empirical analysis of price-curves at the eex
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Empirical Analysis of Price-Curves at the EEX
Nicolas Samyn
Matriculation Number 04 607 438
Etzelbüntstrasse 5a, 9011 St. Gallen, Switzerland
+41 (0) 78 603 05 92, nicolas.samyn@alumni.unisg.ch
Master Thesis
University of St. Gallen (HSG), Switzerland
Institute for Operations Research and Computational Finance (ior/cf-HSG)
Prof. Dr. Karl Frauendorfer
November 5th, 2010
[intentionally left blank]
I
Abstract
This paper provides an empirical analysis of price curves for the German electricity market at the
EEX with regard to the production margins, respectively the percentage of used capacity for each
generation type. The following fields of research are of particular interest: what is the impact of
changing generation capacities on price, on market volatility and on the shape of the demand and
supply curves.
The findings suggest that production margins respectively the percentage of used capacity per gen-
eration type in the German electricity market are a rather powerful indicator for prices, as well in the
day-ahead market as in the intraday market. On the other hand, their influence on market volatility
and on the shape of the demand and supply curve is rather marginal.
II
Acknowledgements
I would like to express my gratitude to everyone who motivated and supported me while I was writ-
ing on this master thesis. Special thanks go to Prof. Dr. Karl Frauendorfer, who sparked my interest
in the electricity market, for his helpful comments and precious suggestions. Furthermore, I owe
many thanks to all the people who assisted me in revising this thesis and to my family who supported
me during this special task.
III
Table of Contents
Abstract I
Acknowledgements II
Table of Contents III
Table of Figures V
Table of Tables VI
Abbreviations, Notions and German Words VII
Goal, Methodology and Build Up of the Thesis 1
1. Introduction 3
1.1 Electricity in General 3
1.2 The German Electricity Market 3
2. Data Set 7
2.1 Installed, Available and Actually Used Generation Capacities 7
2.1.1 General Information 7
2.1.2 Reporting Companies 8
2.1.3 Installed Capacities 9
2.1.4 Available and Forecasted Capacities 10
2.1.5 Actually Produced Electricity 12
2.2 Demand and Supply Curves 14
2.3 Price and Quantity 17
3. Preparing the Data Set 20
3.1 Analysing Production Capacities 20
3.1.1 Reserve Margin 20
3.1.2 Degree of Capacity Utilisation 23
3.1.2.1 Generation from Uranium 25
3.1.2.2 Generation from Lignite 25
3.1.2.3 Generation from Run-of-the-river 25
IV
3.1.2.4 Generation from Wind 25
3.1.2.5 Generation from Coal 26
3.1.2.6 Generation from Gas 26
3.1.2.7 Generation from Pumped Storage and Seasonal Storage 26
3.1.2.8 Generation from Oil 26
3.2 Elasticity 27
3.2.1 Point Elasticity 27
3.2.2 Arc Elasticity 34
3.2.3 Elasticity in the Literature 36
3.3 Volatility 38
3.3.1 Volatility of Day-ahead Prices 38
3.3.2 Volatility of Intraday Prices 43
4. Empirical Results 45
4.1 Dependent variables 45
4.2 Explanatory variables 45
4.3 Results 46
4.3.1 Regression Analysis: Day-ahead Prices 46
4.3.2 Regression Analysis: Intraday Prices 48
4.3.3 Regression Analysis: Price Elasticity of Demand 50
4.3.4 Regression Analysis: Price Elasticity of Supply 51
4.3.5 Regression Analysis: Day-ahead Price Volatility 53
4.3.6 Regression Analysis: Intraday Price Volatility 54
5. Concluding Remarks 56
References 58
Appendix 66
Declaration of Authorship 72
V
Table of Figures
Figure 1: Installed generation capacity by fuel type 4
Figure 2: Electricity production by fuel type 4
Figure 3: Grid of the transmission system operator 5
Figure 4: Generation capacities under 100 MW by generation type 9
Figure 5: Available capacity for each generation type on a daily basis 11
Figure 6: Expected electricity generation through wind turbines on an hourly basis 11
Figure 7: Actual production with respect to different generation types (in MW) 13
Figure 8: Price (in EUR per MW) – Quantity (in MW) bids for the demand 15
Figure 9: Price (in EUR per MW) – Quantity (in MW) bids for the supply 15
Figure 10: Intersection of the demand and supply curve on hour 1, June 6th 2010 16
Figure 11: Hourly intraday and day-ahead prices 17
Figure 12: Hourly intraday and day-ahead quantities 18
Figure 13: Hourly margin for the German electricity market 22
Figure 14: Margin distribution for the German electricity market 22
Figure 15: Used capacity over time with respect to generation type 24
Figure 16: Point elasticity of demand for the German electricity market 33
Figure 17: Point elasticity of supply for the German electricity market 33
Figure 18: Arc elasticity of demand for the German electricity market 35
Figure 19: Arc elasticity of supply for the German electricity market 35
Figure 20: ����,�� , average hourly volatility over a time window of 1 week 40
Figure 21: Hourly volatility using a rolling window 42
Figure 22: Relationship between intraday price (average, low, high) and day-ahead prices 43
Figure 23: Hourly intraday price fluctuation for the German market 44
Figure 24: Intraday volume to difference between expected and actual wind production 49
VI
Table of Tables
Table 1: Companies reporting to the transparency platform 8
Table 2: Installed capacity by generation type (Voluntary publication) 9
Table 3: Available production capacities with respect to different generation types (in MW) 10
Table 4: Actual production with respect to different generation types (in MW) 14
Table 5: Price and Quantity for intraday and day-ahead markets 18
Table 6: Margins in the German electricity market 23
Table 7: Used capacity with respect to generation type 23
Table 8: R2 for polynomials of different order fitting the demand and supply curves 30
Table 9: Point elasticity of demand and supply 32
Table 10: Arc elasticity of demand and supply 34
Table 11: Demand elasticity in the electricity market – a summary 36
Table 12: Daily volatility figures for intraday, trans-day and trans-week prices 39
Table 13: Hourly volatility over each day 40
Table 14: Hourly volatility for the German market 41
Table 15: Hourly volatility computation using a rolling window 42
Table 16: Relationship between intraday and day-ahead prices in the German market 43
Table 17: Hourly intraday price fluctuation: key figures 44
Table 18: Regression analysis: day-ahead prices 46
Table 19: Regression analysis: intraday prices 48
Table 20: Regression analysis: price elasticity of demand 50
Table 21: Regression analysis: price elasticity of supply 51
Table 22: Regression analysis(2): price elasticity of supply 53
Table 23: Regression analysis: day-ahead price volatility 53
Table 24: Regression analysis: intraday price volatility 54
VII
Abbreviations, Notions and German Words
Bundesministerium für Wirtschaft und Federal Ministry of Economics Technologie [BMWi] and Technology
Bundesnetzagentur Federal Network/Grid Agency
Bundesverband der Energie- und German Federal Association for Energy- Wasserwirtschaft and Watermanagement
Bundesverband WindEnergie German Federal Association for Wind Energy
EEX European Energy Exchange
EEG (Erneuerbare-Energien-Gesetz) Renewable Energies Source Act
EnWG (Energiewirtschaftsgesetzt) Energy Industry Act
EUR Euro
Hour 1 Hour from 00:00 – 01:00 am
kWH Kilowatt hour
MW Megawatt
MCP Market Clearing Price
MCQ Market Clearing Quantity
OTC Over The Counter
RTP Real Time Pricing
Statistisches Bundesamt German/Federal Statistical Office
TOU Time Of Use
TSO Transmission System Operator
TWh Terawatt hour
Empirical Analysis of Price-Curves at the EEX
- 1 -
Goal, Methodology and Build Up of the Thesis
This paper’s purpose is to explore the effects of varying generation capacities in the German electric-
ity market. Installed generation capacity in Germany is constant in the short to mid- term, however
readily available generation capacities do vary over time as production units have to be taken off the
grid for maintenance, or for lack of natural resources (wind, water, etc.) to activate the generating
units. The focus of this study will lie on three main topics. Firstly: how are prices influenced by
changing generation capacities. Secondly: how is the shape of the demand and supply curve affected
by changes in the available generation capacities. Thirdly: how is the market volatility affected by
varying generation capacities in the German electricity market. The math, wherever needed, will be
mostly performed by using MATLAB 2009a.
In order to reach that goal, this paper will proceed as follows. Chapter 1 will give a brief introduction
on the characteristics of electricity as well as on the German electricity market in general. The focus
will clearly be on introducing the generation capacities of Germany as well as on presenting the
European Energy Exchange (EEX) in Leipzig which has advances to a neuralgic player in the Euro-
pean energy market in general, and in the German electricity market in particular.
Chapter 2 will present the data set used in this paper. First, the data for the generation capacities will
be explored. The focus will lie on answering the following questions: Who is providing the data?
How much of the market is covered? How much production capacity is installed? How much pro-
duction capacity is available? How much electricity has actually been produced on an hourly basis?
In a second part, the results of the day-ahead auctions for the German electricity market at the EEX
will be presented. The focus will here be to provide on the one hand some insights into the bidding
process which leads to the price-quantity bids for every hour of the following day as well as to pre-
sent on the other hand the demand and supply curve resulting from the bidding procedure and their
general shape. In a third section, Chapter 2 will briefly summarized two time series of prices and
quantities for the German electricity market. The first time series is the resulting price-quantity of the
day-ahead auction, while the second is the resulting time series of the intraday auction. Their respec-
tive role as well as their “raison d’être” will be introduced.
Chapter 3 will prepare the introduced data so that they can be used for further analysis in Chapter 4.
Production margins will be computed with respect to the generation capacities. These margins are
calculated for the German electricity market on an hourly bases, as well on a global generation level
as on an individual (generation unit type) level, for which case it has been decided to use the per-
centage of used capacity metric for convenience purposes. This section aims at quantifying the re-
Empirical Analysis of Price-Curves at the EEX
- 2 -
sulting demand and supply curves from the day-ahead auction so that each curves is described by an
individual measure. Two possibilities will be introduced: on the one hand, point elasticity and on the
other hand, arc elasticity. Market volatility is another key aspect of the market, this is the reason why
the goal of the last section of Chapter 3 is to propose a volatility measure for each hour of either set
of hourly prices (day-ahead and intraday). The general methodology as well as the main problems
will be discussed along with the results obtained.
Chapter 4 will start discussing how varying generation capacities affect the electricity market by
running single and multiple regression analysis such as to describe their role in price changes, in
changes with regard to the shape of the demand and supply curve as well as their influence on market
volatility.
Chapter 5 will yield some concluding remark.
Empirical Analysis of Price-Curves at the EEX
- 3 -
1. Introduction
1.1 Electricity in General
Electrical power is with respect to many aspects a peculiar commodity. Economic activity and daily
life in the western world in particular has become unimaginable without electricity. Be it for trans-
portation, production or recreation, the use and needs for electricity is omnipresent. The peculiar
characteristics of electricity have been major drivers for the electricity market and its design.
Thereby, especially physical and technical characteristics play an important role. From the technical
point of view, the need to service a grid for the distribution of electricity to end consumers is one
reason why the electricity business is very capital intensive. Furthermore, the physical supply from
generators and the physical demand from consumers must be equilibrated at all point in time and on
all points on the electrical grid, with essentially zero tolerance. Any disruption in this equilibrium
can have severe consequences for the power systems and equipment connected with the grid. An-
other trait of electricity is that it cannot be stored easily, so that you cannot produce your electricity
in advance and store it for whenever the demand will be higher (Purtscher, 2000). The only possibil-
ity to store electricity is to use water as a storage medium by pumping it up into a storage lake. Using
this methods however means to take into account (small) energy losses (Egger, 1997). For these rea-
sons, the production and distribution of electricity was for many years a monopolistic issue. As the
benefits of competitive markets have been proven by economic theory and empirical evidences in
many markets, especially in deregulated western industries, many countries started deregulating their
power sector. Nevertheless, the electric industry has been the last of the major industries to be de-
regulated due to its peculiar characteristics that make competition problematic (Kwoka & Madjarov,
2007). Furthermore, electricity prices exhibits unconventional characteristics. The price of electricity
is greatly inclined to change at each delivery period, exhibiting daily, weekly, monthly and even
yearly seasonality’s (Eyeland & Wolyniec, 2003).
1.2 The German Electricity Market
The liberalisation of the electricity market in Europe started back in the late 1980s with the deregula-
tion of the electricity industry in England and Wales after the election of Mrs. Thatcher, followed in
the next couple of years by the deregulation of the Nordic market (Norway, Sweden, Finnland). The
European Union started to prepare an EU-wide policy of electricity market liberalisation (Directive
96/92/EC) which came into force in February 1997. (Green, 2006)
Empirical Analysis of Price-Curves at the EEX
- 4 -
lignite
23%
nuclear
22%coal
18%
gas
13%
renewable
16%
others
8%
lignite
15%nuclear
16%
coal
20%
gas
13%
renewable
24%
others
12%
To comply with the European Union’s regulation, Germany established the New German Energy
Law (Energiewirtschaftsgesetz, EnWG) in 1998 which induced the liberalisation of the energy mar-
ket in Germany. Since then, the German electricity market has undergone profound changes charac-
terized by mergers, cooperation, strategic partnership and the emergence of power exchanges of
which the European Energy Exchange (EEX) emerged in 2002 and remains as the unique electricity
exchange for Germany. According to official authorities in Germany, there are around 1’100 elec-
tricity producers, grid operators and traders which account for roughly 82% of the domestic electric-
ity production. Out of those 1’100 companies, four large utilities (RWE, E.ON, Vattenfall, and
EnBW) dominate the market, holding close to 84.7% of the production capacities of the German
electricity market (Krisp, 2008). To that, 360 companies owning own generators must be added
which account for another 8% of the German production. The remaining 10% are accounted for by
the EEG law (renewable energy sources act) and includes mostly electricity production from renew-
able energy sources; a sector whose importance is steadily increasing (Statistisches Bundesamt,
2009). The quantity of electricity produced in 2009 amounted to a total of 596.8 Billion kWh,
whereas the main energy sources where: lignite (24%), nuclear (23%), coal (18%), natural gas
(13%), renewable energies (16%) and others (8%) (Bundesverband der Energie- und Wasser-
wirtschaft, 2010). In order to produce this amount of electricity, generators with a production capac-
ity of around 132’700 MW are installed in 2009 (Bundesnetzagentur, 2009). Figure 1 and Figure 2
show that the installed generation capacities by fuel type differ largely with regard to the actually
produced electricity by fuel type. This can be explained by the fact that different production units
generate electricity during a different amount of hours throughout a year (Bundesministerium für
Wirtschaft und Technologie [BMWi], 2010).
