This paper approaches the subject of Weather Derivatives, more exactly their basic element the weather index. The weather index has two forms, the Heating Degree Day (HDD) and the Cooling Degree Day (CDD). We will try to explain their origin, use and the relationship between the two forms of the index. In our research we started from the analysis of the weather derivatives and what they are based on. After finding out about weather index, we were interested in understanding exactly how they work and how they influence the value of the contract. On the national level the research in the field is scares, but foreign materials available. The study for this paper was based firstly on reading about Weather Derivative, and then going in the meteorogical field and determining the way by which the indices were determined. After this, we went to the field with interest in the indices, such as the energy and gas industries, and figured out how they determined the weather index. For the examples we obtained data from the weather index database, and calculated the value for the period. The study is made on a period of five years, in 8 cities of the European Union. The result of this research is that we can now understand better the importance of the way the indices work and how they influence the value of the Weather Derivatives. This research has an implication on the field of insurance, because of the fact that weather derivative are at the convergence point of the stock markets and the insurance market. The originality of the paper comes from the personal touch given to the theoretical aspect and through the analysis of the HDD and CDD index in order to show their general behaviour and relationship.Weather derivatives, Weather Index, HDD, CDD

Botos Horia Mircea

Ciumas Cristina

English

Research Papers in Economics

 
362 
WEATHER INDEX- THE BASIS OF WEATHER DERIVATIVES 
Ciumaş Cristina 
Babeş-Bolyai University, Faculty of Economics and Business Administration 
Botoş Horia Mircea 
Babeş-Bolyai University, Faculty of Economics and Business Administration 
This paper approaches the subject of Weather Derivatives, more exactly their basic element the 
weather  index.  The  weather  index  has  two  forms,  the  Heating  Degree  Day  (HDD)  and  the 
Cooling Degree Day (CDD). We will try to explain their origin, use and the relationship between 
the two forms of the index. 
In our research we started from the analysis of the weather derivatives and what they are based 
on. After finding out about weather index, we were interested in understanding exactly how they 
work and how they influence the value of the contract. On the national level the research in the 
field is scares, but foreign materials available. 
The study for this paper was based firstly on reading about Weather Derivative, and then going 
in the meteorogical field and determining the way by which the indices were determined. After 
this, we went to the field with interest in the indices, such as the energy and gas industries, and 
figured out how they determined the weather index. For the examples we obtained data from the 
weather index database, and calculated the value for the period. The study is made on a period of 
five years, in 8 cities of the European Union. 
The result of this research is that we can now understand better the importance of the way the 
indices work and how they influence the value of the Weather Derivatives.  
This research has an implication on the field of insurance, because of the fact that weather 
derivative are at the convergence point of the stock markets and the insurance market.  
The originality of the paper comes from the personal touch given to the theoretical aspect and 
through the analysis of the HDD and CDD index in order to show their general behaviour and 
relationship. 
 
Keywords:  Weather derivatives, Weather index HDD, CDD   
JEL: G22 
 
Weather index - the basis of Weather Derivatives 
In  order  for  giving  protection against  the  consequences  of  extreme  weather events,  Weather 
derivatives have as underlying assets a variety of weather variables. Weather Derivatives can be 
structured accordingly to one or more variables. The most common used variable is temperature, 
either hourly, daily minimum or maximum, or as a daily average. By international consensus, in 
most  countries,  the  average  daily  temperature  is  the  arithmetic  mean  of  the  maximum  and 
minimum temperatures recorded for a period. In some countries, however, the average daily 
temperature is calculated as weighted average of values recorded per two day. The time of day 
when  the  recording  of  these  temperatures  takes  place,  the  method  of  determining  these 
temperatures can also vary from a country to another. To participate in the weather derivatives 
market  transactions  it  is  needed  to  examine  in  detail    the  meteorological  measuring  system 
practiced by each of the country in which weather derivatives are composed and then traded. It is 
generally known that in the U.S. the measurements are made in Fahrenheit degrees, and in the 
rest of the countries they are made on Celsius scale. 
As an example of heat minimum and maximum values, the chart below shows the minimum, 
maximum and daily average recorded in Cluj-Napoca, Romania, in 2008. 
  
363 
Chart 1. Evolution of daily minimum, maximum and average daily temperatures, in 2008 in 
Cluj-Napoca, Romania 
 
Source: Data processed by author using information available on www.wunderground.net 
 
