Weather DerivativesA Report submitted in partial fulfillment of the requirements of the course

Derivatives Management

Under the Guidance of Dr. Alok Pandey

PGDM (International Business) 2007-09

Animesh Verma (07IB-007) |Prateek Sinha (07IB-038)| Sudarshan Bhutra (07IB-055)

CONTENTS

INTRODUCTION..........................................................................................................................................................3

WEATHER MEASURES.................................................................................................................................................4HDD and CDD.......................................................................................................................................................4

WEATHER DERIVATIVES STRUCTURE.........................................................................................................................5Call and Put Options..............................................................................................................................................6Weather Swaps.......................................................................................................................................................7Collars (Fences).....................................................................................................................................................7

PRICING OF WEATHER DERIVATIVES..............................................................................................................9

PRICING MODELS FOR WEATHER DERIVATIVES.........................................................................................................91. BLACK-SCHOLES AND WEATHER DERIVATIVES...............................................................................................122. SIMULATIONS BASED ON HISTORICAL DATA OR “BURN ANALYSIS............................................................143. MONTE CARLO BASED SIMULATIONS..............................................................................................................15

WEATHER DERIVATIVES IN INDIA...................................................................................................................16

Hedging Weather Risk Using Weather Derivatives.....................................................................................................23

INTRODUCTION

The weather derivates market started in 1997 in the US as the first transaction in this regard

was recorded there but now this weather derivatives market has spread to all major markets.

According to US energy market, US$ 1 trillion of the US economy is affected by the weather risk.

By the year 2000 about US$ 3.5 billion worth of weather derivates were traded in the US.

There are 4 major players in the weather derivates market :

MARKET MAKERS

BROKERS

INSURANCE AND REINSURANCE COMPANIES.

END USERS such as Gas and power marketers and utilities etc.

Derivative is a contract or a security whose value or payoff derives from the price of an

underlying asset. Derivatives help an investor to control the risks of changes in the prices of the

underlying asset. For eg. An exporter who receives his payments in foreign currency is exposed

to currency risk ie the risk of home currency appreciating with respect to the foreign currency.

When Rupee started appreciating against the US Dollar the textile exporters and IT companies

faces heavy losses if they had not hedged their positions.

Weather Measures

Weather measures are considered underlying assets of the weather derivatives, as the price of

a futures contract is an asset for an option on a commodity. The two most common weather

measures are – Heating Degree Days (HDD) or Cooling Degree Days (CDD) – depending on the

specifics of the contract. It is estimated that 98-99% of the weather derivatives are now using

these temperature parameters. Other measures are based on precipitation, which can be

measured by the amount of rain over a given time period or on Snowfall, measured by the

amount of snow (or sleet) over a given time period.

HDD and CDD

These weather measures are used to measure the demands that arise due to the departure of

the average daily temperatures from a base level.

An HDD (or CDD) is the number of degrees the day’s average temperature is above (or below) a

base temperature. They are calculated as follows:

Daily HDD = Max (0, base temperature – daily average temperature)

Daily CDD = Max (0, daily average temperature – base temperature)

Where,

Base temperature is defined as, the pre-defined base temperature, and,

Daily average temperature is measured as the average between the daily high and the daily

low.

To calculate the accumulated HDDs (or CDDs) over a specified time period, a simple addition of

the daily HDDs (or CDDs) is performed.

A few other measures used in Weather derivatives are: Energy Degree Days (EDDs), measured

as the sum of HDD or CDD for each day, Growing Degree Days (GDDs) defined as the degrees

between a certain range. GDDs are used often in agriculture.

Weather Derivatives Structure

Most weather derivative trading are either swaps, or call and put options or a combination of

these. Customized structures have started coming up based o specific needs, like binary or

digital options. These either pay a fixed sum or zero depending on whether the pay-off is

satisfied. Double trigger options are another example, which pay-off only if the two conditions

are met.

Pay-off = Specified dollar amount * (“Strike” HDD or CDD level – actual cumulative HDD or

CDD level)

Contracts are usually capped, i.e. only a maximum amount of payout can change hands. This is

done so as to limit the maximum amount of payout by any of the counterparties.