Currently, there are four transmission system operators (TSO) in Germany which are responsible for
the transmission of electrical power from the generators to the end consumers. Those TSO have their
Figure 2: Electricity production by fuel type
Based on: Bundesnetzagentur (2009)
Figure 1: Installed generation capacity by fuel type
Based on: Bundesnetzagentur (2009)
Empirical Analysis of Price-Curves at the EEX
- 5 -
origin with the big four (RWE, E.ON, EnBW and Vattenfall) in the German electricity market that
were forced over the course of the last 2 years to separate their grid from their other activities. Today
the 4 TSOs are: 50hertz, transpower, amprion and EnBW Transportnetze, whose control areas can be
seen on Figure 3 (Frontier Economics, 2009).
Beside the changes on the supply and distribution side, one major novelty brought about by the de-
regulation of the German electricity market is the introduction of power exchanges. Today, the Euro-
pean Energy Exchange (EEX) which emerged from the merger of the Leipzig and the Frankfurt ex-
changes in 2002 is the leading energy exchange in Continental Europe and offers trading possibilities
for power, natural gas, CO2 emission allowances and coal. Regarding the power market, the EEX is
offering the possibility for spot trading (day-ahead auctions, intraday auctions) as well as the possi-
bility for derivatives trading (futures and options trading), as well for Germany, France, Austria and
Switzerland (EEX, 2010a). The EEX is therefore offering a trading platform which co-exists with
the very large OTC market that is found in the electricity market. As of 2009, the power spot market
of the EEX observed a volume of 203 TWh, which represents roughly 34% of the total German elec-
tricity production (EEX, 2010a). Prices observed on both OTC and spot market are very similar,
since diverging prices would invite arbitrageurs to make riskless profits from the price differences,
Figure 3: Grid of the transmission system operator
Based on: Ice gixxe (2010)
Empirical Analysis of Price-Curves at the EEX
- 6 -
therefore closing the gap. Even though roughly 66% of the electricity produced is sold OTC, traders
find it convenient to use to spot market of the EEX which allows trading on a day-ahead or even in-
traday time frame to balance their portfolios in the short term, since demand and supply of electricity
must always match.
Empirical Analysis of Price-Curves at the EEX
- 7 -
2. Data Set
This chapter will provide a brief overview over the data sets that is used in writing this paper. First,
the data set regarding the generation capacities will be introduced before exploring the price quantity
bids the market participants place on the day-ahead auction at the EEX and closing with the market
clearing prices and quantities which do result from those auctions as well as the prices and quantities
that do result from the intraday trading for every hour. The time series of the data set account for 9
weeks, from the June 2nd
, 2010 to August 3rd
, 2010. These are 63 days, respectively 1512 hours. 1
2.1 Installed, Available and Actually Used Generation Capacities
2.1.1 General Information
On October 28th
2009, the EEX and the four German TSOs (Amprion GmbH, EnBW Transportnetze
AG, Transpower Stromübertragungs GmbH and Vattenfall Europe Transmission GmbH) announced
that “Transparency in Energy Markets” goes live. They have implemented a new central transpar-
ency platform for generation and consumption data. With this step, new publication requirements
under the “Congestion Management Guidelines”, which is an annex to the “EC Directive No.
1228/2003”, are implemented for the first time in this form in Continental Europe, integrating to the
platform the already existing practice of some market participants of voluntary publication. The aim
of this platform is to strengthen the confidence placed in the market by increasing the comprehensi-
bility of market pricing. The new platform can be found on www.transparency.eex.com and provides
all time series discussed in this part. (Amprion, EEX, EnBW, Transpower & Vattenfall, 2009)
The generation and consumption data that are published on the transparency platform can be divided
into two categories:
1. Statutory Publication Requirements of the Transmission System Operators: These publi-
cation are based on the “Congestion Management Guidelines” and on section 4.3 of the
“Report on Transparency”.2
2. Voluntary Commitment of the Market Participants: These data were already being pub-
lished before and the tried and tested structure of the EEX transparency platform were
perpetuated. (EEX-Transparency, 2010a)
1 The length of the time series was restricted to 9 weeks due to the fact that most data on generation capacities had to
be retrieved by hand. 2 The publication requirements are provided on the website of the Bundesnetzagentur:
http://bundesnetzagentur.de/cln_1931/DE/Sachgebiete/ElektrizitaetGas/AllgemeineInformationen/TransparenzStrom
markt/VeroeffentlichungErzeugungsdaten_Basepage.html
Empirical Analysis of Price-Curves at the EEX
- 8 -
The actual degree of coverage reaches 79.26% and is established with regards to the Statutory Pub-
lication Requirements of the Transmission System Operators on the basis of the ratio of the installed
capacity reported on the platform and the entire installed generation capacity in Germany, which is
according to the Monitoring Report 2009 of the Federal Network Agency roughly equal to 132’700
MW. (EEX-Transparency, 2010b)
2.1.2 Reporting Companies
As of August 11th 2010, 12 companies are reporting to the transparency platform. Their name and
installed generation capacities can be taken out of Table 1.
Corporate Name Installed capacity in MW
E.ON 19’817
EnBW 9’606.1
EVN AG 1’120
Grosskraftwerk Mannheim AG 1’143
RheinEnergie AG 531
RWE Power AG 25’642.1
Stadtwerke Leipzig GmbH 167
SWM Services GmbH 1’009
TIWAG, Tiroler Wasserkraft AG 361.1
Trianel Gaskraftwerk Hamm GmbH & Co.KG 850
Vattenfall Europe AG 15’176
VSE AG 118
Total 75’540.3
Table 1: Companies reporting to the transparency platform
Based on: EEX-Transparency (2010c)
The figures presented in Table 1 involve the generation capacities from coal, gas, lignite, oil,
pumped storages, run-of-the-river, seasonal storage, uranium and others with production capacities
above 100MW. Next to those 75’540.3MW of installed capacities, Figure 4 on the next page shows
the installed facilities with generation capacities of less than 100MW which are not accounted for in
Table 1.
In total, 31’858.3MW of installed capacity belong to this later category and are distributed according
to Figure 4. (EEX-Transparency, 2010c)3
3 The total generation capacity installed for generators under 100MW has been updated since August 11
th and is now,
on 31th
October, equal to 49’649.6 MW.
Empirical Analysis of Price-Curves at the EEX
- 9 -
Coal
1%
Garbage
2%
Gas
10%
Lignite
3%Oil
2%
Others
9%
Pumped storage
4%
Run-of-the-river
5%
Seasonal
storage
1%
Solar power
2%
Wind
61%
2.1.3 Installed Capacities
All further discussions will be based on the data published under the heading Voluntary commitments
by the market participants which cannot be directly compared with the installed capacity mentioned
above since the degree of coverage is smaller, as not all market participants do publish their data on a
voluntary basis. The reason for choosing this set of data is, that there is a clear fracturing between the
different generation types. The data are ex-ante information regarding the generation capacities and
include some generation units with less than 100MW of nominal output. Table 2 shows following
generation capacities that are installed according to the data published voluntarily by the market par-
ticipants.
Generation Type Installed capacity in MW
Uranium 20’279
Lignite 19’823
Coal 16’141.6
Gas 8’609
Pumped storage 5’993
Oil 1’135.9
Seasonal storage 594
Run-of-the-river 478.6
Total 73’054.1 Table 2: Installed capacity by generation type (Voluntary publication)
Based on: EEX-Transparency (2010d)
As electricity generated through wind energy plays an important role in the electricity generation in
Germany, the installed wind turbine capacities must be taken into account. According to the Bundes-
verband WindEnergie e.V. (2009), wind turbines with a generation capacity of 25’777MW were in-
Figure 4: Generation capacities under 100MW by generation type
Based on: EEX-Transparency (2010c)
Empirical Analysis of Price-Curves at the EEX
- 10 -
stalled at the end of 2009. Data from the transparency platform show that wind generating units with
an installed production capacity of 19’494.5MW do report their expected output as well as their ac-
tual electricity production (EEX-Transparency, 2010e). Therefore, 92’548.6MW of installed capacity
are considered as our maximal possible output if all generating units are working under full load
which represents roughly 69.74% of the totally installed generation capacity in Germany and which
is, as already mentioned before, slightly lower than the total coverage provided by the transparency
platform of the EEX.
2.1.4 Available and Forecasted Capacities
Installed generation capacities are not always available for electricity production. On the one hand,
regular maintenance have to be realized while on the other hand, natural resources to power the tur-
bines might not be available, especially water (run-of-the-river, nuclear for cooling purposes) and
wind (not enough or too strong). For this reason, installed generation capacities are only interesting
from the point of view of the maximal generation capacity of a country. Much more insights into the
actual situation on the supply side is provided by the available power plant capacity, respectively by
the forecasted production when thinking of wind turbines. Wind turbines prove to be very peculiar
power plants since wind speed is very difficult to forecast accurately. Unlike all other generating
units (expect for solar generating plants which are not considered here since their importance for the
German electricity market is only marginal), wind turbines most important factor when deciding over
their availability to produce electricity is not only mankind but to a very large extend nature. This
explains the unpredictability of this energy source. The available power plant capacities for all gen-
eration types are provided on a daily basis. Expected wind turbine generation however is projected
on a quarter-hourly base for the following day.4 Figure 5 provides a graphical overview over the
availability of conventional generation capacities (lignite, nuclear, coal, gas, oil, run-of-the-river,
seasonal & pumped storage) for the German market from June 2nd
2010 to August 4th
2010, Figure 6
4 The quarter-hourly figures are compounded such as to have one hourly figure.
Average Median St. Deviation Maximum Mininum Difference St.Dev/Average
Uranium 14330.2 14277.9 1027.9 16586.7 12104.6 4482.1 7.17%
Lignite 15986.8 15993.3 721.1 17366.7 14291.2 3075.5 4.51%
Coal 13375.2 13536.2 718.1 14586.8 11580.1 3006.7 5.37%
Gas 6277.8 6353.5 552.2 7093.8 5002.3 2091.5 8.80%
Pumped storage 4445.3 4521.7 363 4868.7 3450.7 1418.7 8.17%
Oil 958.5 1033.2 167.5 1035.1 121.9 913.2 17.48%
Seasonal storage 456.3 477 70 522 288 234 15.35%
Run-of-the-river 419.9 421.2 8.4 435 400.8 34.2 2.00%
Wind 2182.1 1575.55 1869.8 12965 234.8 12730.3 85.69%
Table 3: Available production capacities with respect to different generation types (in MW)
Based on: EEX-Transparency (2010d)
Empirical Analysis of Price-Curves at the EEX
- 11 -
provides furthermore the hourly expected wind production while Table 3 briefly summarizes the key
features of those available generation capacities.
0
2000
4000
6000
8000
10000
12000
14000
Exp
ect
ed
pro
du
ctio
n [
in M
W]
H [Hourly value for every day]
Figure 6: Expected electricity generation through wind turbines on an hourly basis
Based on: EEX-Transparency (2010f)
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000
Av
ail
ab
ilit
y [
in M
W]
T [in days]
Uranium
Lignite
Coal
Gas
Pumped storage
Oil
Seasonal storage
Run-of-the-river
Figure 5: Available capacity for each generation type on a daily basis
Based on: EEX-Transparency (2010d)
Empirical Analysis of Price-Curves at the EEX
- 12 -
The available generation capacities for production with uranium, lignite, coal and run-of-the-river
have a much lower volatility than the one with gas, pumped storage, oil and seasonal storage. Even
though electricity production (respectively consumption) is not looked at, weekly patterns are ob-
servable, especially in the availability of gas and to a lesser extend of coal fired power plants.
Regarding wind power generation, the most important aspect is wind forecast. Based on their wind
forecast, the transmission system operator publish daily at 6.00 pm the expected wind power genera-
tion for the next day on every specific quarter-hour (EEX-Transparency, 2010f). In order to reduce
the different time windows used, the quarter-hourly forecast is condensed to provide an hourly fore-
cast by taking the average over the 4 quarter-hourly quantities as is done by the EEX.
As could be anticipated, expected wind power generation does not follow any daily or weekly pattern
since it is only depended on available wind. Furthermore, as Table 3 on the page 10 shows, the vola-
tility in expected wind power generation is extremely large which requires an increased flexibility of
the electricity system in order to be able to handle those fluctuations.
