Harvey Stern Bureau of Meteorology

1. The application of financial market mathematics to translating climate forecasts into decision making. Harvey Stern Bureau of Meteorology 3rd International Conference on Climate Impacts Assessments (TICCIA) Cairns, Australia, 24-27 Jul., 2006.

2. THE RISING GLOBAL TEMPERATURE

3. INTRODUCTION Fund managers rate climate change as the second most important influence (after globalisation) on asset performance over the next five years (Mercer Investment Consulting, 2006). Increasingly, the application of financial market mathematics in the context of developing strategies to address the impact of climate change is becoming the subject of research (Tang, 2005). The presentation:Firstly, discusses several issues raised by contributors to Tang’s (2005) publication on the finance of climate change, and,Secondly, illustrates the application of some of these strategies with a case study presented to the 2005 Annual Meeting of the American Meteorological Society.

4. PART ONE Several issues raised by contributors to Tang (2005)

5. CLIMATE CHANGE ANDTHE FINANCE & INSURANCE SECTOR Climate change will affect the finance sector from lending to investing, and from advising to financing.While not as pronounced as the insurance sector with its direct impact on property and physical assets, nevertheless the impact on financial institutions could be far-reaching.Lending institutions need to include climate change systematically in their risk assessment procedures.Banks need to develop tools to quantify the risk management implications associated with their lending decisions. At present, there is an obvious lack of innovative financing instruments.

6. CLIMATE CHANGE AND CAPITAL Investing capital in emission reductions, carbon sequestration, and related clean technologies brings return in climate policy delivered as well as profits.Models can predict carbon market fundamentals with some accuracy.Just as companies are familiar with dealing with exchange rates, interest rates and commodity prices, so they will start managing the carbon market in a similar way and start hedging their risks.

7. POLICY CONDITIONS The key requirement for policy designed to promote renewable energy investment is that it is “loud, long, and legal”, to positively affect project bankability, and to reflect a strong governmental commitment to delivery in this arena:. A solid (legal) basis for long-term contracts. Conditions that lead to big, liquid markets, if using tradeable market incentives. Implementing a clear process for planning and approval. Tackling existing subsidies, and other distortions in the market. A strong compliance regime

8. RENEWABLE ENERGY The investment models that support coal and oil are so well established and profitable that renewables with lower immediate returns are not considered bankable.While the risk of committing to the purchase of carbon credits is limited, these funds are not able to finance the development phase of projects.There are some funds that will offer a partial prepayment against future credits, but this is typically only a small percentage of the overall capital cost of a project.

9. COMMODIFYING CARBON Most carbon assets are based on a common unit of 1 tonne of carbon dioxide reduced or sequestered, or an allowance to emit 1 tonne of carbon dioxide.The carbon asset is becoming a material consideration in the expected rate of return of projects and, ultimately, the financial worth of companies that are involved in projects that create such assets ( for example, renewable energy companies or sustainable plantation developers).Emission reduction projects have an ability to create a carbon asset that has real value to investors for compliance purposes or as a source of additional revenue.

10. SECURING INVESTMENT A cornerstone of the Kyoto Protocol is that it should stimulate foreign investment in “green technologies” in developing countries, thus encouraging alternatives to fossil-fuel driven growth. Because Carbon Dioxide abatement costs among OECD countries can range from 5 to 30 times that of developing countries, these offset instruments also provide a low-cost source of “carbon credits” to carbon-constrained buyers.

11. LIABILITY - ATTRIBUTION The distinction between weather and climate is important because it it is impossible in principle, because of the chaotic nature of the weather, to associate a particular weather event with externally driven climate change.A change in climate can result directly in financial losses when the losses in question result directly from changes in weather-related risk, rather than from events that actually occur.This assumes a perfectly informed and rational market response to changing risk.

12. LIABILITY - IMPLICATIONS Climate change is often cited a a paradigmatic example of market failure.The climatic impacts of GHG emissions occur decades to centuries after the emissions occur.It is often taken for granted that the only solution is either a mandatory cap- and trade- system or heavy government intervention in technology research and development in order to steer energy markets away from fossil fuels.However, by the late 2020s, more than half the excess carbon dioxide will be due to emissions made after 1990 (when the consequences of the emissions began to be accepted).Will this allow a litigation based approach to the social cost of carbon?

