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Weather Derivatives
-Kaushank Khandwala
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Weather Derivatives an Introduction
Weather has significant influence on many commercial businesses. Many businesses are
impacted positively or unfavorably by weather. For this reason, new set of weather risk
protection instruments called weather derivatives have emerged.
A derivative is a contract whose value depends on the value of underlying variable. The main
types of derivatives are futures, forwards and options. Derivatives are primarily used as
hedging instruments, though they also find place in speculation and arbitrage. Most common
underlying instruments are stocks, bonds, or commodities. In case of weather, the underlying
variable could be average Temperature, precipitation, snow fall or wind.
Weather derivatives are instruments used to reduce risk associated with unanticipated weather
movements. For example: A shopping mall in a snowy area may use weather derivatives to
stabilize its earnings
Weather derivatives v/s Weather Insurance
Weather derivatives cover low-risk, high-probability events. Weather insurance, on the other
hand, typically covers high-risk, low-probability events, as defined in an insurance policy. For
example, a company might use a weather derivative to hedge against a summer 3° more than
the average (a low-risk, high-probability event). In this case, the company protects its revenues
from adverse future weather. But the same company can purchase an insurance policy for
protection against damages caused by a (typhoon)(high-risk, low-probability events)
Weather Derivatives History and Major Exchanges
Historically, the first weather derivative transaction was contracted in July 1996. Aquila
Energy entered a commodity transaction with Consolidated Edison Co. This involved purchase
of electric power in August from Aquila. Consolidated Edison was to be offered a rebate if
August was cooler than predicted. These predictions were based on Cooling Degree Days
measured at New York City's Central Park weather station.
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Weather derivatives slowly began trading over-the-counter in 1997. As the market for these
products grew, the Chicago Mercantile Exchange introduced the first exchange-traded weather
futures contracts (and corresponding options), in 1999. The CME currently trades weather
derivative contracts for 18 cities in the United States, nine in Europe, six in Canada and two in
Japan. Most of these contracts track cooling degree days or heating degree days, but recent
additions track frost days in the Netherlands and monthly/seasonal snowfall in Boston and New
York.
In USA, weather derivatives are traded in the Chicago Mercantile Exchange (CME). In 2006,
traded CME Weather derivatives had a notional value of $22 billion. In Europe, London
International Financial Futures Exchange (LIFFE) is a major exchange for Weather Derivatives
London. LIFFE traded Weather derivatives had an estimated notional value of $9billion.
In Japan, Weather Derivative products are not exchange -traded in Tokyo stock Exchange.
Most of the contracts are Over-the-counter. The Japanese market for weather derivative
products (OTC temperatures, snowfall) grew a third to about 80 billion yen ($680 million) in
the year to April 2007. Japan's TIFFE is believed to start trading weather derivatives in early
2009.1
Modeling Weather Derivatives
Weather Derivatives are recent class of financial instruments. There are few widely accepted
pricing and modeling methodologies for such instruments. Here we explore Black Scholes
Model, Burns model and Monte Carlo Simulations for weather derivatives.
Black Scholes Model
Black Scholes Metron Model (BSM) is used to price derivative options.
Standard Black-Scholes Formula’s Inputs
1
•
S = Underlying Asset Price
•
X = Strike Price
•
T = Time before Maturity
•
σ = Volatility
•
R = Risk Free Rate
http://www.energyrisk.com/public/showPage.html?page=166714
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BSM model has many assumptions which do not apply to weather variables and so cannot
be used to price weather derivatives. BSM Model is probably inadequate because of
following reasons:2
1.Weather does not “walk” quite like an asset price. In BSM, asset price can theoretically
move from 0 to infinity. Weather variables such as temperature in general fall within a
narrow bands because of mean –reversion tendency.
2.Weather is partially predictable in the short-run and partially random around the
averages in the long run. So, it is not completely “random”.
3.Underlying variables (e.g. snow fall) are not tradable and market for weather
derivatives are illiquid, so pricing cannot be free of economic risk aversion factors.
4.Black Scholes option payoff depends on the asset value at expiration. Weather
derivatives would require average value of the variable and are more “Asian” in nature.
5.Many Weather derivatives are capped in pay-off, unlike the standard Black-Scholes
option.