Call and Put Options

As mentioned earlier, HDDs and CDDs act as the underlying asset for the weather derivatives.

Since weather is not a tradable asset, a dollar value is linked to every degree day in the pay-off

calculation.

Pay-offs of the weather puts and calls calculated as:

Pay-off Call: p ($ / DD) *(Max(0, Xt|T – K)

Pay-off Put: p ($ / DD) *(Max(0, K - Xt|T)

where,

p ($ / DD) is the per degree pay-off,

Xt|T is the underlying HDD (or CDD), and

K is the strike (in terms of the underlying measure)

An investor, who has purchased (is long) the call option, will receive the pay-off if the recorded

HDD or CDD for the season are greater than the strike K. An investor who has purchased the

put option on the other hand will receive the pay-off if the HDD or the CDD are lower than the

strike.

Call and put options with a maximum pay-off (cap)

The reason a cap is specified on the call and put options is to avoid excessive pay-offs. The pay-

offs are then defined as,

Pay-off call: Min (p ($ / DD) *(Max(0, Xt|T – K), h)

Pay-off put: Min (p ($ / DD) *(Max(K - 0, Xt|T), h)

where h is the maximum pay-off in dollars.

Weather Swaps

A swap is a combination of put and call options, which have the same strike and are on the

same underlying location. Revenue stability can be provided by degree day swaps.

Pay-off swap: {Min (p ($ / DD) *(Max (0, Xt|T – K), h)} – {Min (p ($ / DD) *(Max (K - 0, Xt|

T), h)}

An investor who is long the swap, will receive payments, if the recorded HDD or CDD are

greater than the strike, and will make payments, if the recorded HDDs or CDDs are lower than

the strike.

Collars (Fences)

A collar is a spread position that insulates the buyer from extreme movements in the underlying

asset. It consists of purchasing an OTM call (or put) with a particular strike, and financing this

with the sale of an OTM call (or put) with a different strike.

Pay-off collar: {Min (p ($ / DD) *(Max (0, Xt|T – K1), h)} – {Min (p ($ / DD) *(Max (K2 - 0, Xt|

T), h)}

PRICING OF WEATHER DERIVATIVES

When the trading of weather derivatives started initially in 1997 there were a very few participants in

this market and there were huge bid ask spreads but currently when the number of participants has

increased significantly this bid ask spread has reduced drastically.

The following table mentions the measuring stations and ticker symbols of futures contracts that are

traded in Chicago Mercantile Exchange.

Pricing Models for Weather Derivatives

One can price weather derivatives using one of the many ways available.

Some models focus on the HDD and CDD directly. The problem with this approach is

that after we calculate the weather measure by modeling HDD or CDD directly, a lot of

information is lost as the values of HDD and CDD can be zero also.

Some models focus on temperature directly and then extract the HDD and CDD for each

temperature scenario. This method is a better and a more comprehensive method.

The example mentioned below clearly shows what information can be lost if we decide to

model HDD and CDD directly. Two locations which are geographically separate and having very

different temperatures can have same number of degree days.

Pricing of weather derivatives requires the future value of local temperature hence we should

have the ability to predict regional weather conditions for the coming months. Hence an

effective model of variations of a weather derivative contract over the course of future months

is essential for pricing of the contract.

Financial traders develop a forecast of the economic conditions before formulating a trading

strategy. Similarly the people who trade in weather derivatives contracts require forecasts of

temperatures expected in the future ie metrological forecasts. A variety of models are made

use of by the weather forecasting firms involving many parameters to predict the weather

conditions.

Short term Vs Long term predictions.

Regional Vs Global predications.

Even though many models of forecasting the weather conditions exist but still accurate

predictions is not possible and is full of uncertainty. However some short-term trends can be

predicted. Hence one can predict today’s weather with more certainty as compared to

tomorrow’s weather and tomorrow’s weather. Similarly tomorrow’s weather can be predicted

with more certainty as compared to next week’s weather.