In this chart we graphically illustrated thermal maximum and minimum records in Cluj-Napoca 
in the year 2008. The dark blue line shows the average temperature in its two forms, maximum 
and minimum. The purple line stands for the daily fluctuations of the temperatures and turquoise 
vertical line, represent the value in the day that the data were extracted. 
This chart shows the evolution of the minimum and maximum daily values, and also of the daily 
average, thus we are able to observe the trend manifested by the weather indices. For Cluj-
Napoca,  the  temperature  reaches  its  highest  level  in  July  (about  40C)  and  the  minimum  is 
recorded in late December (approx.-24C). 
Alongside the temperature, wind and rain measurements can also underpin weather derivatives. 
Protection against wind currents, for example, are of interest to wind ”farms” that want to 
contract these weather derivatives to protect themselves against the decline in wind speed, or in 
the construction industry, which would have to stop work in the winds blows too strong( e.g. for 
“sky-scrapers”). These contracts can be also used to replace traditional insurance policies for 
events such as damage caused by powerful winds, protection of future investments against events 
as  abundant  rainfall  in  the  agricultural  sector  or  drought  for  the  hydro-electric  industry. 
Protection of these events are relevant as are heavy snow falls of interest to mountain resorts, 
municipalities that must clean the roads in winter, but also for companies that sell products 
related to the cold-season, such as sport equipment or winter car-tires.  
These are contracts that are based on such variables as the number of sunny hours in the day, the 
temperature of sea water or river flows. 
In order to plan and build such a weather derivative we require accurate and reliable weather 
data. 
Correlation between relevant meteorological variables and their impact on economic activity that 
needs protection will vary from one weather event to another and from a company to another. 
Thus, the contracts will be individualized and constructed on indices that accurately reflect both 
probability of occurrence and its effects. 
Meteorological  indices  can  be  defined  as  the  number  and  characteristics  attributed  to  a 
phenomenon, process or other complex weather events. Indices that are most commonly used as 
base  for  weather  derivatives  contracts  are  indices  of  daily  temperature,  average  temperature 
index, average cumulative index and heat index weather event. In this paper we will explain the 
importance of daily temperature index. 
 
    
364 
Daily temperature index 
Using Daily indices is rooted in the energy industry and they are so constructed as to show 
domestic demand for heating or cooling. Weekly and monthly records of the index can be used 
also for monitoring and planning further needs, its costs and the heating cost for buildings which 
have  performing  air-conditioning  systems.  Annual  records  may  help  in  predicting  future 
expenditure for this purpose. 
It should be noted that the United States, where the temperature is measured on the Fahrenheit 
scale, the core temperature (base temperature) for contracts is of 65F (18.33C), and in other 
countries, where they use the Celsius scale, the basis temperature is set at 18C (64.44F). 
 
Heating Degree Days (HDD) 
The Heating Degree Days is a measure designed to reflect the daily need of heating of a home or 
office space, and thereby is a way of measuring how cold it is (if it is colder the heat demand is 
higher).  There  are  a  variety  of  ways  of  defining  HDDs  used  by  the  energy  industry,  thus 
reflecting  the  differences  in  consumption  between  cities,  showing  that  there  is  a  correlation 
between the ways of defining heat necessity and how well the index reflects the demand. The 
most common definition of the HDD index for the weather market is: 
     max        ,0            ,0                           1.1  
Where: Ti- the average temperature in day i 
T0- base temperature 
11determined by the contract 
During this paper we will assume that the formula depicted above is the calculating formula for 
HDDs. On a period of Nd days is defined as the sum of daily HDDs during the study: 
          
  
   
                  1.2  
The daily heat is higher in winter and weaker, almost zero, during summer. In many locations 
where the heat daily index is of interest, average temperature are recorded in certain periods do 
not exceed the 18C/65F limit, so the HDD index is always positive. 
 
                                                       
11 Base temperature= temperature that by its variation determines the Heating Necessity or Cooling Necessity. This 
temperature is often regarded of having the optimal value of 18C(65F)  
365 
 
Table 1 Monthly average number of HDD used in the period 01.01.2006 to 31.12.2010, for 8 European cities. Data are related to a 
contract with the base temperature of 18C. 
 
Month/City  London  Amsterdam  Stockholm  Paris  Vienna  Budapest  Bucharest  Sofia 
January  374  475.2  581.2  Id
12  505.8  494  547.6  535 
February  335.8  421.2  496.6  Id  401.4  389.2  411  442.6 
March  315.2  383.8  444.2  Id  323.8  287.8  302.8  339.2 
April  245.4  246.2  290.8  Id  176.2  148.8  154.4  183 
May  173.2  190  187.6  37.2  119.2  84.2  67  101.2 
June  79.8  96.2  125  12.6  44.4  33  17  42.4 
July  39.6  44.8  61  3.2  26.4  21.2  6  28 
August  59  95.8  89.8  9.4  42.6  30.4  8.2  28.6 
September  108.8  127.4  257.8  19.8  129.4  162  131.6  95.2 
October  200  231.6  409.8  41.6  305.8  274  263.6  271.8 
November  308.4  315  474.6  66.8  363.4  340.6  413  322.6 
December  423.4  473  596.2  111.8  501.2  511.2  561  505.6 
Source: Authors processing data available on www.degreeday.net 
 
 
                                                       
12 ID – Incomplet  Data  
366 
Our purpose is to highlight the monthly HDD values. In the study we chose to analyse cities from 
Europe, in order for the information to be relevant to the study. The data from (Tabel1) shows 
eight cities from the EU. In the selection process we tried chose the cities in such a way to 
minimize errors from the calculations. The period of study is of five years, from 01.01.2006 to 
31.12.2010, 
Processing the data presented difficulties for Paris, because of the lack of data for this location, 
only the data of 2010 are available. This lack of data explains why the general data for Paris are 
less than for the cities nearby, one such example is London. 
We can also see that the highest values were recorded in January and December. 
From (Chart2), we note that this index is at maximum level in Stockholm in December. At the 
opposite point is London, which presents the lowest values for all the studied period. Although 
the graph shows that Paris would have the lowest value, we can’t prove it because of lack of data. 
Chart2.  Chart interpretation of Tabel1. 
 