“Seeking a Standard Pricing Model”, Financial Engineering associates, Environmental Finance, March
2000
2
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Burn Analysis
Burn Analysis are simulations based on Historical Data. Using historical data, we can
determine the expected payoff every year. The fair price of the option would be the average
of the historical payoffs. Burn Analysis is widely used by insurance companies. Main steps
involved are:
1. First, collect the historical data
2. Make adjustments to make the data comparable across different periods
3. Create an appropriate variable such as (Snow Depth/Fall, precipitation index)
4. For every year in the past, determine the option payoff.
5. Find the average of these payoffs.
6. Discount them to settlement date.
There are some problems in Burn Analysis:
1. Burn Analysis does not account for weather forecasting. Over a period of time, weather
variables change. Even though, we assume mean-reversion behavior for weather variables,
weather models /forecasts should be a part of analysis to obtain value.
2. Weather is local to a region. Gathering historical data can be cumbersome process and
authentic weather need not be always available. Even when data is available, there are
possible gaps and errors. The historical data must be adjusted before they are used for burn
analysis.
3. It is quite tricky to consider the historical period. A city, town or village may undergo
urbanization wherein due to heavy industrialization and construction, the weather grows
warmer over time. These trends must be accounted for when pricing the option.
Monte Carlo Based Simulations
Monte Carlo is a simulated method of generating random numbers. Monte Carlo simulations
provide a convenient way to contract and price derivatives.
This process can be used to statistically construct weather scenarios. For Monte Carlo
simulations, it is important to choose the right model for the random walk of weather variable.
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In general, weather variables follow mean reversion. Models that only assume pure random
walk behavior are not suitable.
Monte Carlo typically involves generating a large number of simulated scenarios to determine
possible payoffs for the instrument. The fair price of the instrument is the average of all
simulated payoffs, which is appropriately discounted to settlement date.
Drawbacks:
Monte Carlo process is very computationally intensive. Using stochastic or statistical weather
models is complicated as there are many variables involved. Many trials would be required to
arrive at a fair price.
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Weather Derivative Structures:
Typical Weather Derivative Structures include Put/Call with Caps/Floors, Weather Swaps and
Collars. The coming section would describe these with examples.
Call and Put Options with a Maximum Payoff (CAP)
Capped option is an option with a pre-established profit cap. A capped option is automatically
exercised when the underlying security closes at or above (for a call) or at or below (for a put)
the Option's cap price. Weather Derivatives typically have such structures wherein there is an
upper limit on profit which can be obtained based on the movement of underlying variable.
Example The city council of a town has spent $3mn to remove 10 cm of snow. The city office
estimates that additional inch of snow causes an increase of $250,000 of snow removal costs.
Solution: A Snowfall calls option which pays $250,000 per inch of snowfall above a strike of
10 cm to a maximum of 20 cm.
5.0
Period = Nov-Mar
Strike = 10 cm
Limit = 20 cm
Tick= $250,000
Limit = $4,000,000
Removal Cost (Millions)
Call Option Features
4.5
Unhedged Costs
4.0
3.5
3.0
Hedged Costs
Price = $500,000
2.5
9
12
Inches of Snow
15
18
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Weather Swaps
A swap instrument combines a call and put option with the same strike. Weather Derivative
Swaps can provide revenue stability as depicted by the following example:
A leading Power company in Japan and Gas Company entered a contract for the period
August-Sept 2001 for a temperature return swap. The underlying variable was temperature with
base (standard temperature) at 26℃. Power Company purchased a PUT option with strike at
25.5℃ and the Gas company purchased Call option at 26.5℃.The profit /payoff diagrams are
as shown below.
Power Company
Gas Company
Fluctuation of Profit
return
No-payment
-2.0
-0.5
No-payment
+0.5
+2.0
Payments
Low
Average Temp.
High
-2.0
-0.5
+0.5
Return
+2.0
Payments
Low
Average Temp.
Time frame
August 1,2001 – September 30,2001
Index
Average temperature (SYNOP Tokyo）
Standard Temp.
Approx. 26℃
Put strike
Standard Temp.-0.5℃
Call strike
Standard Temp. +0.5℃
Maximum payment
Approx.\700,000,000-
Actual temp.
24.8℃
Actual payoff
TEPCO received approx.\320,000,000-
Contract between power company and Gas company for total return swap
High
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Situation in Minami Uonuma City
Minamiuonuma city is situated in a valley in a mountainous region of Niigata Prefecture
The city is bounded by Uonuma city and the Echigo-Sanzan mountains in the north, and
Yuzawa, a popular ski resort town, in the south. The Uono river flows through most of the
city. It is known as “Snow Country” (Yuki Guni) because of the heavy snowfall in winter.