2.1.5 Actually Produced Electricity
The next step is to explore actually produced electricity with regard to each individual generation
type. The time series for those data are on an hourly basis, since demand for electricity is very vola-
tile and production capacities therefore have to adjust on a regular basis. Table 4 summarizes the re-
sults from Figure 7 with respect to the actually produced electricity in the German market between
June 2nd
2010 and August 4th
2010.
Electricity produced through wind turbines has to be considered from a different point of view since
transmission system operators are committed by the Erneuerbare-Energien-Gesetz (EEG) to purchase
it prior to electricity from other sources (§21 and §8 Abs. 1 EEG). Practically speaking, electricity
produced by wind energy reduces the demand, which leads in theory to a lower market clearing price
(Fürsch, Nicolosi & Lindenberger, 2010).
Table 4 clearly shows that the actual production of the power plants generated by uranium, lignite as
well as run-of-the-river power plants have a fairly low volatility. This is the case because they are
used to cover the Baseload demand. The actual production for the remaining power plants (e.g. coal,
gas, pumped storage, oil and seasonal storage) exhibit on the other hand a much higher volatility.
Figure 7 displays clearly the daily and especially weekly pattern of those production facilities, with a
higher production on weekday rather than on Saturdays and Sundays coupled with an increasing pro-
duction during day time, in short during the on-peak hours.
Empirical Analysis of Price-Curves at the EEX
- 13 -
0
2000
4000
6000
8000
10000
12000
Act
ua
l pro
du
ctio
n [
in M
W]
H [Hourly value for every day]
Coal
Oil
Gas
0
500
1000
1500
2000
2500
3000
Act
ua
l pro
du
ctio
n [
in M
W]
H [Hourly value for every day]
Pumped-storage
Run-of-the-river
Seasonal storage
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
Act
ua
l pro
du
ctio
n [
in M
W]
H [Hourly value for every day]
Wind
Uranium
Lignite
Figure 7: Actual production with respect to different generation types (in MW)
Based on: EEX-Transparency (2010g and 2010h)
Empirical Analysis of Price-Curves at the EEX
- 14 -
Table 4: Actual production with respect to different generation types (in MW)
Based on: EEX-Transparency (2010g and 2010h)
Coal and gas power plants always have a minimum production even though both are typical Peak-
load power plants: Fürsch et al. argues that this is due to some “must-run” facilities which have to
provide system services (2010), another reason could be the lead-up time that most thermal power
plants face.
2.2 Demand and Supply Curves
The EEX offers a spot market that is used by the trading participants to optimise their procurement
and sale of electricity in the short term. As of August 12th
2010, there are 166 trading participants in
the spot auction market for Germany as well as 164 trading participants in the spot intraday market
for Germany (European Power Exchange [EPX], 2010). The day-ahead auctions for Germany have
the following characteristics (EEX, 2010a):
- Minimum volume is 0.1 MW
- Minimum price change is EUR 0.1 per MW
- Underlying is electricity traded on the following day
- Electricity has to be delivered within one of the TSO zones
- Daily auction at 12:00 noon, 7 days a week, 365 days a year including holidays
- Results of the daily auction are published between 12:35 and 12:45 am.
- Orders comprises up to 250 price/quantity combinations for every hour of the following
day
- Technical limits for the prices are between EUR -3000 per MW and EUR 3000 per MW.
The curves that result from this bidding process can be called demand respectively supply curve. On
the one hand, the demand side bids for each price the quantity it is willing to purchase and on the
other hand, the supply side bids for each price the quantity it would be ready to produce. This is ex-
actly the definition provided by Pindick and Rubinfeld: “The demand curve is the relationship be-
tween the quantity of a good that consumers are willing to buy and the price of the good”, and “The
Average Median St. Deviation Maximum Mininum Difference St.Dev/Average
Uranium 13527.4 13774.5 1561.3 16629.8 8145.8 8484.0 11.54%
Lignite 14879.8 14954.6 967.6 17050.4 11004.9 6045.5 6.50%
Coal 5784.7 5505.7 2905.9 11200.3 414.3 10786.0 50.23%
Gas 1297.9 1296.7 638.0 4890.8 382.4 4508.4 49.16%
Pumped storage 615.6 443.2 541.4 2570.2 6.6 2563.6 87.95%
Oil 90.9 0.0 187.6 768.0 0.0 768.0 206.36%
Seasonal storage 94.2 77.2 88.6 558.5 0.0 558.5 94.06%
Run-of-the-river 410.5 427.5 63.1 495.6 93.1 402.5 15.37%
Wind 2196.9 1555.8 2066.2 13597.9 120.7 13477.3 94.05%
Empirical Analysis of Price-Curves at the EEX
- 15 -
supply curve is the relationship between the quantity of a good that producers are willing to sell and
the price of the good” (2005). Figure 8 and Figure 9 illustrate the general form of the demand curve
Figure 8: Price (in EUR per MW) – Quantity(in MW) bids for the demand
Based on: EEX (2010b)
Figure 9: Price (in EUR per MW) – Quantity (in MW) Bids for the Supply
Based on: EEX (2010b)
Empirical Analysis of Price-Curves at the EEX
- 16 -
respectively supply curve. These figures have been generated by using 302’400 price quantity bids
(200 price and quantity bids per hour, for 24 hours a day during 63 days) for both demand and sup-
ply.
The general form of the demand curve already reveals that the demand curve is almost flat for most
price bids, with the most interesting part of the demand curve, that is where the actual slope is, being
found in a range from -10 EUR per MW to +100 EUR per MW; in other words the range in which
prices normally fluctuates.
The general form of the supply curve also reveal a flat curve for most of the time, especially for
negative price bids. Again, the slope of the supply curve increases in a range from -10 EUR per MW
to +100 EUR per MW.
The auction procedure of the EEX basically combines the demand and supply curve of every hour
and determines in such a way the market clearing price and quantity. Figure 10 shows the result of
such an auction for June 6th
for hour 1, that is from 00:00 to 01:00 am. Please note that the scale of
the x-axis does not reflect reality but allows for a better overview of the behaviour of the demand and
supply curve for price bids between -10 EUR per MW and + 100 EUR per MW, since as already
described, the remainder of the curves is very uninteresting.
10000120001400016000180002000022000240002600028000
-30
00
-19
50
-90
0
-20
1.5
7
-11
6.7
3
-47
.45
-5.4
5
-0.0
9
2.0
5
12
.55
18
.55
24
.55
30
.55
34
.8
35
.6
36
.3
36
.9
37
.8
38
.6
42
.55
48
.93
57
.55
63
.55
68
.05
10
2.5
5
14
4.5
5
45
0
15
00
25
50
Qu
an
tity
[in
MW
]
Price in EUR per MW
Supply/Demand curve PHELIX-Spot Hour 1; MCP: €36.55,
MCQ: 19'132 MW
Demand
Supply
Figure 10: Intersection of the demand and supply curve on hour 1, June 6th
2010
Based on: EEX (2010b)
Empirical Analysis of Price-Curves at the EEX
- 17 -
2.3 Price and Quantity
This section introduces two time series for prices and quantities. On the one hand side, the prices and
quantities which result from the day-ahead auction will briefly be summarized while on the other
hand the prices and quantities which result from the intraday auction will be analysed. The idea be-
hind offering intraday trading is to give market participants the possibility to buy and sell power at a
very short notice in order to optimise their procurement and sale. Each hour can be traded until 75
minutes before the beginning of the delivery hour starting at 3:00 pm the day before (EEX, 2010a).
Due to the very volatile nature of electricity market, especially with regards to the production from
wind turbines which is very hard to forecast accurately on a day-ahead basis, intraday trading offers
a valuable opportunity to market participants.
Figure 11 shows the evolution of day-ahead prices and intraday prices during the observation period
from June 2nd
2010 to August 4th 2010, while Figure 12 displays the quantity traded in the respective
hours. Table 5 summarizes the key findings.
0
20
40
60
80
100
Act
ua
l Pri
ce in
EU
R p
er
MW
H [Hourly value for every day]
Day-ahead
Intraday
Figure 11: Hourly intraday and day-ahead prices
Based on: EEX (2010c) and EEX (2010d)
Empirical Analysis of Price-Curves at the EEX
- 18 -
Day-ahead
Prices (in EUR)
Day-ahead Quan-
tity (in MW)
Intraday Prices (in
EUR)
Intraday Quantity
(in EUR)
Average 44.24 22'936.66 44.29 1'121.02
Median 45.30 21'690.20 44.95 927.00
Standard Deviation 12.54 4'584.17 14.26 839.37
Maximum 83.89 38'198.10 96.40 7'466.80
Minimum -0.08 15'185.40 2.04 68.00
St. Dev / Average 28.34% 19.99% 32.19% 74.87%
Table 5: Price and Quantity for intraday and day-ahead markets
Based on: EEX (2010c) and EEX (2010d)
Day-ahead and intraday prices exhibit very similar price paths and follow the expected daily and
weekly pattern. Furthermore, average prices for intraday and day-ahead markets are very close to
each other, even though the intraday market is somewhat more volatile, showing for the observation
period a higher maximum price. The day-ahead quantity also follows as expected a clear daily and
weekly pattern. On the other hand, intraday quantities follow a very random pattern in between 68
MW and 7’466.8 MW, which explains the very high volatility. The main reason for the lack of daily,
0
5000
10000
15000
20000
25000
30000
35000
40000
Act
ua
l Qu
an
tity
in M
W
H [Hourly value for every day]
Intraday
Day-ahead
Figure 12: Hourly intraday and day-ahead quantities
Based on: EEX (2010c) and EEX(2010d)
Empirical Analysis of Price-Curves at the EEX
- 19 -
respectively weekly pattern is the fact that intraday auctions are used to balance procurement portfo-
lio in the very short term, for example in the case that the expected electricity production from wind
falls short of the forecast, or if a power plant has to be shut down on a short notice.
Empirical Analysis of Price-Curves at the EEX
- 20 -
3. Preparing the Data Set
To be able to work with the data sets introduced during Chapter 2, the described generation capaci-
ties, the demand and supply curves and the day-ahead and intraday prices must be prepared. This
section will help to quantify reserve margins, demand and supply curve elasticity’s as well as volatil-
ity figures for the market prices.
3.1 Analysing Production Capacities
3.1.1 Reserve Margin
Reserve margins have been intensively discussed in late years in Europe, the US but also in other
countries, for example South Africa. In a study by Constable and Sharman (2008) which explores the
fundamental drivers and probable trends in the U.K. electricity market, the authors come to the con-
clusion that the actual reserve margin of 24% will be more rapidly eroded and eventually even be-
come negative in a future closer than expected. A bleak outlook is also drawn by RWE (2007) for
most of continental Europe, with the average reserve margin5 (as computed by the Cambridge En-
ergy Research Association) declining under 15% before 2010. Countries like Hungary and Poland
are even expected to exhibit negative reserve margins as soon as 2015. Just to name another exam-
ple, South Africa’s reserve margins has fallen in recent years to around 8%, a situation which has
placed considerable pressure on the industry since the reliability of the power grid was not ensured
anymore (Department of Minerals and Energy, 2008). The reliability of the generation capacities was
in such a poor shape in South Africa that the crucial mining companies even had to shut down their
activities since Eskom (South African electricity monopolist) was not able to ensure electricity deliv-
ery to run the elevators that move miners up and down into the mine (Timberg, 2008). Eskom argues
that relief is five to seven years away, since generation capacities cannot be build much faster. These
acute problems, especially in South Africa but more generally in many other countries, illustrate why
there might be good reasons to be nervous about reserve margins, especially very low ones.
The reserve margin is a key system characteristic which is used to describe the operational safety and
reliability as well as the price stability of an electricity system. The reserve margin describes the ex-
cess available generation capacity, if any is available, relative to the load and gives therefore a meas-
ure of how resistant the power system is to unforeseen generation capacity fall out. (Rochlin &
Huang, 2005)
5 Reserve margin in this case as the difference between dependable capacity and peak demand divided by peak de-
mand
Empirical Analysis of Price-Curves at the EEX
- 21 -
� ������� �!�"#$ = �%&&'( − *��!$**��!$* +
Demand is in this case the actual quantity demanded at the prevailing electricity price while the sup-
ply refers to the amount of generating capacity available to serve the load at a specific point in time.
This is why Rochlin et al. describe the reserve margin as a stochastic variable which depends on the
distribution of the demand as well as on the distribution of the supply, both of which vary over time
(2005). The most common form of reserve margin found in the literature is the one looking at peak
demand. Among others, the U.S. Energy Information Administration (2010) defines reserve margin
“as the amount of unused available capability of an electric power system at peak load as a percent-
age of capacity resources”. For this paper, it is however more convenient to use the more general
definition of reserve margin which takes into account all hours of a day.
In practice, the proposed minimum value for reserve margin vary considerably from one regulator to
another. For example, the Federal Energy Regulatory Commission’s Notice of Proposed Rulemaking
(2003) proposes a minimum value of 12%, the California Public Utilities Commission (2003) sees a
reserve margin between 15-17% as adequate, the Electric Reliability Council of Texas (2005) be-
lieves that a 12.5% reserve margin is adequate while the New York Independent System Operator
(2006) prefers to keep a margin of at least 18%. Now that the reserve margin is defined and the re-
quired margin throughout the world have been discussed, it is time to take a closer look at the situa-
tion on the German market during the period from June 2nd
2010 to August 4th
2010. In a first step,
the overall reserve margin is computed while a second step will have a closer look at the used gen-
eration capacity with respect to each generation type separately. When considering wind energy, it
makes sense to assume the expected production to be treated like the available production capacity
for the non-wind generating units. This is not strictly a reserve margin since it estimates how well
electricity generation through wind was forecasted, nevertheless, it works in the same way as the re-
serve margins for conventional power plants.