Long-term weather forecasting requires thorough understanding of past weather patterns and

seasonal effects. The major controversy in the weather derivatives market is the choice of

pricing methodology used which will help us ascertain the fair value of the different derivative

contracts. There is no one such pricing methodology which is widely used and accepted by

everyone.

1. Black-Scholes and weather derivatives.

Fisher Black and Myron Scholes developed option pricing model which is used to determine

prices of Call and Put options and is used currently also. Unfortunately, the Black-Scholes model

is based on certain assumptions that do not apply realistically to weather derivatives. One of

the main assumptions behind the model is that the underlying of the contract (in our case HDD

or CDD) follows a random walk without mean reversion. In other words, their model predicts

that the variability of temperature increases with time, so temperature could wander off to any

level whatsoever. In the figure attached below, we can see different simulated daily

temperature values for a three month period assuming that there is no mean reversion. The

simulated temperatures differ substantially from expected temperatures, and we can see how

the variability increases with time. We can see how these simulated temperatures are totally

unrealistic, since towards the end of the simulation, we have temperatures as high as 140 and

as low as 0 degrees for the same day of the year.

The Black-Scholes model is probably inadequate for weather derivatives for the following

reasons:

• Weather does not “walk” quite like an asset price “random walk”, which can in principle

wander off to zero (think of degrees Kelvin) or infinity (hotter than the sun). Instead, variables

such as temperature tend to remain within relatively narrow bands, probably because of a

mean-reverting tendency, i.e. a tendency to come back to their historical levels.

• Weather is not “random” quite like an asset price random walk. Because of its inherent

nature, weather is approximately predictable in the short run and approximately random

around historical averages in the long run. This means that short-dated weather derivatives

may behave fundamentally different than their long-dated counterparts.

• Black-Scholes option payoff is determined by the value of the underlying exactly at the

maturity of the contract. Weather derivatives usually provide for averaging over a period of

time, and are therefore are more akin to “Asian” or average price options, i.e. have a non-Black-

Scholes payoffs.

• Many weather derivatives are also capped in payoff, unlike the standard Black-Scholes option.

• The underlying variables (e.g. temperature or precipitation) are not tradable prices, and so

pricing cannot be free of economy risk aversion factors, unlike the Black-Scholes model.

2. Simulations based on historical data or “BURN ANALYSIS

The “burn analysis” approach is very simple to implement and tries to answer the question:

What would have been the average payoff of the option in the past X years? The main objection

is that it does not incorporate temperature forecasts in its pricing.

Using the yearly series of historically realized cumulative degree-days over the relevant

instrument period we can determine the expected payoff for each year. The fair price of the

option would be the average of those historical payoffs.

3. Monte Carlo Based Simulations

“Monte Carlo” is a computer-based method of generating random numbers which can be used

to statistically construct weather scenarios. Such Monte Carlo simulations provide a flexible

way to price different weather derivatives structures. Various types of averaging periods, such

as those based on cumulating HDDs or CDDs, can be specified easily. Similarly, and as easily, a

contractual cap placed on the price of the derivative can be taken into account.

Monte Carlo typically involves generating a large number of simulated scenarios of HDDs or

CDDs to determine possible payoffs for the instrument. The fair price of the instrument is then

the average of all simulated payoffs, appropriately discounted to account for the time value of

money.

For Monte Carlo based simulations, it is important to choose the right random process for

temperature. It is reasonably clear that temperature is mean reverting, and therefore any

models that only assume Black- Scholes style “random walk" behavior will be inadequate to

model temperature. Indeed, measurement of the reversion rate parameter in temperature

data indicates that temperatures tend to revert to normal levels in 2 or 3 days.

Weather Derivatives in India

We have seen the how popular the weather derivatives have been U.S.A. there the major customers for

weather derivatives have been utility companies but by Chicago mercantile exchange’s own admission

the real potential will be tapped when farming related activities start using the weather derivatives.