Minami Uonuma City has 4-5 months of heavy snow fall. The region has many ski resorts.
Snow significantly impacts the business and livelihoods of individuals and corporations in this
region favorably or adversely. The region is famous for its rice production and also ski tourism.
For our Project, we present a detailed analysis of snow fall, potential impact on snow removal
companies and Minami Uonuma City office and potential weather derivative products.
We interviewed and collected data from Minami Uonuma City office and leading snow
clearing companies for the last 15 years.
Our Methodology:
Main Steps in our project were:
1. Identification of potential businesses directly affected by snow fall
2. Interviewing of a few of these businesses and collecting data
3. Analysis of snow depth or snow fall data in surrounding data
4. Choosing the correct underlying variable for our weather derivative product
5. Analysis of the financial impact of variable/extreme snow fall for businesses
6. Exploration of appropriate Weather Derivative products based on Snow fall
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The following table depicts the businesses impacted favorably or unfavorably by snow fall.
Businesses impacted Positively by
Businesses impacted negatively by
extreme Snow fall
extreme Snow fall
1. Tourism, Ski industries
•
Hotels
•
Resort operators
•
Ski equipment sellers
2. Retailers
1.Retailers,Supermarkets
2.Construction Companies
Winter goods sellers
3.Community-based shops
3. Agriculture (need to secure water
supply)
4. Road Transportation
5.Amusement Industries :Pachinko shops,
4. Snow Removal Business
(construction companies)
arcades
6. City Governments
Ski resorts are primarily dependent on tourists from Kanto region and abroad for their revenues.
Heavy Snowfall is favorable for many tourism dependent businesses. On the other hand,
construction businesses, retailers and road transportation prefer low snowfall. Also, agriculture is
significantly impacted by the duration and snowfall depth. Heavy Snowfall would mean a delay in
the harvesting season since snow would require more time to melt and clear off.
For our project we interviewed Uonuma City government, Retailer (AEON) and a leading snow
removal company. We also collected data from them about the snow fall and the cost budget for the
last 15 years.
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Findings from Interview with Minami Uonuma City office, and Snow
removal company:
From our survey, we could find that the snow removal activities are carried out by
construction companies and businesses in Minami Uonuma region. In fact, the president of
a leading construction company quoted ““In winter, we rely on snow removal business”.
Construction companies have the following main advantages to engage in snow removal business:
1. In winter the constructions business is minimal. Engagement in snow removal business
provides a good opportunity in winter months.
2. Employees at construction companies are familiar with operating machines for snow removal.
3. Employees at construction companies have drivers license of large-size car. So the employees
can be directly deployed in snow removal activities.
Types of Snow Removal businesses:
1
Type
Client
Road Maintenance
Government (s)
Avalanche Patrol
Government (s)
2
(Elimination of Avalanche Risk)
3
Maintenance of Snow-Covered Roofs
Individuals
4
Motor Park Maintenance
Private Companies
5
Piste Maintenance
Ski Resorts
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There are 5 main types of snow removal businesses that these companies engage in. Details
are shown in the table above. Road maintenance is the biggest business. City government
and municipalities are the clients. Avalanche patrol is also done by construction companies
to eliminate or mitigate avalanche risk. The Snow removal companies do Motor Park
maintenance and maintenance of snow-covered roofs for individuals and private companies.
Piste refers to a designated path down a mountain for snow sports. Minami Uonuma Area
has many ski resorts. Maintenance of the Piste is done by Construction companies.
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Issues with snow removal business:
Forecasting of snow fall:
We interviewed the President of a leading Snow removal company (Anonymity requested).
As per our interview, we found that it is almost impossible to forecast how snowfall they
would before winter season. However, the amount of snow fall tends to fall within the
certain range. For example, if November and January had more snowfall than average,
February and March tend to have less snowfall.
Regarding short-term (daily, weekly) forecast, the company uses 1) isopiestic line, 2)
aerotonometer and 3) meteorological chart at Noto area to alert and station work force for
snow removal activity.
Wage costs:
For a snow removal company, fuel costs and labour costs are the major cost drivers.
Sales= (wage rate contracted with city office) x (working hours). Working hours could be
affected by snow fall, whereas wage rates have been pushed down by city office recently.
Thus, the president suggested that it will be meaningless if we simply compare sales with
snowfall. We should consider the wage rate paid by city office.