Figure 13 shows the evolution of the margin over the two month period between June 2nd
2010 and
August 4th
2010. The daily pattern which is typical for the electricity consumption can also be ob-
served here. In order to grasp further information, Figure 14 provides insights into how those mar-
gins are distributed and Table 6 summarizes the key results. Interestingly enough, Germany only ex-
perienced a margin slightly below 20% during 5 hours (0.03% of the time), while the average margin
(as can be taken out of Table 6) is 51.43% with a standard deviation of 15.62%. Even though the
sample is not representative for the situation in Germany, it seems that the German electricity market
is not at stake to run out of electricity in the next couple of years.
Empirical Analysis of Price-Curves at the EEX
- 22 -
Figure 13: Hourly margin for the German electricity market
Based on: own computation
0
10
20
30
40
50
60
17
.00
%
20
.00
%
23
.00
%
26
.00
%
29
.00
%
32
.00
%
35
.00
%
38
.00
%
41
.00
%
44
.00
%
47
.00
%
50
.00
%
53
.00
%
56
.00
%
59
.00
%
62
.00
%
65
.00
%
68
.00
%
71
.00
%
74
.00
%
77
.00
%
80
.00
%
83
.00
%
86
.00
%
89
.00
%
92
.00
%
95
.00
%
98
.00
%
10
1.0
0%
Occ
urr
en
ce
Distribution
Histogramm
Figure 14: Margin distribution for the German electricity market
Based on: own computation
0.00%
20.00%
40.00%
60.00%
80.00%
100.00%
120.00%
Ma
rgin
H [Hourly value for every day]
Margin
Empirical Analysis of Price-Curves at the EEX
- 23 -
One might however want to consider that the electricity consumption in Germany somewhat dropped
due to the heavy financial and economic crisis of 2008-2009. Moreover, considering the German
wish to exit, at least in the long run, nuclear electricity production, there might be some very tight
margins ahead. Under current consumption, removing the nuclear power plants would lead to nega-
tive margins in 10.6% of the hours for the observed time window and replacing their generating
power through renewable energy might prove challenging when considering their extreme volatile
production (wind and solar).
3.1.2 Degree of Capacity Utilisation
Having showed that Germany did not face really tight production capacities during the observed two
month, it is certainly interesting to have a closer look at the individual generation types. Instead of
using the reserve margin computation, it is more intuitive to compute the actual percentage of gen-
eration capacity that has been used. For wind generation, this yields an estimate of how good the
production forecast was.
, %��* -!&!-#.(/012 3 = �%&&'(/012 3 − *��!$*/012 3�%&&'(/012 3 4
This measure gives us an idea which power plant were actually producing at what time respectively
how good the production forecast for wind was. The later is a relevant information since large differ-
ences between the actual wind production and its forecasted production must be compensated by
other power plants, either by producing more or by producing less. Figure 15 illustrated how used
capacity evolved between June 2nd
2010 and August 4th
2010, while Table 7 summarizes the key
findings.
Average Median St. Devia- Maximum Mininum
Margin 51.43% 50.14% 15.62% 101.21% 17.07%
Table 6: Margins in the German electricity market
Average Median St. Deviation Maximum Mininum
Uranium 95.30% 95.23% 2.98% 103.90% 76.97%
Lignite 93.04% 94.05% 5.02% 108.38% 71.13%
Coal 42.91% 40.96% 20.92% 83.40% 6.85%
Gas 20.35% 20.49% 9.17% 69.59% 6.87%
Pumped storage 13.85% 9.95% 11.93% 57.01% 0.14%
Oil 6.48% 0.00% 16.10% 80.06% 0.00%
Seasonal storage 16.51% 9.45% 18.86% 106.99% 0.00%
Run-of-the-river 100.02% 101.23% 7.06% 111.54% 63.21%
Wind 98.39% 95.36% 36.79% 268.94% 19.14%
Table 7: Used capacity with respect to generation type
Based on: own computation
Empirical Analysis of Price-Curves at the EEX
- 24 -
0.00%
20.00%
40.00%
60.00%
80.00%
100.00%
120.00%
Use
d C
ap
aci
ty
H [Hourly value for every day]
Oil
Pumped-storage
Gas
Seasonal storage
0.00%
50.00%
100.00%
150.00%
200.00%
250.00%
300.00%
Use
d C
ap
aci
ty
H [Hourly value for every day]
Wind
0.00%
20.00%
40.00%
60.00%
80.00%
100.00%
120.00%U
sed
Ca
pa
city
H [Hourly value for every day]
Uranium
Lignite
Run-of-the-river
Coal
Figure 15: Used capacity over time with respect to generation type
Based on: own computation
Empirical Analysis of Price-Curves at the EEX
- 25 -
3.1.2.1 Generation from Uranium
On average, available generation capacities were used up to 95.30% with a lowest degree of capacity
utilisation at 76.97%. Hence, uranium fired power plants are the typical Baseload providers. In some
cases, figures above 100% can be observed. This might have several reasons: on the one hand, there
might be some errors in the data due to non-communicated stops of production, while on the other
hand, it might be due to changes in available capacities from one day to the other. From June 4th
23:00 to June 5th
00:00, available capacity dropped from 14’612.6 MW to 12’914 MW, while the
production of electricity only slowly retreated from 13’817.9 MW to 13’417.2 MW before dropping
further to 12’627 at 01:00. The registered 103.90% is here due to the fact that reducing actual nuclear
generation capacity takes some time into account, while the reported available capacities are daily
averages and might therefore show small differences with actually available capacities on boarder
hours to the previous or following day.
3.1.2.2 Generation from Lignite
On average, generation capacities were used up to 93.04%, with a minimum at 71.13% and a maxi-
mum at 108.38%. The argumentation for coal fired power plants is very similar to the one for the
uranium fired power plants since lignite fired power plants also belong to the typical Baseload pro-
viders. The volatility is somewhat higher for generators using lignite, which can be explained by
tighter regulations for uranium fired power plants (Fürsch et al., 2010).
3.1.2.3 Generation from Run-of-the-river
Run-of the-river power plants show an average use of their available capacity of 100.03%, with val-
ues ranging from 121.95% to 63.21%. Run-of-the-river also belongs to the typical Baseload provid-
ers. The volatility is somewhat higher than for nuclear and lignite power plant which is due to the
fact that the electricity production of run-of-the-river power plant can be changed very easily. There
is no ramp-up time per se.
3.1.2.4 Generation from Wind
Actual wind generation was on average 98.36% from the expected wind generation. However, the
lower bound is found at 19.14% while the upper bound reaches 268.94% which is among other a rea-
son why the volatility (36.79%) is very high. What these figures show is that forecasting wind inten-
sity is very difficult. However, on average, the wind forecast is pretty accurate. As already men-
tioned, electricity produced through renewable energy (among others: wind) is always induced into
the grid and is therefore considered as Baseload providing power plant with peculiar characteristics.
Empirical Analysis of Price-Curves at the EEX
- 26 -
3.1.2.5 Generation from Coal
The average use of available coal generation capacity is 42.91% with the highest value reaching
83.40% and the lowest value being at 6.85%. Coal power plants are used to satisfy Peakload demand
and their electricity production is therefore very volatile (20.92%). The reason why their use doesn’t
drop to 0% is that there might be some generation units which offer system services and must there-
fore be kept running (Fürsch et al., 2010).
3.1.2.6 Generation from Gas
On average, 20.35% of available gas generation capacity are used with a peak at 69.59% and a low-
est value around 6.87%. Gas power plants are also used to satisfy Peakload demand and exhibit very
similar characteristics to coal power plants.
3.1.2.7 Generation from Pumped Storage and Seasonal Storage
Pumped storage and seasonal storage exhibit very similar numbers. The lower bound for used avail-
able generation capacities is at 0%. Both, pumped storage and seasonal storage are Peakload satisfy-
ing facilities which can concentrate their electricity production in period where prices are highest.
They do not face any run-up time and are therefore extremely flexible.
3.1.2.8 Generation from Oil
Available capacities of oil generation power plants are only used on average to an extend of 6.48%,
with a peak at 80.06% while the lower bound is, not surprisingly for a very flexible Peakload satisfy-
ing power plant at 0%. Interestingly, their median use is 0% which means that most of the time, oil
generation units are never used.
Empirical Analysis of Price-Curves at the EEX
- 27 -
3.2 Elasticity
In order to analyse the relationship between the demand and supply curves formed through the bid-
ding procedure in the day-ahead auction market and other variables of the German electricity market,
both demand and supply curve must be characterised. Pricing policies were long considered as a
good instrument to improve energy efficiency; however, as Narayan, Smyth and Prasad note, pricing
policies to promote the efficient use of electricity do also depend on the price elasticity of demand
(and supply) for electricity (2007). Even so, demand and supply curves are often described using
elasticity as a measure, since it provides the percentage change in quantity demanded divided by the
percentage change in price, therefore providing a measure of the demand responsiveness that is uni-
versally used in economics. Eilon (1983) finds two definitions of elasticity that are commonly used
in the literature. On the one hand, point elasticity is defined for a given point on the demand (or sup-
ply) curve and therefore relies on the derivative of the curve, respectively function at that point
(which means that the eligible curve must be described by a function). On the other hand, arc elastic-
ity is defined for the midpoint of an arc connecting two points, irrespective of the shape of the de-
mand function since the construction assumes a straight line. The crucial point in this case is to de-
cided on how far apart the two points can be distant from each other. Eilon argues that point elastic-
ity is the most widely cited in the literature even though it is often difficult to determine and practi-
tioner therefore mostly prefer to use arc elasticity which does not require fitting a function to the de-
mand (or supply) curve (1983).
3.2.1 Point Elasticity
The first step in order to compute the point elasticity of the demand and supply curves that result
from the bidding process of the market participants in the day-ahead auction is to fit a function to
every single curve seen in Figure 8 and Figure 9. The method used here was already discussed by
Stone (1977) and Fan (1992, 1993) to name only two. They used a polynomial to fit a data sample.
The general equation of a polynomial regression has the following form:
[ 5(.) = &8 + &: ; + &< ;< + &> ;> + … … … … + &? ;? ] With &8 being an optional constant and &: through &? being coefficients of increasing power of ;.
The order of the polynomial is described by m and must be decided before searching for a polyno-
mial to fit the data. A polynomial of order one has the form of a linear equation, while a polynomial
of order two takes the form of a quadratic equation. Polynomials of higher order (4th or 5
th) are useful
to describe data points accurately, but the terms cannot generally be interpreted in any physical
Empirical Analysis of Price-Curves at the EEX
- 28 -
sense. Furthermore, it is often not reasonable to choose polynomials of order beyond 12 since this
could lead to odd and unreasonable results. (Abdolkhalig, 2008)6
The polynomial that best fits the data is the one with the least squared error. Therefore, as-
suming a polynomial of the above described form is used to approximate the price quantity combina-
tions bid by the market participants.; the following set of data is given: (;� , ��), (!", �"), and so forth
to (!# , �#), where $ ≥ & + 1. The curve with the best fit ('(!))) is the one with the least squared
error that minimise the following equation:
- = .[�) − '(!))]"#)0� = .[�) − (23 + 2� !) + 2" !)" + 24 !)4 + … … … … + 25 !)5)]"#
)0�
The coefficients 23, 2� , … , 25 are unknown while all �) and !) are given. To minimise this equation,
the first derivatives of each coefficient must be equal to zero. Therefore:
6∏623 = 2 .[�) − (23 + 2� !) + 2" !)" + 24 !)4 + … … … … + 25 !)5)]#)0� = 0
6∏62� = 2 . !) [�) − (23 + 2� !) + 2" !)" + 24 !)4 + … … … … + 25 !)5)]#)0� = 0
and so forth...
6∏625 = 2 . !)5 [�) − (23 + 2� !) + 2" !)" + 24 !)4 + … … … … + 25 !)5)]#)0� = 0
These equations can be expanded so as to end up with a system of linear equations which can then be
solved to obtained the coefficients. The following expanded equations are obtained:
. �)#
)0� = 23 . 1#)0� + 2� . !)
#)0� + 2" . !)"#
)0� + … + 25 . !)5#)0�
6 Various types of curve fits do exist, with the main categories being least square curve fits, nonlinear curve fits and
smoothing curve fits. The decision to use polynomial to fit the data set is that is has the advantage of being relatively
simple in term of required computing power and it is well understood. Furthermore, there are no outliers in the data
set, therefore avoiding one of the main drawbacks for using this methodology.
Empirical Analysis of Price-Curves at the EEX
- 29 -
. !)�)#
)0� = 23 . !)#
)0� + 2� . !)"#)0� + 2" . !)4#
)0� + … + 25 . !)5:�#)0�
. !)"�)#
)0� = 23 . !)"#)0� + 2� . !)4#
)0� + 2" . !);#)0� + … + 25 . !)5:"#
)0�
and so forth...
. !)5�)#
)0� = 23 . !)5#)0� + 2� . !)5:�#
)0� + 2" . !)5:"#)0� + … + 25 . !)"5#
)0�
The fundamental mathematical notions to compute the polynomial that best fits the data being intro-
duced, the next step can be taken.
The second step is to decide what kind of polynomial to take, that means to determine of
which order the polynomial ought to be. A straight forward possibility is to compute polynomial of
different order (from 1 to 12) and to assess their goodness of fit using R-Square. Based on that, the
polynomial which best suits the purposes of this paper can be chosen.