Weather derivatives have been launched in India as well. Here the major customers will be the farming

community. We don’t see a huge potential for the derivatives by utility companies as India is a power

shortage nation and we don’t see the chances of excess power due to cooler summers or warmer

winters. The reasons why we think the weather derivatives will be success in India are:

● Farmers

● Agriculture credit off-take in ninth plan – Rs. 2,31,798 crores (grew @ 20% pa); Target

for X plan – Rs. 7,36,570 crores

● 90% crop losses on account of weather related risks

● Rural Economy is highly weather dependent

● Commodity Traders

● Weather related supply bottlenecks make dry-land commodities very volatile

● Intraday volatility of Guar, chilly touches 10-15% (daily trading at national

exchanges touches Rs.1000 crore daily)

● Vegetable and fruit Mandis highly dependent on temperature (Delhi Mandi trade alone

touches Rs.1000 crore annually)

● Trader income dependent on weather vagaries

● Industries like agro-input companies, food processing industry, companies, plantations, FMCG,

Banks, Power sector etc

● Not uncommon to find Agri-Input companies, whose sale dips by over 30-40%

due to fluctuation in rainfall

One more thing that we need to change before we implement weather derivatives in India is to have

them for rain fall changes as well

The major U.S firms that trade in weather derivatives are utility companies whose business is more

affected by temperature as compared to rainfall patterns. Whereas in India farming community is more

dependant on rainfall patterns as compared to the temperature fluctuations.

Some company reports supporting how weather impacts their business

● EID Parry sales, net down 86 pc on monsoon failure. - The Hindu, Jan 17, 2003

● The Company's business is seasonal in nature and the performance can be impacted by weather

conditions - Notes to Accounts, Syngenta (I) Ltd.

● Monsanto India continued its strong profit growth on the back of positive all-round business

performance aided by a good monsoon. - Annual Report 2003-04, Monsanto Ltd

● The delayed monsoon has hit the fertilizer stocks badly. - Analyst, Hindu Business Line

● Over 1000 farmers commit suicide in vidarbha and Telangana in last two years – TOI

● An average drought costs upto Rs 4 bn to the state exchequer, Gujarat earthquake resulted in

direct damages of about Rs.153 billion –NDMC

● Agricultural loss in many parts of the country is weather dependent

● Weather Derivatives can fill in the gap

● Loss can be monitored real time

● Cost of risk transfer can be reduced through weather trading

● Weather (esp. rainfall) is the common commodity across diverse agri-products, industries

● Explains up-to large variation in prices for commodities in the dry land

● Entities on both the long and short side

Commodity/

Index/Scrip

Extent of linkage

with economy*

Trading Turnover (in $ Trillion)*

Forex Derivatives $ 7.5 tr of foreign

trade

Approx. $1500-1600 trillion

Interest rate

derivatives

$ 20-25 trillion of

bond

Equity Derivatives $ 10-15 trillion of

equity portfolio

Illegal Betting ----------- $ 2.15 trillion (vis-à-vis, a total annual global savings of

$7.5 tr)

Weather Derivatives $ 150 bn (for

Indian economy)

?

● Linkage of the underlying with economy is important

● Ensures buyers & Sellers

● Base liquidity further deepens the market

● Weather impacts approx.

● GDP of $150 bn in India

● GDP of $ 200-250 bn in India & China

● GDP of $ 400-450 bn in top 8 developing economies

What needs to be done to establish a market for weather derivatives in India

First thing that needs to be done is to create the much needed cash/spot market in India. Then we need

to create an active futures/options trading market in India

Deepening the Primary market

● Technology development

● Resolving the key constraints

Developing the secondary market in tandem

● Launching the Indices for key regions

● Approaching the key market segments

● Commodity funds, Agri-funds, Rainfall speculators, International trading funds

● Push for regulations on participation by Banks and MFIs

● Presence in both the OTC and exchange traded market

● Developing the Hybrid market

● Quantos, Satellite Image – weather indices, Weather-Area yield

● Cat indices

To achieve these goals we need to cover important agricultural zones real time, at a cost of approx.

Rs.500 per sq.km or Rs.5 per hectare. This figure has been worked out by weather risk management

services.