Construction companies usually sign a contract with city office one year before snow season.
Fluctuations in fuel price can affect profitability during this period.
We try to investigate suitable hedging techniques using weather derivatives for the road
construction business. In the next section we will describe analysis of snow data followed
by investigation of suitable derivative structures.
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Analysis of Snow data to determine the underlying variable:
We had this challenge of deciding the correct and most suitable underlying variable for our
weather derivative product. From the limited data (we got detailed data from City office
only); we had 2 options for choosing the underlying variable: i) snow fall; ii) snow depth.
We decided to take “snow fall” as our underlying for mainly 3 reasons:
a) Strong correlation:
We tried to find out which one is better correlated to the cost figures. Below graphs show
the trend of snow fall and the snow removal expenses. These trends look very similar
which means snow removal costs are directly proportional to the snow fall. Statistically, we
verified this hypothesis by correlating the 2 variables (cost and snow fall).
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As shown below we found a strong correlation (Coefficient of Determination = 0.929)
between snow fall and the removal cost. So we decided to take snow fall as our underlying
variable.
E xpens e (millions )
250
200
150
100
50
-5 0
0
200
400
600
800
1000
S now Fall (cm)
b) Nature of business and budgeting:
We also looked at the nature of business and the budgeting process. The snow removal
companies are usually commissioned to start removing the snow as soon as the snow fall
reaches 10 cams on the road and 20 cms on the footpath. So cash transaction between the
counterparties (city office and snow removing companies) is usually more dependent on
the snow fall rather than snow height.
c) Clarity in Measurement system:
We also found that snow fall is easy to measure and easily agreeable between parties. Snow
depth can be confusing. There might be snow depth even if there is no snow fall on one day.
Snow depth will be very complex to measure and structure as an underlying.
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After deciding the underlying variable as ‘snow fall’, we hit the another road block. If we
should take the “total snow fall” or the “total snow days” as our underlying variable. Here
we would like to clarify the meaning of “total snow days”. Total snow days are the days
when the snow fall is more than 10 cms. When the city office pays to the snow removal
companies, it usually uses snow days as the criteria of payment. So we were also tempted
to take the “total snow days” as our underlying. When we looked at the trend of both these
variables with that of the snow removal expenses (as shown below), they both looked
similar, so it was difficult to decide. Then we employed Burn analysis to see the payoff
patterns for these two variables.
When we did Burn analysis, we found that for the past years if we take “total snow days”,
the error (difference between the actual payment and the calculated payment from Burn
analysis) was far more than that of “total snow fall”. The error in case of total snow days
was 13.9 mil yen and in case of total snow fall was 6.6 mil yen. So, we decided to choose
“total snow fall” in cm as our underlying variable.
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Shiozawa Expense vs. Total Snow Fall
D a y s S n o w F a ll
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Shiozawa Expense vs. Total Snow Days
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Our main pricing methodology is Burn’s model which is a historical approach. So before
applying the model, we wanted to check the data- how the snow removal cost is behaving.
When we plotted the snow removal cost with year, we found that the volatility is increasing
as clear from the below graph. As expected the cost would be proportional to the snow fall.
We wanted to know then how the cost per cm of snow behave.
Total Snow Removal Cost (in Yen, Shiozawa Area)
2000
1800
1600
1400
1200
1000
800
600
400
200
0
1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
- 18 -
The slow increasing trend(shown below) of unit snow removal cost was not a big surprise.
Although we did not do a complete analysis of the factors responsible for this trend. We
believe that the increasing energy price, wage rate and inflation might be possible reasons.
Cost of Removal of 1cm of snow
300,000
E xpense (millions)
250,000
200,000
150,000
200
150
100
50
100,000
-
50,000
0
10
20
30
-5 0
0
Days S now F all
1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
The observations from the snow fall and snow removal cost trend analysis can be
summarized as follows:
 The trend is a slow increasing trend indicating that the cost of snow removal has
been increasing more or less steadily
 One myth is broken: If this year it snows heavy, next year it will snow less. This fact is
quite clear from the snow fall graph above. For example please notice
 Volatility of snow removal cost is increasing.
 Trend is similar to total snow fall. This is quite expected.
 Rate of increase is more than that of the snow fall probably because of the increasing other
cost (Petroleum).