R-Square is the square of the correlation between the response values (that is the actual val-
ues) and the predicted response values (that is the values that would have been obtained using the
polynomial). R-Square is defined as the ratio of the Sum of Squares of the Regression (SSR) and the
Total Sum of Squares (SST), as illustrated hereafter. (Abdolkhalig, 2008)
<>>? = .(') − �@)"#)0� A
<>>B = .(�) − �@)"#)0� A
C? − >DEFGH = >>?>>BI
In order to enhance the results from the polynomial fit, one further restriction is added. As seen in
Chapter 2 the slope of the demand and supply curve does exhibit some steepness only in a fairly
short interval (from roughly -10 EUR per MW to roughly + 100 EUR per MW) being more or less
flat for all other price quantity combinations. To take this into account, the dataset for which poly-
Empirical Analysis of Price-Curves at the EEX
- 30 -
nomials will be generated has been restrained to all price-quantity combinations found in between –
450 EUR per MW and + 450 EUR per MW. This restriction has been chosen after early computa-
tions had been performed without imposing it and the fit of the resulting function was, comparing to
later results, very poor7. Table 8 shows the mean R-Square for polynomials of different order fitted
to the demand and supply curve.
Polynomial R-Square (Demand) R-Square (Supply)
1 0.625829415 0.633393403
2 0.633093057 0.703197944
3 0.792929152 0.799777043
4 0.800402947 0.847787241
5 0.892619394 0.883441748
6 0.89836004 0.91421344
7 0.94149664 0.93605434
8 0.95167656 0.95335101
9 0.96587901 0.96139181
10 0.97334162 0.97014305
11 0.97897038 0.97706397
12 0.98262149 0.98171485 Table 8: R
2 for polynomials of different order fitting the demand and supply curves
Based on: own computation8
Without surprise, higher polynomial do fit the data in a better way, especially in the range (-10 EUR
per MW to + 100 EUR per MW) that is relevant. The R-Square found are fairly low for polynomials
of lower order, which is not astonishing since the demand and supply curve are far from being
straight lines. The size of the increase gets very small for polynomials of order higher than 10. Based
on those findings, the decision is taken to use a polynomial of order 12 to fit the data for further tasks
since the use of polynomials of higher order is not recommended.
Having decided how to describe each of the demand and supply curve, the point elasticity for each
hour, as well for the demand and supply curve, can be computed. Point elasticity of demand is de-
fined as:
C 2JK$L HMFNLKOKL� J' PH&F$P = 2Q(2) Q′(2)I with 2 being the market clearing price, Q(2) the demand function (the polynomial) and Q′(2) the
first derivative of the demand function. (Wilson, 2010)
7 A polynomial of order 12 used to fit the whole demand and supply curve exhibits an R-Square of 69.57% without re-
strictions, which is a very poor fit. 8 Please refer to Appendix 1 on page 66 for more details on the computation.
Empirical Analysis of Price-Curves at the EEX
- 31 -
Computing the elasticity starting from the polynomial requires several steps:
1. Find the polynomial that fits the demand or supply curve for every hour
2. Compute the first derivate of it
3. Plug in the market clearing price of that hour, to get a numerical result.
A brief illustration for a random hour shall be provided in order to enhance the understanding of
what is being done. The demand curve for Hour 1 on June 6th
2010 is chosen.
1. Find the polynomial of order 12 that fits the demand curve for Hour 1, June 6th
2010
D(p) = 25′332 + (−143.3758)! + (1.5589)!"+ (0.0191)!4 + (2.1789Y;)!;+ (−1.3104YZ)!\+ (−1.2896Y_)!Z+ (4.0694Y��)!` + (3.5959Y�4)!_+ (−5.5850Y�Z)!a + (−4.6023Y�_)!�3 + (2.7087Y"�)!��+ (2.1370Y"4)!�"
2. Take the first derivative of it
D'(p) = − 143.3758 + (−3.1179)! + (0.0574)!"+ (8.7157Y;)!4 + (−6.5521YZ)!;+ (−7.7378Y_)!\+ (2.8486Y�3)!Z+ (2.8767Y�")!` + (−5.0265Y�\)!_+ (−4.6023Y�`)!a+ (2.9796Y"3)!�3+ (2.5644Y"")!��
3. Plug in the market clearing price of EUR 36.55 per MW
D(p) = 19'219.9466
D'(p) = -153.9604
2JK$L HMFNLKOKL� J' PH&F$P = 36.5519'219.9466 ∗ (−153.9604) = −0.2928
The point elasticity of supply can be computed in an analogous way, with >(2) being the supply
curve function and > ′(2) being the first derivative of the supply curve function.
C 2JK$L HMFNLKOKL� J' NE22M� = 2>(2) > ′(2) I
Empirical Analysis of Price-Curves at the EEX
- 32 -
Figure 16 and Figure 17 (on page 33) provide an insight into how the point elasticity of supply and
demand evolves on an hourly basis during the observation period from June 2nd
2010 to August 4th
2010, while Table 9 gives more detailed numerical information. 9
Point Elasticity of
Demand [PEoD]
Point Elasticity of
Supply [PEoS]
Mean -0.343149 0.26452606
Median -0.34575799 0.26286074
St. Deviation 0.12078777 0.10255025
Max 0.00028229 0.57948729
Min -0.76419749 -0.00024799 Table 9: Point elasticity of demand and supply
Based on: own computation
The mean point elasticity of demand is -0.3431, which means that a price cut of 1% would lead to an
increase in quantity consumed of only 0.3431%. In such a case, economist would describe the price
elasticity of demand as being inelastic. The same hold for the mean point elasticity of supply which
is of 0.2645, meaning that an increase in prices of 1% would lead to an increase in production of
only 0.2645%. Regarding the shape of the price elasticity of demand and supply, a weak daily and
weekly pattern can be observed.
Before comparing the results obtained for the German electricity market during the observation pe-
riod with earlier empirical studies for other markets found in the literature, the arc elasticity of de-
mand and supply shall be computed.
9 Please refer to Appendix 2 on page 67 for more details on the computation.
Empirical Analysis of Price-Curves at the EEX
- 33 -
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
Po
int
ela
stic
ity
of
De
ma
nd
H [Hourly value for every day]
PEoD
Figure 16: Point elasticity of demand for the German electricity market
Based on: own computation
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Po
int
ela
stic
ity
of
Su
pp
ly
H [Hourly value for every day]
PEoS
Figure 17: Point elasticity of supply for the German electricity market
Based on: own computation
Empirical Analysis of Price-Curves at the EEX
- 34 -
3.2.2 Arc Elasticity
The arc elasticity of demand between two prices is defined as the proportional change in the quantity
divided by the proportional change in price (Wilson, 2010). Mathematically, this gives:
C FGO HMFNLKOKL� = % OℎF$fH K$ DEF$LKL�% OℎF$fH K$ 2GKOH = g" − g�(g� + g")/2 / i" − i�(i� + i")/2 I Arc elasticity basically assumes a linear relationship between price and quantity. Regarding the de-
mand and supply curves at hand, this might be true for small intervals. The following procedure was
used to compute arc elasticity:
1. Determine market clearing price and quantity for every hour
2. Set g� as the quantity bid directly smaller than the market clearing quantity
3. Set g" as the quantity bid directly larger than the market clearing quantity
4. Set i� as the price bid directly smaller than the market clearing price
5. Set i" as the price bid directly larger than the market clearing price
6. Compute the arc elasticity of demand and supply
Figure 18 and Figure 19 plot the results for the arc elasticity of supply and demand for every hour of
the data set. Table 10 gives a numerical overview over the results.10
Arc Elasticity of De-
mand [AEoD]
Arc Elasticity of
Supply[AEoS]
Mean -1.15321566 0.79224908
Median -0.37567054 0.19459266
St. Deviation 1.79926319 1.53742455
Max 0.02786809 19.3270189
Min -19.3594741 -0.00078644 Table 10: Arc elasticity of demand and supply
Based on: own computation
Using arc elasticity, we find a mean demand elasticity of -1.1532 which would mean that a increase
in the price by 1% would lead to a decrease in the demand by 1.1532%; in such a case, economists
speak of an elastic demand. The mean arc elasticity for the supply curve is found to be 0.7922. With
regard to the high volatility of the computed elasticity, it makes more sense to consider the median
results, which are much closer to the results found when computing the point elasticity of demand
and supply. For this reason, all further work will be accomplished using point elasticity rather than
arc elasticity. Arc elasticity figures were computed as a control variable to check whether the values
obtained by fitting polynomials to the demand and supply curve were realistic.
10
Please refer to Appendix 3 on page 68 for more details on the computation.
Empirical Analysis of Price-Curves at the EEX
- 35 -
-20
-15
-10
-5
0
Arc
Ela
stic
ity
of
De
ma
nd
H [Hourly value for every day]
AEoD
Figure 18: Arc elasticity of demand for the German electricity market
Based on: own computation
0
2
4
6
8
10
12
14
16
18
20
Arc
Ela
stic
ity
of
Su
pp
ly
H [Hourly value for every day]
AEoS
Figure 19: Arc elasticity of supply for the German electricity market
Based on: own computation
Empirical Analysis of Price-Curves at the EEX
- 36 -
3.2.3 Elasticity in the Literature
A large array of literature on demand responsiveness in electricity markets, that is to measure the
change in demand for electricity due to a change in price – in other words, elasticity – relies on rig-
orous econometric analysis that have high data requirements (especially with regards to information
on household-specific appliance holding and residence features) and therefore influence the outcome
of a study due to different characteristics of these durable goods (Fan & Hyndman, 2008). Two kinds
of studies have to be distinguished, there are the non- time of use (TOU) studies on price elasticity
and the time of use (TOU) studies on that subject (Lafferty, Hunger, Ballard, Mahrenholz, Mead,
Bandera, 2001).
Non-TOU Literature deals with flat electricity rates in the context of vertically integrated utilities and
are therefore in most cases somewhat older than TOU studies which deal with rates with different
unit prices for usage during different hours of a day, usually in block of time defined for a 24 hours
day. TOU rates therefore reflect the average cost of generating and delivering power during those
time periods. Some authors (for example Fan & Hyndman, 2008) distinguish between Real-time
pricing (RTP) and TOU, with RTP being a rate in which the price for electricity typically fluctuates
hourly, therefore reflecting changes in the wholesale price of electricity. One finding all studies have
in common is that the elasticity of electricity depends on the time frame (in that case, whether we
look at the short or at the long rate) and on the sector, this means whether they are looking at the
residential, industrial or an aggregation of both. Table 11 gives a summary on the price elasticity for
electricity demand in various studies performed in different markets.
Authors Year Region Sector Elasticity
Bohi & Zimmerman 1984 U.S. Residential Short-run: -0.2
Long-run: -0.7
Patrick & Wolak 1997 England and Wales Water supply Industry -0.142 to -0.27
Filippini 1995 Switzerland Residential -1.25 to -2.30
Filippini 1999 Switzerland Aggregation -0.3
Beenstock et al. 1999 Israel Residential and industrial Residential: -0.21 to -0.58
Industrials -0.002 to -0.44
Tishler 1991 Industrial -0.02 to -0.09
Tishler 1998 Israel Industrial -0.01 to -0.47
Earle 2000 California Aggregation Mean: -5.3
Median: -0.02
King & Chatterjee 2003 California Residential and commercial -0.1 to -0.4
Reiss 2005 California Residential -0.39
Faruqui & George 2005 California Aggregation 0.09
Taylor et al. 2005 U.K. Industrial -0.05 to -0.26
Empirical Analysis of Price-Curves at the EEX
- 37 -
Fan & Hyndman 2008 Australia Aggregation -0.4165 Table 11: Demand elasticity in the electricity market – summary
Based on: Authors as mentioned here over, for further details, please find further details in the references on page 58-65
The results found for the point elasticity of demand in the present study are more or less in line with
findings in other studies, even though the range of variation is pretty large, with values between -
0.01 and -2.3. Most value however where found to be clustered between elasticity values of -0.1 and
-0.4 as compared to the -0.34 found in this study for the German electricity market.
There is no extensive literature on the elasticity of supply in electricity market, however most re-
search papers agree that the elasticity of supply is very inelastic (for example Borenstein, 2002), may
however vary with regard to the available generation capacities (in other words margins) in the mar-
ket (Boogert & Dupont, 2006).
Empirical Analysis of Price-Curves at the EEX
- 38 -
3.3 Volatility
The aim of this section is to attribute a measure of fluctuation to each hour of our time series, as well
for the prices resulting from the day-ahead auction as for the prices resulting from intraday trading.
This however proves more difficult than expected.
3.3.1 Volatility of Day-ahead Prices
Volatility (j) is a measure of the uncertainty about the returns provided by an asset. Volatility is de-
fined as the standard deviation of the return provided by an asset over a time window B if the return
is expressed using continuous compounding. The usual estimate, s, of the standard deviation is given
by: (Hull, 2009)
N = k 1$ − 1 . (Gl,m − G̅m,o)"#l0� pℎHGH Gl,m = ln s >l>lYmt pKLℎ ℎ uHK$f NJ&H LK&H 2HGKJP
As already mentioned, electricity prices tend to follow the general trend of electricity demand and it
is therefore not surprising to face significant price fluctuation during one day, especially when mov-
ing from off-peak hours to on-peak hours. This is the reason why, unlike in most volatility studies
where the time period for returns is chosen to be ℎ = 1, the time period can be selected to be ℎ = 24
to study trans-day price fluctuations (Simonsen, 2005) or ℎ = 168 to study the trans-week price fluc-
tuations (Zareipour, Bhattacharya, Canizares, 2007). Generally speaking, the definition of historical
volatility is based on the assumption that the continuous return observation follow an i.i.d. random
variable. Those assumptions are correct for most stochastic returns in economic and finance, how-
ever, electricity market prices, as already mentioned, follow daily, weekly and seasonal patterns due
to the seasonal nature of electricity demand. As a result, continuous returns from electricity prices
are highly correlated and do not behave as an i.i.d. random variable. This is the reason why Zarei-
pour et al. (2007) proposes to use a time window B that is short enough in order to have negligible
return correlations and which furthermore allows analysing the original price time series without
considering separation of the periodic and random parts of the price data. This is for example the
case when choosing a time window B of 24 hours. Zareipour et al. furthermore suggests to use mar-
ket price data in two ways: in the first scenario, a price time series is treated as a whole signal for all
24 hours and volatility indices are computed such that the overall price behaviour can be analysed
while in a second scenario, a price time series is broken up into 24 time series corresponding to each
of the 24 hours such as to provide an insight into the risk associated with the price at each particular
hour of the day (2007).
