1. Managing Weather Risk Dr Harvey Stern, Bureau of Meteorology, Australia Dr Harvey Stern, Bureau of Meteorology, Australia

2. 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)

3. Outline of Presentation Viewing weather & climate (anomaly) forecasts as risk management tools. Applying weather derivatives. Utilising forecast accuracy & weather pattern data bases. Ensemble forecasting - a new improved approach to weather risk management. Viewing weather & climate (anomaly) forecasts as risk management tools. Applying weather derivatives. Utilising forecast accuracy & weather pattern data bases. Ensemble forecasting - a new improved approach to weather risk management.

4. 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 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 that has, so far, taken best advantage of the growing weather-risk market.

5. BackgroundBackground 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. 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.

6. Weather & Climate Forecasts Weather forecasts provide specific detail as to what one might expect over the next few days. Climate (anomaly) forecasts indicate how the forthcoming month’s (or season’s) conditions might depart from normal. Weather forecasts provide specific detail as to what one might expect over the next few days. Climate (anomaly) forecasts indicate how the forthcoming month’s (or season’s) conditions might depart from normal.

7. Forecasts and Risk Management 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). These forecasts are based on a combination of solutions to the fundamental equations of physics, and some statistical techniques. 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). These forecasts are based on a combination of solutions to the fundamental equations of physics, and some statistical techniques. With the focus upon managing risk, the forecasts are increasingly being couched in probabilistic terms.

8. 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.

9. SecuritisationSecuritisation 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.

10. Catastrophe Bonds Catastrophe bonds are examples of securities that are issued to provide capital in case of a catastrophic event. Investors purchase bond from the issuer, and funds provided by investors are deposited into a trust account. The issuer similtaneously enters into a contract (with an insurer) that gives protection in the event of a such an event. Earnings on initial deposit (+ insurance premium) are periodically paid as bond coupon to the investors. Catastrophe bonds are examples of securities that are issued to provide capital in case of a catastrophic event. Investors purchase bond from the issuer, and funds provided by investors are deposited into a trust account. The issuer similtaneously enters into a contract (with an insurer) that gives protection in the event of a such an event. Earnings on initial deposit (+ insurance premium) are periodically paid as bond coupon to the investors.

11. Investor Outcomes for the Catastrophe Bond If no (qualifying) event during the period, the principal amount is returned to investors with their final coupon payment. - under this scenario, investors receive a high rate of interest, and have also retained their original investment. If there is an event during the period, amount due is to the issuer is paid, and the balance is returned to investors. - under this scenario, investors receive a high rate of interest, but have lost part (or all) of their original investment. If no (qualifying) event during the period, the principal amount is returned to investors with their final coupon payment. - under this scenario, investors receive a high rate of interest, and have also retained their original investment. If there is an event during the period, amount due is to the issuer is paid, and the balance is returned to investors. - under this scenario, investors receive a high rate of interest, but have lost part (or all) of their original investment.

12. Issuer Outcomes for the Catastrophe Bond If no (qualifying) event during the period, the principal is returned to investors with their final coupon payment. - under this scenario, the issuer provides a high rate of interest, but has not had to pay-out for an event. If there is an event during the period, the amount due to the issuer is paid, and the balance is returned to investors. - under this scenario, the issuer provides a high rate of interest, but has been able to pay-out (to the insurer) for the event. If no (qualifying) event during the period, the principal is returned to investors with their final coupon payment. - under this scenario, the issuer provides a high rate of interest, but has not had to pay-out for an event. If there is an event during the period, the amount due to the issuer is paid, and the balance is returned to investors. - under this scenario, the issuer provides a high rate of interest, but has been able to pay-out (to the insurer) for the event.

13. Weather Derivatives Weather derivatives are other examples of financial instruments 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 other examples of financial instruments 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.

14. 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.

15. An Early Example (cont.) The cost of a call option contract on the value of a Futures Global Mean Temperature (GMT) contract was calculated. In determining the cost, the volatility of the GMT, calculated over 130 years of data, was applied. One application given was that of the cost of protecting against diminished industrial output as a consequence of global warming. Another application was protecting against decreased value of a manufacturer of ski equipment as a consequence of warming. The cost of a call option contract on the value of a Futures Global Mean Temperature (GMT) contract was calculated. In determining the cost, the volatility of the GMT, calculated over 130 years of data, was applied. One application given was that of the cost of protecting against diminished industrial output as a consequence of global warming. Another application was protecting against decreased value of a manufacturer of ski equipment as a consequence of warming.