- 19 -
Pricing Assumptions
Base on the model analysis, we chose the simplest model for pricing the proposed weather
derivative. We thought that beside being simple and less time consuming, Burn’s model will
give us a good starting point in fixing the price. As we know pricing has many dimensions
amongst which supply and demand condition is probably the most important. But in this
project we have tried to find out the indicative price or the cost plus basis which gives us a
break even opportunity.
Here we give an example of Burn model approach. Burns Model is based on Historical data
analysis. Price of the Option should equal to Average Payoff. For Example: If two years ago seller
pay 10M Yen and last year we pay 5M Yen, Option price should equal to 7.5 M Yen
Before we proceed, we fix our assumptions as follows:
1. Underlying: “Total Snow Fall in cm for Winter (Dec to Mar)”
2. Snow fall: Uncertain and Difficult to forecast
3. Snow removal cost: increasing at a linear rate of 3 %. But we have ignored this increase for
simplification in our calculations.
4. Snow measurement source is City Office
5. Snow removal Area in Shiozawa is constant
6. IUJ will act as an intermediary for Weather derivative products, matching the demands for
customers.
7. We have ignored time value of money for simplification of the price calculations.
- 20 Pricing Result:
The counterparty would expect to be compensated at the rate of 0.22 Million Yen per one cm
of snow above strike value of 995 cm of snow fall. After applying Burn’s model we found that
the break even Option Price should be 27.4 Millions Yen.
- 21 -
Exploring Product Structures:
We have tried 3 simple product structures for our project namely a) Call and Put Options, b) Call
and Put with a Cap for Call, c) Forward. We know that the swap is like a series of forward contracts.
So, the forward contract can be modified to swap structure easily if the counterparties agree to take
a multiple year contract. Interestingly IUJ’s role and risk profile will vary depending on the
selection of the product structure.
a) Call and Put Options
The idea here is that city government (known as Party A for our project) wants to hedge against the
adverse effect the heavy snow fall as it has to spend more for cleaning the snow. So party A wants a
call options where in the extra cost incurred will be compensated by the payoff from the call option.
For the snow cleaning construction companies (known as Party B for our project), the case is just
opposite. Counterparty B will be interested to have a compensation for less snow as they lose
money during winter time as they will have idle equipments.
So there is a business opportunity to satisfy these 2 parties by meeting their demands. IUJ can act as
a dealer of call and put options and sell them to party A and party B. The Pay offs for party A or
City Govt. and party B or Construction companies will look as shown below. City office would buy
a Call option whereas Construction Company would buy an offsetting Put option.
-20000000
-2 0 0 0 0 0 0 0
-30000000
-3 0 0 0 0 0 0 0
1093
1105
-1 0 0 0 0 0 0 0
1057
1069
1081
-10000000
1021
1033
1045
0
997
1009
0
961
973
985
10000000
925
937
949
10000000
1081
1093
1105
20000000
1009
1021
1033
1045
1057
1069
20000000
937
949
961
973
985
997
30000000
901
913
925
30000000
901
913
Construction Company Pay Off
City Office Pay-Off
- 22 -
Let’s see how the contract will affect the cash flows of city office. As we can see from the
below graph, the cost pattern is smoothened by the call option as shown in the yellow line.
Particularly in the heavy snow fall years the hedging impact is significant as in 2005.
Please note that here we have taken a negative scale which means expenses/cost is on the
positive side of Y axis and profit on the negative side of Y- axis.
5 0 0 ,0 0 0 ,0 0 0
4 0 0 ,0 0 0 ,0 0 0
3 0 0 ,0 0 0 ,0 0 0
2 0 0 ,0 0 0 ,0 0 0
N o r m a l E xp e n s e
1 0 0 ,0 0 0 ,0 0 0
O p ti o n L o s s
T o ta l E xp e n s e
05
20
03
20
01
20
99
19
97
19
95
19
19
19
91
- 1 0 0 ,0 0 0 ,0 0 0
93
0
- 2 0 0 ,0 0 0 ,0 0 0
- 3 0 0 ,0 0 0 ,0 0 0
City Office Total Expense by First Model
As above it can be shown that the construction companies will also be hedged by the put
option. Now let us look at the IUJ side story. The payoffs and profit diagrams are shown
below. The striking point is that IUJ will bear infinite loss in case of extreme snow fall
which is not out of question.