Empirical Analysis of Price-Curves at the EEX
- 39 -
The time window is in a first part selected to be one full day (24h), such that one figure is obtained
for every day. The following formula for the historical volatility where we have the possibility to
vary ℎ such as to have hourly (ℎ = 1), daily (ℎ = 24) and weekly (ℎ = 168) logarithmic returns as
the basis for the analysis is therefore faced.
v jm,";(B) = k 123 . (Gl,m − G̅m,o)" ";∗ol0�:";∗(oY�) w
In such a scenario, the averages of jm,";(P) is used as volatility indices. Table 12 summarizes the
results.
# of results Mean Median Max Min St. Dev � ,!" 63 0.1723 0.10851 1.5611 0.0415 0.2286
�!",!" 63 0.3008 0.1494 2.1185 0.0431 0.4264
� #$,!" 63 0.2309 0.1104 1.9990 0.0419 0.3573
Table 12: Daily volatility figures for intraday, trans-day and trans-week prices
Based on: own computation11
Simonsen (2005), who did analyse the Nordic electricity market over a longer time period (12 years)
did find a volatility for %&',&' of 0.16 which is in comparison to most financial markets fairly high;
even though the Nordic power market is known for its actually “low” volatility. In fact, Zareipour et
al. finds volatility measures that are slightly higher for the Ontario market in his study ( %(,&' = 0.2469, %&',&' = 0.3203 and %(*+,&' = 0.3222) (2007). In the German electricity market %&',&'
= 0.3008 and is therefore found in between the results of both studies. However, unlike in Zareipour
et al.’s study for the Ontario market, the intraday price fluctuation %&',&' for the German electricity
market is higher than the trans-week price volatility %(*+,&', which means that price changes tend to
be higher going from one day to the next where they tend to be lower when going from one week to
the next. This can be explained by the fact that prices during Saturdays and Sundays are much lower
than during the rest of the week, therefore affecting the intraday price volatility very strongly.
Considering now the second scenario introduced by Zareipour et al. (2007), which uses a time win-
dow of 7 days (one full week), the following equation is considered:
- %&',(*+(/) = 1163 (45,7 − 4̅7,:)& ;∗:5>(?;∗(:@() A
11
Please refer to the Appendix 4 on page 69 for further details on the computation.
Empirical Analysis of Price-Curves at the EEX
- 40 -
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Vo
lati
lity
H [Hour of the day]
Here ℎ = 24, this implies that market prices for two consecutive days are compared. The aim of this
calculation is to quantify the fluctuation of price at a particular hour in subsequent days over a 7-day
period. The sum in the equation is made over hour ℎ of each day during a 7-day period. The result
obtained is shown in Table 13. Note, for each week, 24 volatility figures (one for each hour) are
computed.
# of results Mean Median Max Min St. Dev �!", #$ 216 (24x9) 0.3777 0.2285 4.2427 0.0369 0.5530
Table 13: Hourly volatility over each day
Based on: own computation12
Much more interesting is however the average volatility at each hour, that is %E&',(*+ and is presented on Figure 20.
The results obtained for %E&',(*+ show a similar volatility as the results obtained for the Ontario mar-
ket by Zareipour et al. (2007). However the volatility pattern over the day is completely different and
the differences between the individual hours are much more important for the German market. This
might be explained by the relatively short period observed in this paper.
The results obtained so far using the methods introduced in the literature do however not provide the
expected aim of this section, since an individual volatility measure for each of the 1512 hours of the
observation period has not been computed yet.
12
Please refer to Appendix 5 on page 70 for further details on the computation.
Figure 20: �F!", #$, average hourly volatility over a time window of 1 week
Based on: own computation
Empirical Analysis of Price-Curves at the EEX
- 41 -
This is the reason why the electricity price volatility will be calculated by using a rolling window
where each hour of a week is treated as a separate asset. Hence, the volatility of 168 individual assets
(hours) is computed. The returns are computed by using ℎ = 168. The volatility is furthermore com-
puted as follows:
- %(*+,H∗(*+(/) = 1163 (45,7 − 4̅7,:)& ;∗:5>(?;∗(:@() A
The length of the rolling window is chosen to be 9 weeks, since the whole observation period is 9
weeks starting from June 2nd
2010 until August 4th 2010. For every time window, 168 volatilities are
obtained. Figure 21 illustrates the volatility obtained during the observation period. Table 14 summa-
rizes the key results13
. Table 15 gives an overview over the rolling windows used and computes as an
example the volatility for Hour 1 on Wednesday between June 2nd
2010 and August 4th
2010. The
star (*) in Table 15 refers to the starting day of the observation period.
The hourly volatility computed using a rolling window exhibits a weekly pattern. On average, vola-
tility peaks are found on weekends, especially Sunday between 12 a.m. and 14 a.m. with a slightly
lower peak on Sunday morning. The hourly volatility is relatively low during weekdays.
# of results Mean Median Max Min St. Dev
Hourly volatility 1512 0.3639 0.1605 3.3704 0.0366 0.6011
13
Please refer to Appendix 6 on page 71 for further details on the computation.
Table 14: Hourly volatility for the German market
Based on: own computation
Empirical Analysis of Price-Curves at the EEX
- 42 -
0
0.5
1
1.5
2
2.5
3
3.5
Vo
lati
lity
h [hour of the day]
volatility
Table 15: Hourly volatility computation using a rolling window
Based on: own computation
Return Period Rolling window(s) 45,7 Volatility of Hour 1
31/03/2010 – 07/04/2010 0.2317
0.1
46
0
07/04/2010 – 14/04/2010 0.0646
0.1
31
3
14/04/2010 – 21/04/2010 -0.2307
0.1
43
6
28/04/2010 – 05/05/2010 0.2323
0.1
13
2
05/05/2010 – 12/05/2010 -0.0196
0.0
85
9
12/05/2010 – 19/05/2010 0.1027
0.0
86
8
19/05/2010 – 26/05/2010 -0.0386
0.0
81
2
26/05/2010 – 02/06/2010* -0.0386
0.0
79
6
02/06/2010* – 09/06/2010 -0.0222
0.0
83
3
09/06/2010 – 16/06/2010 -0.1128
16/06/2010 – 23/06/2010 0.1762
23/06/2010 – 30/06/2010 0.0271
30/06/2010 – 07/07/2010 0.0390
07/07/2010 – 14/07/2010 -0.0352
14/07/2010 – 21/07/2010 0.0474
23/07/2010 – 28/07/2010 0.0076
28/07/2010 – 04/08/2010 -0.0756
Figure 21: Hourly volatility using a rolling window
Based on: own computation
Empirical Analysis of Price-Curves at the EEX
- 43 -
3.3.2 Volatility of Intraday Prices
Since intraday prices are also considered; a second volatility index for every hour of the day has to
be constructed. Since volatility computation for hourly electricity prices turns out to be very com-
plex, another methodology is chosen for intraday prices. The intraday price volatility will be base on
the hourly price fluctuation, which can be computed due to the fact that, next to an average intraday
hourly price, a minimum as well as a maximum price during each hour are published.
Before computing an index for its volatility, it is first of interest to analyse how intraday prices are
related to the prices set through the day-ahead auctions. Figure 22 shows the relationship between
intraday (average, minimum and maximum price) and the price set through day ahead auction on
June 2nd
2010. Table 16 summarizes the findings for the overall period. The mean difference be-
tween intraday and day ahead prices is -8.32%, whereas the median difference is found to be -0.43%.
This means that intraday prices are on average slightly below the prices found in the day-ahead mar-
ket during the observation period with the highest difference found when day-ahead prices were
negative (here -179.5%). This means nothing else that market participants are willing to pay a pre-
mium to lock in prices early.
# of results Mean Median Max Min St. Dev
Price difference 1512 -8.3288% 0.4362% 6485.7% -17950% 553.5%
Table 16 : Relationship between intraday and day-ahead prices in the German market
0
10
20
30
40
50
60
70
Pri
ce in
EU
R p
er
MW
H [Hour of the day]
Intraday Low
Intraday High
Day-ahead
Intraday
Figure 22: Relationship between intraday price (average, low, high) and day-ahead prices
Based on: EEX (2010b)
Empirical Analysis of Price-Curves at the EEX
- 44 -
Having showed the very close relationship between day-ahead prices and intraday prices, an index
expressing the fluctuation during every hour regarding the intraday prices can be computed using
following formula:
I JKLMNLOMNPQR PRSTU = VWXYZ[\]@VWXYZ[^_ VWXYZ\`ab\ca d
The fluctuation index is a relative index whose value will be highest when the proportional price
movements during an hour are highest. Higher price uncertainty can therefore be recognized. Figure
24 gives an overview for the changes in intraday price fluctuation during the observation period
while Table 17 picks out the key numbers.
# of results Mean Median Max Min St. Dev
Price fluctuation 1512 52.2% 35.89% 1372.5% 5% 70.18%
Table 17: Hourly intraday price fluctuation: key figures
Based on: own computation
Intraday price fluctuation is not influence by any notable daily or weekly pattern.
0
2
4
6
8
10
12
Intr
a-d
ay
pri
ce f
luct
ua
tio
n
H [Hourly value for every day]
Fluctuation
Figure 23: Hourly intraday price fluctuation for the German market
Based on: own computation
Empirical Analysis of Price-Curves at the EEX
- 45 -
4. Empirical results
The aim of this paper is to determine how generation capacities do affect the market price for elec-
tricity, the shape of the demand and supply curve as well as the market volatility. This chapter de-
fines the dependent and independent variables before performing simple and multiple regression
analysis in order to understand the effect of generation capacities on electricity prices as well as on
the shape of the demand and supply curve and on market volatility.
4.1 Dependent variables
The dependent variables which will be used in the following regression analysis are the price result-
ing from the day-ahead auction, the price resulting from the intraday trading activities, the price elas-
ticity of demand and supply which are used as proxis for the shape of the demand and supply curve
as well as the volatility figures computed for the day-ahead prices and intraday prices. Each variable
is described by a time series of 1512 data points corresponding to each hour during the observation
period.
4.2 Independent variables
As already seen the prices in the German electricity market are set through a bidding procedure,
where each market participants places his bids according to his costs of production (the merit order)
which leads to the demand and supply curves seen in Chapter 2.2. Therefore, market participant have
an influence on the outcome of the market as they decide how much to charge for their electricity
depending on their costs of production, which itself depends on their means of production, in other
words on their types of generators. The ten explanatory variables chosen are the one global margin
for the German electricity production as well as the nine individual capacity utilisation figures for
each generation type.
The ten explanatory variables are:
- Global margin (GM) - Capacity utilisation lignite (CL)
- Capacity utilisation uranium (CU) - Capacity utilisation coal (CC)
- Capacity utilisation gas (CG) - Capacity utilisation pumped-storage (CP)
- Capacity utilisation oil (CO) - Capacity utilisation seasonal-storage (CS)
- Capacity utilisation run-of-the-river (CR)- Capacity utilisation wind (CW)
All data is on an hourly basis, which therefore means that 1512 hours of data for each explanatory
variable is available. The data was tested for multicollinearity which was found to be not relevant,
Empirical Analysis of Price-Curves at the EEX
- 46 -
expect between GM and CC. However, since GM is to some extend an aggregate of CU, CL, CG,
CC, CP, CO, CS, CR and CW, it makes no sense to use all 10 explanatory variables in a multiple re-
gression analysis. GM will only be used in a single regression analysis to avoid any multicollinearity
issues. In some cases, the day-ahead prices (DAP) and the day-ahead volumes (DAV) will be used as
explanatory variables. Both variables have been tested for multicollinearity.
4.3 Results
For each dependent variable, single and multiple OLS regression using the ten explanatory variables
were run using Newey-West standard errors. The decision to use Newey-West is motivated by the
fact that the residuals of the standard OLS regression show a high degree of autocorrelation. In such
a case, the OLS estimates are still unbiased and consistent but they are inefficient. Furthermore,
standard errors will tend to be underestimated, R2 overestimated and the confidence intervals too nar-
row (Greene, 2002). For this reason, Newey-West introduced a procedure to correct the variance of
the estimates to draw conclusion on their significance; this is done by using HAC (heteroskedasticity
and autocorrelation consistent) estimators for the covariance matrix. (Newey and West, 1994)14
4.3.1 Day-ahead Prices
Table 18 shows the regression on day-ahead prices of the global margin (GM) as well as the capacity
utilisation of uranium (CU), lignite (CL), gas (CG), coal (CC), oil (CO), pumped power plants (CP),
run-of-the-river (CR), seasonal power plants (CS) and wind energy (CW).
Reg.
No.
Con-
stant GM CU CL CG CC CO CP CR CS CW
Adj.
