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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.
THE RISING GLOBAL TEMPERATURE
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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.
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PART ONE
Several issues raised by contributors to Tang (2005)
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CLIMATE CHANGE AND
THE 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.
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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.
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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
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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.
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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.
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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.
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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.
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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?
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DROUGHT
http://www.bom.gov.au/inside/eiab/reports/ar02-03/index.shtml
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FLOODS
http://www.bom.gov.au/weather/qld/charleville/images/cv9.jpg
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PART TWO
An application of financial market mathematics
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CASE STUDY
“The cost of climate change”
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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.
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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).
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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.
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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].
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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.
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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.
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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 value
H = 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 expiry
d1 = ((ln(S/X)+(R+2/2)T)/(T), d2 = d1-T, H = N(d1)
B = Xexp(-RT) N(d2)
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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.
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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.
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PROTECTING AGAINST
DIMINISHING INDUSTRIAL OUTPUT
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PROTECTING AGAINST
DIMINISHING INDUSTRIAL OUTPUT
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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).
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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.
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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. .
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PROTECTING AGAINST THE VALUE
OF A COMPANY DECLINING
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PROTECTING AGAINST VALUE
OF A COMPANY DECLINING
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PROTECTING AGAINST VALUE
OF 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.
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PROTECTING AGAINST VALUE
OF 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%
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PROTECTING AGAINST VALUE
OF 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.
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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.
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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
thence
To accelerate to reach about 15 cents in the dollar in 2003.
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THE GROWING COST OF
PROTECTION
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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.
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TRANSLATING CLIMATE FORECASTS
INTO DECISION MAKING.
Thank You
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