- 23 -
IUJ PayOff
IUJ ProfitDiagram
60,000,000.00
0
50,000,000.00
-5000000
40,000,000.00
30,000,000.00
20,000,000.00
-15000000
10,000,000.00
-20000000
0.00
-25000000
-10,000,000.00
-30000000
-20,000,000.00
688
726
764
802
840
878
916
954
992
1030
1068
1106
1144
1182
1220
1258
1296
-10000000
901
914
927
940
953
966
979
992
1005
1018
1031
1044
1057
1070
1083
1096
1109
5000000
So below we summarize our first product structure-options.
Advantages
1. Product Meets Demand: Market needs Insurance.
Disadvantages:
1. IUJ needs to take positions. As an academic institution this is not advisable.
2. Liquidity of this product will be low because of very few potential customers. So this
will increase the risk further.
3. Statistical speaking this venture would be very risky also as the snow fall goes ±0.73
standard deviations of the average snow fall of 995 cms, IUJ loses money.
After analyzing the Option product structure, we decided not to continue with this and explore
other product structures. The biggest limitation in this structure was the extreme events of
either heavy or less snow fall. To mitigate this limitation, we thought of modifying our product
by adding cap to the options as explained next.
- 24 b) Call and Put Options with Caps
This structure is very similar to the simple call and put options except the fact that there will be a
extra constraint of cap in the contract at 2 sigma level. The Pay offs for City Govt and Construction
Pay off will look as shown below. City office would buy a Capped Call option whereas
Construction Company would buy an offsetting Capped Put option.
1409
1356
1303
1250
1197
1144
1091
985
1038
932
879
826
773
720
-1 0 0 0 0 0 0 0
667
1409
1356
1303
1250
1197
1144
1091
-1 0 0 0 0 0 0 0
985
10000000
1038
10000000
932
30000000
879
30000000
826
50000000
773
50000000
720
70000000
667
70000000
614
90000000
561
90000000
614
C ons truction C ompany Pay Off
561
C ity Office Pay Off
-3 0 0 0 0 0 0 0
-3 0 0 0 0 0 0 0
Obviously this is a less attractive product to the counterparties as they are not being compensated in
the extreme snow fall scenarios when they need hedging the most. However this structure makes
more sense to IUJ as an option dealer as the risk profile is better than that of plain vanilla options
structure.
IUJ Profit Diagram
IUJ Pay Off
60000000
30000000
50000000
10000000
1409
1356
1303
1250
1197
1144
1091
1038
985
932
879
826
773
720
667
614
561
-1 0 0 0 0 0 0 0
40000000
30000000
20000000
-3 0 0 0 0 0 0 0
-5 0 0 0 0 0 0 0
10000000
0
-1 0 0 0 0 0 0 0
-7 0 0 0 0 0 0 0
-9 0 0 0 0 0 0 0
-2 0 0 0 0 0 0 0
-3 0 0 0 0 0 0 0
1
59 117 175 233 291 349 407 465 523 581 639 697 755 813 871
- 25 Let us see how this structure hedges the expenses of the city government. (Shown below).
Obviously the expenses are smoothened but not to the extent in earlier case.
500000000
400000000
300000000
N o rm a l E x p e n s e
200000000
O p t io n L o s s
100000000
T o ta l E x pe n s e
05
20
03
20
01
20
99
19
97
19
93
95
19
19
-1 0 0 0 0 0 0 0 0
19
91
0
-2 0 0 0 0 0 0 0 0
City Office Total Expense by Second Model
So below we summarize our second product structure-Options with Cap
Advantages
1. Product Meet Demand
2. Less Riskier for IUJ as there is a limit/Cap on payoff for either party.
Disadvantages
1. IUJ still needs to take position
This product structure can be a potential structure if we carefully design the cap. But IUJ’s
role as a dealer does not change and poses lots of risk. We tried to explore more structures.
- 26 c) Forwards
There is big shift in IUJ’s role here in forward type of contract. Probably this is the reason
why we anted to explore this structure. Here IUJ acts like an agent or a broker facilitating
the matching of the counterparties. City office and Construction Company have offsetting
requirements. So, IUJ can create a forward contract between the counterparties to match the
offsetting demands. The payoff diagrams for City Govt. and Construction Company have
been shown below.
City Office Pay Off
-1 0 0 0 0 0 0 0 0
-1 0 0 0 0 0 0 0 0
-1 5 0 0 0 0 0 0 0
-1 5 0 0 0 0 0 0 0
In this case IUJ’s payoff does not have any negative side as shown below as IUJ is not
taking any position.