R2
(1) 79.30***
(1.35)
-68.15***
(2.72) 72.19%
(2) -3.34
(29.89)
50.04
(31.19) 1.34%
(3) -109.25***
(9.51)
164.99***
(10.22) 43.54%
(4) 24.80***
(1.64)
95.62***
(7.39) 49.24%
(5) 23.60***
(1.18)
47.97***
(2.25) 63.91%
(6) 42.29***
(0.72)
30.83***
(3.14) 15.80%
(7) 35.44***
(0.86)
63.95***
(3.90) 37.13%
14
The computation was done using regstats2 for MATLAB by Komarov (2010).
Empirical Analysis of Price-Curves at the EEX
- 47 -
(8) 39.32***
(8.67)
5.00
(8.58) 0.01%
(9) 43.91***
(0.85)
2.42
(3.14) 0.06%
(10) 49.78***
(1.79)
-5.57***
(1.66) 2.61%
(11) -82.69***
(18.30)
47.39***
(14.54)
67.85***
(9.38)
22.88***
(2.43)
18.77***
(4.89)
28.89***
(2.31)
4.58***
(1.67)
-4.91***
(1.44)
0.89
(4.35)
0.62
(0.84) 77.90%
*** 1% significance level,
** 5% significance level,
* 10% significance level, numbers in brackets are the standard deviation of the coefficients
Table 18: Regression analysis: day-ahead prices
Regression (1) to (10) show the single regressions while regression (11) depicts the multivariate re-
gression where nine factors were combined.
The adjusted R2 for regression (1), which shows the influence of GM on the day-ahead price, is
72.19%. The negative sign for the coefficient, which is significant at the 1% level, signals that lower
margins tend to favour higher prices and vice versa. Without doubt, such a result could be expected,
since prices tend to increase during peak hour, and on the other side, capacity margins tend to be re-
duced during peak hours due to higher electricity consumption.
The adjusted R2 for regression (2), (8) and (9), which show the influence of capacity utilisation for
uranium, run-of-the-river and seasonal storage respectively, is very low, with 1.34%, 0.01% and
0.06% respectively. Furthermore, the obtained coefficient are not significant. According to these sin-
gle regression, the capacity utilisation for uranium, run-of-the-river and seasonal storage has almost
no impact on day-ahead electricity prices. A possible explanation for this finding is the fact that both
uranium fired power plants and run-of-the-river power plants produce Baseload electricity and there-
fore run and produce electricity no matter what the price is.
The adjusted R2 for regression (3), which shows the influence of CL, is 43.54%. The constant, which
is negative and the coefficient that is positive are significant at the 1% level. Even though, lignite
fired power plants are used to cover Baseload consumption and therefore exhibit similar characteris-
tics as uranium fired power plants, their influence on day-ahead prices seems to be much more im-
portant. As mentioned on page 25, lignite power plant exhibit a higher flexibility than nuclear power
plant, which might be the main reason for explaining their higher adjusted R2.
The adjusted R2 for regression (4), (5), (6) and (7), which show the influence of capacity utilisation
for gas (49.24%), coal (63.91%), oil (15.80%) and pumped power plants (37.13%) are fairly high.
Both the constant and the coefficients are positive and significant on the 1% level for all four regres-
sions. The role of oil-fired power plants is very limited, therefore it is not unexpected that their ex-
planatory power is smaller than the one of gas, coal and pumped power plants. All four power plant
Empirical Analysis of Price-Curves at the EEX
- 48 -
type are used for Peakload generation and are therefore often the price setting power plants which
explains their importance with respect to day-ahead prices.
The adjusted R2 for regression (10), that shows the influence of capacity utilisation (the goodness of
the forecast) for wind electricity production, is very low with 2.61%. This result could be expected
since the goodness of forecast is not a known measure when day-ahead prices are computed. The
goodness of the forecast is an ex-post measure which can be approximated fairly closely on a short
time horizon (1-2 hours in advance) but by no mean on a day-ahead basis.
The adjusted R2 for the multivariate regression (11) is 77.90%. The results obtained do not contradict
per se the results of the single regressions. The main differences are the coefficient for the capacity
utilisation of uranium which has become significant at the 1% level and the one for run-of-the-river
which has also become significant at the 1% level. On the other hand, the coefficient for the good-
ness of the forecast for wind electricity generation is not significant anymore and has turned positive.
4.3.2 Intraday Prices
Table 19 shows the regression on intraday prices on the global margin (GM) as well as the capacity
utilisation of uranium (CU), lignite (CL), gas (CG), coal (CC), oil (CO), pumped power plants (CP),
run-of-the-river (CR), seasonal power plants (CS) and wind energy (CW).
Reg.
No.
Con-
stant GM CU CL CG CC CO CP CR CS CW
Adj.
R2
(1) 80.15***
(2.16)
-69.54***
(3.74) 58.23%
(2) 14.50
(32.71)
31.43
(34.22) 0.37%
(3) -109.79***
(10.68)
165.71***
(11.53) 34.01%
(4) 21.64***
(1.97)
111.74***
(9.89) 52.10%
(5) 20.67***
(1.12)
55.06***
(2.45) 65.22%
(6) 42.09***
(0.79)
35.77***
(4.87) 16.47%
(7) 35.44***
(0.96)
64.88***
(4.82) 29.60%
(8) 41.48***
(8.57)
2.97
(8.52) 0.04%
(9) 43.37***
(1.01)
6.46*
(3.84) 0.06%
(10) 55.64***
(2.07)
-11.42***
(1.95) 8.65%
Empirical Analysis of Price-Curves at the EEX
- 49 -
(11) -37.12*
(20.73)
34.38**
(16.64)
34.74**
(13.82)
32.90***
(3.15)
27.49***
(8.08)
20.15***
(3.02)
2.65
(3.08)
-1.87
(1.81)
-1.25
(4.87) -4.90
***
(1.18) 73.34%
*** 1% significance level,
** 5% significance level,
* 10% significance level, numbers in brackets are the standard deviation of the coefficients
Table 19: Regression analysis: intraday prices
The results obtained for the regressions (1) to (9) are very similar to the results obtained for the day-
ahead prices.
Regression (10), which shows the effect of the goodness of forecast of wind electricity generation on
intraday prices exhibits an adjusted R2 of 8.65% and a negative coefficient that is significant at the
1% level. Since intraday prices are generated on a very short time interval before the actual hour, the
electricity generation from wind turbines that is expected is much more precise which increases the
relevance of the goodness of forecast for wind generation. The negative coefficient means that elec-
tricity prices tend to be lower if more electricity is generated through wind turbines. A very interest-
ing figure with respect to the ability to better predict on a very short term the actual electricity gen-
eration from wind turbines is found when comparing the volumes of intraday trading and the actual
difference between expected generation from wind energy and actual generation from wind energy,
as shown on Figure 24.
A single regression analysis using as independent variable the absolute difference in quantity be-
tween the forecasted wind generation in MW and the actually generated electricity through wind
generation in MW and using as dependent variable the volume for intraday trading exhibits an ad-
justed R2 of 37.67% with a coefficient of 0.5340 which is significant at the 1% level when using
Newey-West. This mean that market participants are able to assess with a fairly good accuracy the
actual production of electricity through wind turbines when intraday trading is still open (which
0
1000
2000
3000
4000
5000
6000
7000
8000
0 1000 2000 3000 4000 5000 6000 7000 8000
Ab
s[fo
reca
st-a
ctu
al]
in M
W
Intraday Volume [in MW]
Volume
Figure 24: Intraday volume with respect to difference between expected and actual wind production
Based on: own computation
Empirical Analysis of Price-Curves at the EEX
- 50 -
means until 75 minutes before the delivery hour starts) and are therefore able to react to large devia-
tions from forecasted production. One could expect the volumes traded during intraday trading to
increase as electricity generation through wind turbines is expected to increase in coming years.
The multivariate regression (11) does not contradict these findings. The adjusted R2 is found to be
73.34% with the main difference to the day-ahead prices being the fact that CW exhibits a negative
coefficient that is significance at the 1% level. The findings that electricity generation through wind
has a negative effect on prices coincides with practical experience. Fürsch et al. (2010) show that
since electricity produced through renewable sources must always be used; a shift to the left in the
demand curve by the produced amount occurs and, in such a case, a power plant with lower marginal
costs will be the price setting unit (merit-order effect). This does however not imply that end-
consumer prices will be lower, since electricity from renewable energy are subsidized and must
therefore be paid for15
.
4.3.3 Price Elasticity of Demand
Table 20 shows the regression of the price elasticity of demand on the global margin (GM) as well as
the capacity utilisation of uranium (CU), lignite (CL), gas (CG), coal (CC), oil (CO), pumped power
plants (CP), run-of-the-river (CR), seasonal power plants (CS) and wind energy (CW).
Reg.
No.
Con-
stant GM CU CL CG CC CO CP CR CS CW
Adj.
R2
(1) -0.57***
(0.01)
0.44***
(0.03) 32.93%
(2) 0.12
(0.27)
-0.48*
(0.28) 0.01%
(3) 0.68***
(0.10)
-1.10***
(0.11) 21.01%
(4) -0.23***
(0.01)
-0.53***
(0.07) 16.38%
(5) -0.20***
(0.01)
-0.32***
(0.02) 31.27%
(6) -0.33***
(0.00)
-0.16***
(0.02) 4.7%%
(7) -0.31***
(0.01)
-0.18***
(0.03) 3.23%
(8) -0.08
(0.08)
-0.26***
(0.08) 2.29%
(9) -0.34***
(0.00)
-0.00
(0.03) 0.04%
15
Further discussion can be found in Sensfuss and Ragwitz (2007) as well as in Erdmann (2008).
Empirical Analysis of Price-Curves at the EEX
- 51 -
(10) -0.35***
(0.01)
0.01
(0.01) 0.17%
(11) 0.75***
(0.26)
-0.32
(0.20) -0.49
***
(0.13)
-0.26***
(0.03)
-0.01
(0.07) 0.09
**
(0.03)
-0.00
(0.03) 0.04
*
(0.02)
-0.21**
(0.08)
-0.01
(0.01) 36.90%
*** 1% significance level,
** 5% significance level,
* 10% significance level, numbers in brackets are the standard deviation of the coefficients
Table 20: Regression analysis: price elasticity of demand
Regression (1), which investigates the effect of the global margin (GM) on the point elasticity of
demand exhibits an adjusted R2 of 32.93%. The coefficient is 0.44 and is significant at the 1% level.
This means that rising margins go hand in hand with higher point elasticity of demand. Since point
elasticity of demand is per definition negative, higher margins push the point elasticity towards ine-
lasticity, in other words to a point elasticity of demand of zero. High margins tend to be an indicator
for relative low consumption and therefore relative lower prices (as has been seen in section 4.3.1),
meaning that the price elasticity of demand is lower when prices are lower and vice versa. This
means that consumers are rather willing to forgo consumption of electricity when higher prices are
observed. This can be tested easily by regressing the price elasticity of demand with respect to the
day-ahead prices (DAP). The adjusted R2 obtained in this case is 37.23%, with a coefficient for DAP
of -0.005 that is significant at the 1% level (when corrected with Newey-West). This means that on
average higher prices lower the price elasticity of demand (the more negative it gets) and therefore
the higher the readiness of the consumers to forgo their electricity consumption. However, as well
the adjusted R2 for GM as the one for DAP points to the fact that other factors do play an important
role in influencing the price elasticity of demand.
Regression (2) to (10), as well as the multivariate regression (11) confirm the findings of regression
(1).
4.3.4 Prices Elasticity of Supply
Table 21 shows the regression of the price elasticity of demand on the global margin (GM) as well as
the capacity utilisation of uranium (CU), lignite (CL), gas (CG), coal (CC), oil (CO), pumped power
plants (CP), run-of-the-river (CR), seasonal power plants (CS) and wind energy (CW).
Reg.
No.
Con-
stant GM CU CL CG CC CO CP CR CS CW
Adj.
R2
(1) 0.29***
(0.02)
-0.06
(0.04) 0.9%
(2) -0.54***
(0.19)
0.84 ***
(0.20) 6.01%
(3) -0.18
(0.12)
0.48***
(0.13) 5.52%
Empirical Analysis of Price-Curves at the EEX
- 52 -
(4) 0.29***
(0.01)
-0.13**
(0.05) 1.41%
(5) 0.24 ***
(0.01)
0.03
(0.02) 0.45%
(6) 0.26***
(0.00)
-0.07***
(0.02) 1.38%
(7) 0.28***
(0.00)
-0.14***
(0.03) 2.94%
(8) 0.17***
(0.06)
0.08
(0.06) 0.29%
(9) 0.27***
(0.00)
-0.06***
(0.02) 1.37%
(10) 0.24***
(0.01)
0.01
(0.01) 0.42%
(11) -1.09***
(0.21)
0.70***
(0.18)
0.77***
(0.14)
0.07**
(0.03)
-0.29***
(0.08)
-0.19***
(0.03)
-0.02
(0.02)
-0.03
(0.02)
0.01
(0.05)
0.01
(0.01) 23.30%
*** 1% significance level,
** 5% significance level,
* 10% significance level, numbers in brackets are the standard deviation of the coefficients
Table 21: Regression analysis: price elasticity of supply
The adjusted R2 obtained for the single regression analysis are very low, ranging between 0.42% and
6.01%. It seems that the influence of the individual capacity utilisation as well as the influence of the
global margin are marginal on the point elasticity of supply.
