.

RecommendationsRecommendations In order to keep abreast of developments in this growing sector of weather services… - That the BoM join the Weather Risk Management Association. - That the BoM be represented at risk management conferences. - That the BoM develop a program of research into weather risk management. - That the BoM subscribe to a variety of risk management journals. In order to keep abreast of developments in this growing sector of weather services… - That the BoM join the Weather Risk Management Association. - That the BoM be represented at risk management conferences. - That the BoM develop a program of research into weather risk management. - That the BoM subscribe to a variety of risk management journals.