IUJ Pay Off & Profit
2500000
2000000
1500000
1000000
500000
1394
1345
1296
1247
1198
1149
1100
1051
1002
953
904
855
806
757
708
659
610
561
0
1428
1377
1326
1275
1224
1173
1122
1071
1020
969
918
867
816
765
714
663
-5 0 0 0 0 0 0 0
612
1 4 2 8
1 3 7 7
1 3 2 6
1 2 7 5
1 2 2 4
1 1 7 3
1 1 2 2
1 0 7 1
9 6 9
1 0 2 0
-5 0 0 0 0 0 0 0
9 1 8
0
8 6 7
0
8 1 6
50000000
7 6 5
50000000
7 1 4
100000000
6 6 3
100000000
6 1 2
150000000
5 6 1
150000000
561
Construction Company Pay Off
- 27 -
To see the impact of hedging on the cash flow of the counterparties we have drawn the
expenses, loss of forward contract and the net/total expenses for City Office below. It is
very clear that the expenses has been smoothened which mean this structure is working as a
good hedging product.
City Office Total Expense by Third model
500000000
400000000
300000000
T o ta l E xp e n s e
20
20
20
19
19
19
91
-1 0 0 0 0 0 0 0 0
06
0
03
F o rw a rd L o s s
00
100000000
97
N o r m a l E xp e n s e
94
200000000
-2 0 0 0 0 0 0 0 0
-3 0 0 0 0 0 0 0 0
We summarize the advantages and disadvantages of the forward structure below.
Advantages
1. This is perfect hedge but parties might want only Insurance against the adverse effect.
2. IUJ doesn’t need to take position, so there is very less risk.
Disadvantages:
1. Parties might easily make contract by themselves and ignore IUJ.
2. They can also make fixed payment contract.
Finally we propose forward structure as the contract arrangement this structure
fulfills the hedging requirements of the counterparties at the same time does not
impose significant risk to IUJ.
- 28 -
Future scope of the project
Due to time constraint we could not explore few aspects of the subject. Below we list the
future scope of the project.
 Modeling of snow fall: It is very important to model the underlying variable using a
stochastic process as this would help to calculate the risk exposure of the business more
accurately, which would help in hedging the exposure better. Also with identification of
a suitable stochastic process for snow, sophisticated pricing models such as Monte
Carlo methods could be used.
 Analysis of snow fall in Shiozawa region: To explore if the area under consideration in
terms of the roads for cleaning is same or varying.
 There is huge potential in terms of growing the business by identifying and bringing in
more parties and counterparties with weather hedging needs.
- 29 -
Appendix
Sample Contract
Type of contract
Forward on snow fall
Seller
City Office
Buyer
Ski industry (resort operator, hotel, equipment),
Road maintenance company
Target areas
Shiozawa
Observation period
From Dec. 1 2009 to Mar 31 (120 days)
Definition of less snow
Day has less than 10 cm snow
Strike price
995 cm of snow fall for Winter
Expiration date
Apr. 30, 2009
Payment date
May. 7, 2009
An example of sample contract
- 30 -
Forward Payoffs
Strike Snow Fall
995
Snow removal cost per cm227,575
Transactional charges
5% of turnover
Year
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
City Office
Transportation Company
Snow fall in
Payoff in cm Payoff in Yen Payoff in cm Payoff in Yen IUJ's Comission
cm
819
-176 -40,138,541
176
40,138,541
2,006,927
886
-109 -24,891,016
109
24,891,016
1,244,551
960
-35
-8,050,466
35
8,050,466
402,523
1120
125
28,361,534
-125
-28,361,534
1,418,077
1260
265
60,222,034
-265
-60,222,034
3,011,102
743
-252 -57,434,241
252
57,434,241
2,871,712
732
-263 -59,937,566
263
59,937,566
2,996,878
1019
24
5,376,459
-24
-5,376,459
268,823
1066
71
16,072,484
-71
-16,072,484
803,624
1262
267
60,677,184