13. DROUGHT http://www.bom.gov.au/inside/eiab/reports/ar02-03/index.shtml

14. FLOODS http://www.bom.gov.au/weather/qld/charleville/images/cv9.jpg

15. PART TWO An application of financial market mathematics

16. CASE STUDY “The cost of climate change”

17. INTRODUCTION In a 1992 paper presented to the 5th International Meeting on Statistical Climatology (Stern, 1992), the author introduced a methodology for calculating the cost of protecting against the onset of global warming. The paper, 'The likelihood of climate change: A methodology to assess the risk and the appropriate defence', was presented to the meeting held in Toronto, Canada, under the auspices of the American Meteorological Society (AMS). In this first application of what later was to become known as 'weather derivatives', the methodology used options pricing theory from the financial markets to evaluate hedging and speculative instruments that may be applied to climate fluctuations.

18. INTRODUCTION Two illustrative examples were presented, namely, protecting against the risk of diminishing industrial output associated with global warming; and, protecting against the risk of decreasing value of a company likely to be adversely affected by global warming (e.g. a manufacturer of ski equipment). Use of these financial instruments leads to those concerned being compensated provided they are on the correct side of the contract. Conversely, those on the wrong side of the contract would have to provide that compensation.The methodology provided a tool whereby the cost of the risk faced can be evaluated (whether it is the case of determining that risk on a global scale, or on a company specific scale).

19. INTRODUCTION Published data from the Carbon Dioxide Information Analysis Center were used in the evaluation. Since the early 1990s, the global mean temperature has risen significantly, and the methodology was 'revisited' in a 2005 paper presented to the 16th Conference on Climate Variability and Change at the AMS Annual Meeting of that year (Stern, 2005), with a view to recalculating the cost taking into account the additional, more recent, data.The same examples were used in 2005 as were used in the 1992 study.

20. PURPOSE Using a data set of land, air, and sea surface temperature anomalies from the United Kingdom Meteorological Office the purpose of the current work is to determine to what extent the cost of protection may have been rising[the data set is accessible at http://www.met-office.gov.uk/research/hadleycentre.html].

21. METHODOLOGY Firstly, one regards the global mean temperature (GMT) in the same manner as one would a financial commodities futures contract and values it, and associated options, accordingly.On this basis the theoretical value of a GMT futures contract will equal the dollar equivalent of the current GMT (for example, the theoretical value of a GMT futures contract, when the GMT is 287.79K, would be $287.79). Secondly, one assumes that GMT futures contracts are available to be bought and sold.

22. METHODOLOGY One also assumes that associated put and call option contracts are available to be written or taken, and so alter the risk-return characteristics associated with the GMT contract. The strategy, therefore, is to establish the economic consequences of movements in the GMT. These economic consequences are then applied across the complete range of scales; that is, from the global economy down to the smallest company.

23. CALCULATION Utilising the Black and Scholes (1973) call option formula, as modified for future style options (Gastineau, 1988)C = HS – B, where C = call option valueH = N(d1), where N( ) is the cumulative standard normal distribution function. S = price, X = strike, R = interest rate = standard deviation of returns (volatility)T = time to expiryd1 = ((ln(S/X)+(R+2/2)T)/(T), d2 = d1-T, H = N(d1)B = Xexp(-RT) N(d2)

24. GASTINEAU’S MODIFICATION Gastineau (1998) proposes a "future style option" contract to replace many conventional options on futures contracts where:"unlike with conventional options, the buyer of the futures style option does not prepay the premium.Buyers and sellers post margin as in a futures contract, and the option premium is marked to the market daily.Valuation differs from conventional options primarily in the analysis of cash flows associated with the buyer's premium non-payment". For this reason one employs the assumption of an interest rate of 0% in the calculation.

25. PROTECTING AGAINST DIMINISHING INDUSTRIAL OUTPUT Hypothetical Example 1 scenario:Assume that the rate of increase in industrial output is unaffected by global warming as the GMT rises, until the temperature reaches 289.34K. A temperature increase from this point is assumed to adversely affect industrial output, causing it to decline in a linear manner as GMT rises further to 290.34K.At this point the annual rate of increase in industrial output is zero. Continued rise in GMT from this point is assumed to lead to an adverse effect increasing at the same rate.So, by the time the GMT 291.34K, the rate of decline in global industrial output is equivalent to the current rate of increase.