16. 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”.

17. 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.

18. Pay-off Chart for the CDD Call Option

19. 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).

20. 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.

21. Gentle Long-term Trends Some weather elements have trended only gently. Nevertheless, these trends still need to be considered when valuing weather securities. The trend in Melbourne maximum temperature is shown here. Some weather elements have trended only gently. Nevertheless, these trends still need to be considered when valuing weather securities. The trend in Melbourne maximum temperature is shown here.

22. Elements that have not Trended Other weather elements have not trended, merely having undergone fluctuations due to natural variability. The example below shows the fluctuations in Melbourne rainfall. Other weather elements have not trended, merely having undergone fluctuations due to natural variability. The example below shows the fluctuations in Melbourne rainfall.

23. Cooling Degree Days (1855-2000) The chart shows frequency distribution of annual accumulated Cooling Degree Days at Melbourne using all data:

24. Cooling Degree Days (1971-2000) The chart shows frequency distribution of annual accumulated Cooling Degree Days at Melbourne using only recent data:

25. Pricing the CDD Call Option The two CDD frequency distributions are quite different. Utilising the different data in valuation results in different prices. Utilising 1855-2000 data yields a price thus: $(.051x2500+.045x7500+.008x12500)= $565.00 Utilising 1971-2000 data yields a price thus: $(.238x2500+.119x7500+.029x12500)= $1850.00 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 1855-2000 data yields a price thus: $(.051x2500+.045x7500+.008x12500)= $565.00 Utilising 1971-2000 data yields a price thus: $(.238x2500+.119x7500+.029x12500)= $1850.00 The more recent frequency distribution should provide a more relevant result.

26. 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.

27. Pay-off Chart for Decile 4 Put Option

28. 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.

29. Evaluating the Decile 4 Put Option 9 cases of Decile 1 yields $(4-1)x9x100=$2700 6 cases of Decile 2 yields $(4-2)x6x100=$1200 4 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=$2700 6 cases of Decile 2 yields $(4-2)x6x100=$1200 4 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.

30. 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.

31. 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.

32. 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.

33. Pay-off Chart: 38 deg C Call Option

34. 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.

35. Historical Distribution of Outcomes

36. 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…. 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….

37. 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. 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.

38. 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. 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.

39. Evaluating the Forecast Error Put Option Historical simulation yields a suggested price of $67 for our put option. Does today’s error influence the price? Does tomorrow’s expected weather pattern influence the price? Historical simulation yields a suggested price of $67 for our put option. Does today’s error influence the price? Does tomorrow’s expected weather pattern influence the price?

40. Answering the First Question Today’s error does influence the price. If today’s forecast is an underestimate, then tomorrow’s is also likely to be, leading to a suggested option price of $75. If today’s forecast is an overestimate, then tomorrow’s is also likely to be, leading to a suggested option price of $41. Today’s error does influence the price. If today’s forecast is an underestimate, then tomorrow’s is also likely to be, leading to a suggested option price of $75. If today’s forecast is an overestimate, then tomorrow’s is also likely to be, leading to a suggested option price of $41.

41. Answering the Second Question Tomorrow’s weather pattern does influence the price. If tomorrow’s weather pattern is moderate anticyclonic NNE, tomorrow’s forecast is likely to be underestimated, leading to a price of $77. If tomorrow’s weather pattern is strong anticyclonic NNE, tomorrow’s forecast is likely to be overestimated, leading to a price of $47. Tomorrow’s weather pattern does influence the price. If tomorrow’s weather pattern is moderate anticyclonic NNE, tomorrow’s forecast is likely to be underestimated, leading to a price of $77. If tomorrow’s weather pattern is strong anticyclonic NNE, tomorrow’s forecast is likely to be overestimated, leading to a price of $47.

42. Improved Forecast Methodologies for Risk Assessment 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 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. 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 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.

43. Concluding Remarks The sophistication of weather-related risk management products is growing. In evaluating weather securities, in particular weather derivatives, one needs to use historical weather data and forecast verification data, and also to take into account climate trends. Ensemble forecasting is a new approach to determining forecast uncertainty. The sophistication of weather-related risk management products is growing. In evaluating weather securities, in particular weather derivatives, one needs to use historical weather data and forecast verification data, and also to take into account climate trends. Ensemble forecasting is a new approach to determining forecast uncertainty.