-267
-60,677,184
3,033,859
788
-207 -47,193,366
207
47,193,366
2,359,668
982
-13
-3,043,816
13
3,043,816
152,191
687
-308 -70,178,441
308
70,178,441
3,508,922
1290
295
67,049,284
-295
-67,049,284
3,352,464
1876
881 200,408,234
-881
-200,408,234
10,020,412
436
-559 -127,299,766
559
127,299,766
6,364,988
Total
0
0
43,816,722
- 31 -
Payoff with Put/Calls
S trike S now Fall
S now rem ovalcost per cm
C allO ption P rice
C allO ption P ut
Snow fall
Year
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
819
886
960
1120
1260
743
732
1019
1066
1262
788
982
687
1290
1876
436
995
227,575
27,385,451
27,385,451
Long Call
City Office
Payoff in cm Payoff in Yen Profit
0
0
0
0
0
0
125
28,361,534
265
60,222,034
0
0
0
0
24
5,376,459
71
16,072,484
267
60,677,184
0
0
0
0
0
0
295
67,049,284
881
200,408,234
0
0
Net
438,167,216
-27,385,451
-27,385,451
-27,385,451
976,083
32,836,583
-27,385,451
-27,385,451
-22,008,992
-11,312,967
33,291,733
-27,385,451
-27,385,451
-27,385,451
39,663,833
173,022,783
-27,385,451
0
Long Put
Short Long Put
Transportation Company
IUJ
Payoff in cm Payoff in YenProfit
Profit
176 40,138,541 12,753,090
14,632,361
109 24,891,016 -2,494,435
29,879,886
35 8,050,466 -19,334,985
46,720,436
0
0 -27,385,451
26,409,368
0
0 -27,385,451
-5,451,132
252 57,434,241 30,048,790
-2,663,339
263 59,937,566 32,552,115
-5,166,664
0
0 -27,385,451
49,394,443
0
0 -27,385,451
38,698,418
0
0 -27,385,451
-5,906,282
207 47,193,366 19,807,915
7,577,536
13 3,043,816 -24,341,635
51,727,086
308 70,178,441 42,792,990 -15,407,539
0
0 -27,385,451 -12,278,382
0
0 -27,385,451 -145,637,332
559 127,299,766 99,914,315 -72,528,864
438,167,216
0
0
- 32 Payoffs with Capped Puts and Calls
S trike S now Fall
995
S now rem ovalcost per cm
227,575
C allO ption P rice
27,385,451
C allO ption P ut
27,385,451
Year
Snow fall
1991
819
1992
886
1993
960
1994
1120
1995
1260
1996
743
1997
732
1998
1019
1999
1066
2000
1262
2001
788
2002
982
2003
687
2004
1290
2005
1876
2006
436
Long Call
Long Put
Short Long Put
City Office
Transportation Company
IUJ
Payoff in cm Payoff in Yen Profit
Payoff in cm
Payoff in YenProfit
Profit
0
0
-27,385,451
176 40,138,541 12,753,090
14,632,361
0
0
-27,385,451
109 24,891,016 -2,494,435
29,879,886
0
0
-27,385,451
35 8,050,466 -19,334,985
46,720,436
125
28,361,534
976,083
0
0 -27,385,451
26,409,368
265
60,222,034
32,836,583
0
0 -27,385,451
-5,451,132
0
0
-27,385,451
252 57,434,241 30,048,790
-2,663,339
0
0
-27,385,451
263 59,937,566 32,552,115
-5,166,664
24
5,376,459
-22,008,992
0
0 -27,385,451
49,394,443
71
16,072,484
-11,312,967
0
0 -27,385,451
38,698,418
267
60,677,184
33,291,733
0
0 -27,385,451
-5,906,282
0
0
-27,385,451
207 47,193,366 19,807,915
7,577,536
0
0
-27,385,451
13 3,043,816 -24,341,635
51,727,086
0
0
-27,385,451
308 70,178,441 42,792,990 -15,407,539
295
67,049,284
39,663,833
0
0 -27,385,451 -12,278,382
881 113,321,990
85,936,539
0
0 -27,385,451 -58,551,088
0
0
-27,385,451
559 113,321,990 85,936,539 -58,551,088
Net
351,080,972
-87,086,244
424,189,440 -13,977,775 101,064,019
- 33 REFERENCES
1. Weather Derivatives Definition: Options, Futures, & Other Derivatives John Hull
2. Derivatives Strategy Magazine 2000: History of weather Derivatives and major
exchanges
3. “Seeking a Standard Pricing Model”, Financial Engineering associates,
Environmental Finance, March 2000
4. Energyrisk.com Reference=16671 :LIFFE origins
5. Options, Futures, & Other Derivatives John Hull: Derivative Structures definitions: Puts
and Calls with Caps, Collars , Swaps
6. Monte carlo methods in Financial Engineering: Paul Glasserman