26. PROTECTING AGAINST DIMINISHING INDUSTRIAL OUTPUT

27. PROTECTING AGAINST DIMINISHING INDUSTRIAL OUTPUT

28. PROTECTING AGAINST DIMINISHING INDUSTRIAL OUTPUT Protecting against hypothetical Example 1 scenario:Calculate the cost of an American call option contract on the value of a futures GMT contract with the following characteristics (protection is required for 100 years – expiry date):Spot = Current GMT (this is regarded as the GMT for the most recent year, 2003, which has a value of 288.49K)Strike = 289.34K Standard Deviation of Returns (Volatility) = 0.000436 (based on the United Kingdom Meteorological Office data series) Interest rate = 0% (assuming that the only money which changes hands is that associated with variation margins).

29. PROTECTING AGAINST DIMINISHING INDUSTRIAL OUTPUT Calculation for protecting against hypothetical Example 1 scenario:Utilising the Black and Scholes (1973) call option formula, as modified for future style options (Gastineau, 1988), the calculation yields:$0.1878 for 2003.So, for protection under the aforementioned assumptions:The full cost of protection is $18.78 for every $100 of the future rate of industrial growth, or 18.78% of that rate of industrial growth.

30. PROTECTING AGAINST THE VALUE OF A COMPANY DECLINING Hypothetical Example 2 scenario:Assume that the value of the company (a manufacturer of ski equipment) is unaffected by global warming as the GMT rises, until the temperature reaches 289.34K.A temperature increase from this point is assumed to adversely affect company value, causing it to decline in a linear manner as GMT rises further to 290.34K.At this point the value is reduced to zero.Continued rise in GMT from this point has no further effect upon the company's value, as it cannot decline in value below zero. .

31. PROTECTING AGAINST THE VALUE OF A COMPANY DECLINING

32. PROTECTING AGAINST VALUEOF A COMPANY DECLINING

33. PROTECTING AGAINST VALUEOF A COMPANY DECLINING Protecting against hypothetical Example 2 scenario:This is equivalent to calculating the difference between the cost of the following two American call option contracts on the value of a futures GMT contract with the following characteristics (protection is required for 100 years – expiry date) :First contract (bought)-This is the same contract as the one valued in Section 5.2, hence, its value is $0.1878.

34. PROTECTING AGAINST VALUEOF A COMPANY DECLINING Second contract (sold)-Spot = Current GMT (this is regarded as the GMT for the most recent year, 2003, which has a value of 288.49K)Strike = 290.34K Standard Deviation of Returns (Volatility) = 0.000436 (based on the United Kingdom Meteorological Office data series) Interest rate = 0%

35. PROTECTING AGAINST VALUEOF A COMPANY DECLINING Calculation for protecting against hypothetical Example 2 scenario:Utilising the Black and Scholes (1973) call option formula, as modified by Gastineau (1988) for futures contracts, the calculation yields $0.0399 for the second contract.So, the cost of protection is the cost of the first contract (which is bought) minus the cost of the second contract (which is sold), namely, $0.1479, or 14.79% of the future value of the company.Note again that no money changes hands initially, and it is possible that only at the end of the options' life will settlement occur.So, for protection under the aforementioned assumptions, the full cost of protection is $14.79 for every $100 of the future value of the company.

36. THE GROWING COST OF PROTECTION The outcomes of calculations for the two examples from 1861 to 2003: They show, in the case of protecting against the risk of reduced industrial output: That the cost has risen from about 4 cents in the dollar circa 1860, To about 9 cents in the dollar 100 years later (circa 1960), and thence To accelerated to reach about 19 cents in the dollar in 2003.

37. THE GROWING COST OF PROTECTION They show, in the case of protecting against the risk of the value of a company declining:That the cost has risen from about 3 cents in the dollar circa 1860, To about 7 cents in the dollar 100 years later (circa 1960), and thenceTo accelerate to reach about 15 cents in the dollar in 2003.

38. THE GROWING COST OF PROTECTION

39. CONCLUSION A methodology for calculating the cost of protecting against the risk of financial loss associated with global warming has been presented.It has been shown - Both in the case of protecting against the risk of reduced global industrial output, And also in the case of protecting against the risk of the value of a company declining,That the cost of that protection has risen over the years, and that the rate of that rise has accelerated recently.

40. TRANSLATING CLIMATE FORECASTS INTO DECISION MAKING. Thank You