We also need to generate historical records for any given longitude latitude positions. Statistical &

Neural Network model models need to be developed and implemented

Real Time Data

availability for

any given long-

lat

Decision Support

system(s) for

major customer segments

Platform enabling

Trading and cost reduction

Marketing Network/Relationships

Processing of data received from sensors and converting it according to specific product

On Site wireless Sensors

Farmers Console (GIS)

Since weather derivatives are needed for specific areas we need to collect data for each particular

region. Since India is a monsoon dependant economy we therefore need to study water imbalances in

each city and region for pricing the contracts

This illustration shows that impact of rain is different during different phases of vegetation. Since there

will be contracts with different maturity dates these factors need to be kept in mind before we price a

derivative

Another factor that should be kept in mind is the modeling extreme weather risk. We need to keep in

mind these losses and thus prepare models to identify and evaluate the risks caused on account of

extreme weather conditions. This will be something in line with value at risk model and stress testing

which is used for the traditional derivative contracts

So considering all this factors and combining it with the satellite images, we will get something like this

which we need to look at while pricing the derivatives.

We will need the standard deviation and the mean of the rainfall and temperature for the area to be

able to compute the price using Gaussian model for pricing of derivative contracts.

Hedging Weather Risk Using Weather Derivatives

Lets consider there is a company which is facing revenue shortage due to abnormally warm winter. The

company maintained enough reserves against normal variations in temperature but not for many

continuous warm winters. One more warm winter can be ruinous for the company. He therefore decides

to hedge the risk using weather derivatives. The company is located in a region where weather records

are available and the nearest measurement site is 100km from the city..

The first thing that the company does is to derive the time series data of 53 winters measured in the city.

Based on the data, the following things become clear:

the town from where the company operates is a cold place. Average monthly temperatures in winter can fall to 14°F

(-5°C), with frequent temperatures below zero.

There is almost perfect correspondence between average winter temperature and November through March

heating degree-days (correlation coefficient is 0.98).

There is no clear and convincing trend in these 53 winters, and

Three warmer-than-average winters in a row have happened twice before in this last half century, but four in a row

have not.

Also the forecast for the coming winters is that it will be warmer than normal.

After obtaining the weather pattern we need to study the basis risk of the company between heating in the

company's distribution region and the weather measurements. We also need to find out the correlation

between the temperature at the measuring site and the regional weather. We also need to find out what is

the temperature which leads to an increase in temperature which results in an increased demand.

We also need to quantify the natural weather exposure of the company. Knowing company’s weather

exposure will help know the risk associated with it.

The chart above shows the gross revenue levels off in extremely cold weathers ( the upper

curve).however when there is extreme demand the company runs out of fuel and has to buy more from

the open market at higher cost. The net revenue can go negative( the lower curve). It can be seen from

the graph that the critical net revenue for the company is not zero but 3 million.

The net revenues become negative when there are less than 4750 heating degree days and when it is

more than 6050 hdd’s

Next we need is the probability distribution of the weather conditions. Using the daily temperatures of last

thirty years we simulate the forecasts. Using the data available in the example we see that 14% of the

times the HDD’S are less than the critical figure of 4750 while 2% times HDD are more than 6050, the two

critical values.

To hedge this risk we need to buy an out of money HDD call which will pay if winters are too cool and sell

a near the money swap that will pay if the winter is warm. The company will have to pay some cash for

the call and sacrifice some revenues in the swap deal but only if winter is cold and revenues are good.

Taking the 30 yr average HDD we price the swap near 5175 HDD. To ensure 3 million revenue we need

to price each HDD at 10,000. The call should be bought below 6050 and should compensate both for

revenue loss and the premium paid for shorting a swap. We can calculate the strike using some software.

Suppose the strike works out at 5850 and the 20,000 for each HDD. The fair value works out at 75,000.

By multiplying the revenue at each degree day occurrence with the probability of that occurrence we get

the probable revenue curve. This way they can ensure that their revenue never goes below the critical

revenue. Thus by buying a swap and selling a call helps them to hedge the risk of revenue falling below

the critical 3 million mark no matter what the weather conditions are.