Source: Data processed by the author using information available on www.degreeday.net 
 
The use of HDDs in the construction and trading of weather derivatives are used in the USA and 
Europe, and rarely in Japan. 
 
Cooling Degree Day (CDD) 
The daily cooling requirement is mainly used to measure summer energy demand for cooling, so 
determining how hot is (if it is warmer, the CDD need is higher). Heating systems are powered 
by electricity or gas, but cooling systems are mainly powered by electricity. This is one reason 
why CDD’s are more relevant to the electricity market. Because electricity is generated recently 
from natural gas, the CDD’s are becoming relevant to the gas industry also. The number of days 
that require CDD’s is calculated: 
     max        ,0            ,0           1.3  
As for the HDDs, the index is the sum over a period Nd of CDDs during the studied period. 
          
  
   
                  1.4  
 
0
100
200
300
400
500
600
700
London
Amsterdam
Stockholm
Paris
Vienna
Budapest
Bucharest 
367 
 
 
 
 
 
 
Tabel3. Monthly average CDD numbers for eight European cities, in the 01.01.2006-31.12.2010 period. Data is consistent for contract 
with a base temperature 18C 
Month/City  London  Amsterdam  Stockholm  Paris  Vienna  Budapest  Bucharest  Sofia 
January  0  0  0  0  0  0  0  0 
February  0  0  0  0  0  0  0.2  0.4 
March  0  0  0  0  0.4  0.6  1.2  2.4 
April  4.6  4.2  2.8  4  10.2  16.6  23.2  16.6 
May  17  8.8  7.4  7.6  27.2  46  64.4  59.8 
June  36.8  32.8  27.6  25.2  64.6  78  145  103 
July  50.6  63.4  76  75.8  121.8  151.2  194  145 
August  38.6  38.6  32.6  36.8  91  122.6  239.6  152 
September  12.2  8.2  2.6  12.4  23  28.2  73.4  59.2 
October  1.6  2  0  5.4  3  4.2  5.4  9.4 
November  0  0  0  0  0.2  0  3.2  3.4 
December  0  0  0  0  0  0  0  0.4 
Source: Data processed by the author using information available on www.degreeday.net 
 
  
368 
In this analysis we used the same location as for the Heating degree days. London is the main 
market for weather derivatives in Europe; thus taking into account the nearby cities that show 
interest in these derivative contracts, as Paris and Amsterdam. I chose Stockholm to exemplify 
the developments and use of thermal indices in Scandinavia. Vienna, Budapest, Bucharest and 
Sofia have been selected because they are located in Central-Eastern Europe.  
(Tabel3) emphasizes that the daily allowance of coolness, the figures show the opposite then in 
the case of the HDD index. The CDD index grows in value over the warmer months, reaching its 
peak in July and August, and in January and December the index is almost null.  
From (Graph4) we can see that the maximum value is recorded in August in Bucharest and the 
lowest in Stockholm also in August. Here we see the formation three groups of cities: Bucharest 
– which is separated with the highest values; followed by Sofia, Budapest and Vienna, and the 
lowest values are in the third group formed of London, Amsterdam, Paris and Stockholm. The 
lowest of the low values are recorded by London and Stockholm. This fluctuation can be also 
explained through Geography, by the cities situations on the meridians.  
Graph 4. Interpretations of the values of Tabel3 
 
Source: Data processed by the author using information available on www.degreeday.net 
 
Derivatives based on CDD’s are usually traded in the U.S., however, they are rarely trade in 
Europe and Japan. 
 
The relationship between and HDD and CDD 
The  total  amount  of  HDD’s  and  CDD’s  sites  in  a  given  day  is  shown  by  the  insignificant 
deviation of the average core temperature: in one day neither HDD nor CDD are zero, or when 
both are zero then the day temperature is equal with the normal values recorded. Thus, it is 
apparent that neither HDD nor CDD can have a negative value. 
 
Conclusion 
The analysis conducted in this paper, shows that the most common indices used in weather 
derivatives contracts are the HDDs and CDDs. 
In my opinion, this is because weather events can be easily reported as temperature fluctuations 
in  different  periods,  fluctuations  that  are  accompanied  by  additional  weather  phenomena’s. 
Examples would be the case of the low temperatures, which often are accompanied by winds; 
moisture that is accompanied by rain and atmospheric pressure increase, or excessive heat that 
can cause drought. 
 
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WEATHER INDEX- THE BASIS OF WEATHER DERIVATIVES

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WEATHER INDEX- THE BASIS OF WEATHER DERIVATIVES

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