The multivariate regression (11) exhibits on the other hand an adjusted R2 of 23.30%. The coefficient
for nuclear and lignite fired power plants are clearly positive and are significant at the 1% level. This
means that the elasticity of supply tends to increase with rising use of those Baseload fired power
plants, or in other words, the variable cost of using those Baseload fired power plants is so low, that
the electricity generators are willing to increase their output even more for every Euro of price in-
crease. On the other hand, the coefficient for the typical Peakload power plants that are gas-, coal-
and oil-fired power plants are either close to zero (gas) or clearly negative and significant at the 1%
level. In other words, the variable costs of those power plants are so high that the producers willing-
ness to sell electricity for every price increase in Euro is decreasing. This means that their point elas-
ticity of supply tends to diminish with rising use of Peakload power plants. However, the low ad-
justed R2 obtained shows clearly that other factors also have an important role influencing the price
elasticity of supply.
A curious result is obtained if the price elasticity of supply is regressed with respect to day-ahead
prices. In this case, the adjusted R2 is of 2.97% with a coefficient of 0.001 which is significant at the
5% level. Electricity prices has therefore almost no affect on the elasticity of supply.
A further result that can be analysed is obtained when regressing the day-ahead volume with respect
to the elasticity of supply. Here, an adjusted R2 of 11.93% is found and the coefficient is slightly
Empirical Analysis of Price-Curves at the EEX
- 53 -
negative (-0.000007) and significant at the 1% level. Therefore, day-ahead volume has a higher in-
fluence on the elasticity of supply as day-ahead prices, even though the influence of both is fairly
marginal.
Adding both DAV and DAP as independent variable to the multivariate regression (11) gives regres-
sion (12) as shown in Table 22 and increases the adjusted R2 to 50.30%. The coefficient obtained for
the variables already present in regression (11) do not vary much, and the coefficient for day-ahead
prices and day-ahead volume are almost identical with respect to the single regression coefficient
obtained and are both significant at the 1% level.
Reg.
No. DAV DAP CU CL CG CC CO CP CR CS CW
Adj.
R2
(12) -0.00***
(0.00)
0.05***
(0.00)
0.66***
(0.14)
0.18
(0.11) 0.06
*
(0.03)
-0.25***
(0.06)
-0.12***
(0.03)
-0.05**
(0.02)
-0.02
(0.01)
-0.09
(0.06) 0.01
*
(0.01) 50.53%
*** 1% significance level,
** 5% significance level,
* 10% significance level, numbers in brackets are the standard deviation of the coefficients
Table 22: Regression analysis(2): Price elasticity of supply
4.3.5 Day-ahead Price Volatility
Table 23 shows the regression of the price elasticity of demand on the global margin (GM) as well as
the capacity utilisation of uranium (CU), lignite (CL), gas (CG), coal (CC), oil (CO), pumped power
plants (CP), run-of-the-river (CR), seasonal power plants (CS) and wind energy (CW).
Reg.
No.
Con-
stant GM CU CL CG CC CO CP CR CS CW
Adj.
R2
(1) -0.08
(0.06) 0.69
***
(0.15) 14.71%
(2) 2.82***
(1.07)
-2.68 **
(1.11) 7.86%
(3) 1.85***
(0.44)
-1.69***
(0.47) 8.96%
(4) 0.38***
(0.04)
-0.55***
(0.18) 3.23%
(5) 0.44 ***
(0.04)
-0.40***
(0.08) 8.76%
(6) 0.26***
(0.01)
0.00
(0.08) 0.06%
(7) 032***
(0.02)
-0.37***
(0.09) 2.40%
(8) 0.51***
(013)
-0.24*
(0.12) 0.32%
(9) 0.23***
(0.01)
0.20**
(0.08) 1.76%
Empirical Analysis of Price-Curves at the EEX
- 54 -
(10) 030***
(0.03)
-0.03
(0.02) 0.18%
(11) 3.92***
(1.35)
-2.28**
(1.10)
-1.32***
(0.48)
-0.22**
(0.10)
-0.10
(0.29)
-0.06
(0.07)
0.14
(0.11) 0.14
*
(0.08)
-0.07
(0.13) -0.08
***
(0.02) 21.29%
*** 1% significance level,
** 5% significance level,
* 10% significance level, numbers in brackets are the standard deviation of the coefficients
Table 23: Regression analysis: day-ahead price volatility
Regression (1) which looks at the influence of GM on the volatility of day-ahead prices exhibits an
adjusted R2 of 14.71%. The coefficient is positive (0.69) and significant at the 1% level, meaning
that rising margin tend to increase the hourly price volatility. Similar information is gained from re-
gressions (2) to (10) which however exhibit fairly low adjusted R2. The coefficients for regressions
(2) to (10) are negative and in most cases significant at the 1% level, meaning that rising capacity
utilisation reduces the day-ahead hourly price volatility.
The multivariate regression (11) confirm those findings, even though most coefficient founds are not
significant anymore. The results obtained show that generation margins respectively capacity utilisa-
tion are not a good indicator for day-ahead price volatility, neither the less, they demonstrate to some
extend that electricity producer might be facing a higher freedom for price setting as more produc-
tion capacities are left unused. In other words, the price spread tends to be higher when more produc-
tion capacities are available.
4.3.6 Intraday Price Volatility
Table 24 shows the regression of the price elasticity of demand on the global margin (GM) as well as
the capacity utilisation of uranium (CU), lignite (CL), gas (CG), coal (CC), oil (CO), pumped power
plants (CP), run-of-the-river (CR), seasonal power plants (CS) and wind energy (CW).
Reg.
No.
Con-
stant GM CU CL CG CC CO CP CR CS CW
Adj.
R2
(1) -0.23
(0.15) 1.47
***
(0.34) 10.70%
(2) 4.64*
(2.61)
-4.33
(2.73) 3.32%
(3) 6.40***
(1.39)
-6.32***
(1.47) 20.43%
(4) 0.90***
(0.10)
-1.85***
(0.38) 5.90%
(5) 0.99 ***
(0.12)
-1.10***
(0.21) 10.73%
(6) 0.55***
(0.04)
-0.44***
(0.09) 1.00%
(7) 0.68***
(0.06)
-1.19***
(0.23) 4.08%
Empirical Analysis of Price-Curves at the EEX
- 55 -
(8) 0.58**
(0.26)
-0.06
(0.25) 0.06%
(9) 0.50***
(0.04)
0.08
(0.14) -0.02%
(10) 0.28***
(0.06)
0.24***
(0.06) 1.58%
(11) 10.23***
(3.24)
-4.63*
(2.53)
-6.12***
(1.73)
-0.05
(0.16)
-0.04
(0.31) -0.19
*
(0.11)
-0.04
(0.12)
0.17
(0.13)
0.31
(0.27) 0.13
*
(0.07) 25.47%
*** 1% significance level,
** 5% significance level,
* 10% significance level, numbers in brackets are the standard deviation of the coefficients
Table 24: Regression analysis: intraday price volatility
The results found for regressions (1) to (11) are very similar with the results found in the previous
section on day-ahead price volatility even though the respective volatility figures are completely dif-
ferent. The major difference is found in the adjusted R2 for CL which is found to be 20.43%. Rea-
sons for this high number cannot be provided readily, since expectation would have rather pointed to
a higher explanatory power of CW since electricity generation from wind turbine underlies heavy
fluctuation and must therefore be compensated for in the very short term, hence in the intraday mar-
ket.
The adjusted R2 for the multivariate regression (11) is 25.47% and therefore slightly higher than for
regression (11) of the previous section. However, most coefficients found are not significant. Again,
it seems that capacity margins are a rather bad indicator for price fluctuation at the intraday market.
Empirical Analysis of Price-Curves at the EEX
- 56 -
5. Concluding Remarks
This thesis aims at analysing the relationship between the production capacities in the German elec-
tricity market and various other aspects of this market: on the one hand side, the influence of produc-
tion capacities on prices; on the other hand, its influence on the shape of the demand and supply
curve and finally its influence on the electricity markets volatility. In this context, this paper presents
an empirical analysis of the German electricity market for the period between June 2nd
2010 and Au-
gust 4th
2010 where the key issues are reviewed.
In a first phase, the German electricity market as a whole is introduced with its key characteristics.
The main producers as well as their means of production are briefly reviewed. Furthermore, a gen-
eral overview is provided with respect to the available information at the EEX and the EEX Trans-
parency portal. These included figures to the installed generation capacities, available generation ca-
pacities as well as actually produced electricity on an hourly bases. Furthermore, the EEX provides
the price/quantity bids placed by the market participants in the day-ahead market which represent the
demand and supply curves, and, finally, the prices and quantity resulting from these day-ahead mar-
kets as well as the prices and quantity resulting from the intraday market are also briefly introduced.
In a second step, the relevant variables for the empirical analysis are generated. In a first section, the
margin generation for the electricity market is computed and is found to be on average very comfort-
able with 51.43%. Instead of computing further margins for every individual type of power plants,
the decision was taken to use the figure “used capacity” since it is more intuitive. Therefore, the used
capacity for every type of generator was computed. Regarding wind generation, the same computa-
tional procedure was used even though it does not per se represent the used capacity. For wind gen-
eration, the computed figure refers to the goodness of forecast, since actually produced electricity
was compared to expected production since, unlike most other generation types where men decide
how much to produce, nature is here the technician. The second section deals with the demand and
supply curves and uses polynomial of 12th
order to describe each curve. Based on the curve fits, elas-
ticity measures, both for the demand and supply curve are computed. The result found for the point
elasticity of demand (-0.34) is within the expected scope as described by various studies in the last
years. The point elasticity of supply (0.26) cannot readily be compared to other researches, does
however seem to be consistent with what could be expected. The third section deals with the hourly
volatility in the German electricity market. On the one hand side, the hourly volatility of the day-
ahead market was computed using a rolling window and was found to be 0.3639 during the observa-
tion period. exhibiting a very high fluctuation. On the other hand, the volatility of the intraday prices
was computed using a different methodology, such as to show how much prices did fluctuate within
Empirical Analysis of Price-Curves at the EEX
- 57 -
an hour. The results obtained show an average hourly volatility for intraday prices of 52.2% with a
very high fluctuation band with.
In a third phase, the empirical analysis per se is performed. Evidences are found that margins and
capacity utilisation in the German electricity market do indeed affect electricity prices, as well in the
day-ahead as in the intraday market. Rising margin have on average a lowering effect on prices,
while rising capacity utilisation tends to lead to higher prices. The one interesting aspect is the fact
that, when more electricity is generated through wind than expected, price tend to get lower. This has
been and is still a major discussion topic in Germany with regards to the subsidies for renewable
electricity. The findings of the present study, which are confirmed by various other studies suggest
that electricity through wind generation has a lowering effect on electricity prices and that therefore
the subsidies are to some extend covered by those lower prices.
The effect of generation margins and capacity utilisation in the German electricity market on the
elasticity of demand and supply has not provided surprising results. Even though the adjusted R2
were relatively moderate (36.90%), the results found are highly significant. Shrinking margins (re-
spectively increasing capacity utilisation) tend to increase the elasticity of demand indicating that
consumers are rather willing to change their consumption habits. The exact opposite effect is ob-
served for the supply elasticity which is increased as margin are reduced, therefore, producers of
electricity are rather willing to produce more electricity when margins are tighter. The adjusted R2
for the elasticity of supply is, with 23.30%, however rather small. Hence, other aspects than the ca-
pacity utilisation of the power plants must have an influence on the elasticity of demand and supply
and might be a question for further research.
With regards to the market volatility, most results of the empirical analysis where highly significant
even though the adjusted R2 are very low. The result show, as well for intraday as for day-ahead
markets that volatility tends to increase with shrinking capacity utilisation. In other words, the higher
the capacity utilisation is, the lower the latitude the electricity producers have to set the price. How-
ever, many other factors do affect price volatility, which might also be a question for further re-
search.
Empirical Analysis of Price-Curves at the EEX
- 58 -
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Appendix
1. Computation of R-Square for the polynomial fitting of the demand and supply curve with
MATLAB
clear clc %we start from the data "Curvestudy" assets = xlsread('Curvestudy.xlsx'); for i = 1:3:192 price(:,(i-1)/3+1) = assets(4802:9601,i); demand(:,(i-1)/3+1) = assets(4802:9601,i+1); supply(:,(i-1)/3+1) = assets(4802:9601,i+2); end Price = 1; Demand = 1; Supply = 1; for i = 1:63 Price = [Price ; price(:,i)]; Demand = [Demand ; demand(:,i)]; Supply = [Supply ; supply(:,i)]; end Price = Price(2:end); Demand = Demand(2:end); Supply = Supply(2:end); %now i have a string for each deamdn, supply and price for z = 1:200:302400 for t=1:200 P(t,1)=[Price(z+t-1)]; D(t,1)=[Demand(z+t-1)]; S(t,1)=[Supply(z+t-1)]; bpos = P>-450; %lower value considered sumbpos = sum(bpos==0); bneg = P<450; %upper value considered sumbneg = sum(bneg==0); end %computation of the polynomial of order x (here 12) for the demand (polyfite) and supply (polyfitesupply) polyfite((z-1)/200+1,:) = polyfit(P(1+sumbpos:200-sumbneg),D(1+sumbpos:200-sumbneg),12); polyfitesupply((z-1)/200+1,:) = polyfit(P(1+sumbpos:200-sumbneg),S(1+sumbpos:200-sumbneg),12); %computation of Rsquare for demand (RSQUARED) and supply (RSQUAREDSUPPLY) Dsim = polyval(polyfite((z-1)/200+1,:),P(1+sumbpos:200-sumbneg)); RSS = sum((Dsim-mean(D(1+sumbpos:200-sumbneg))).^2); TSS = sum((D(1+sumbpos:200-sumbneg)-mean(D(1+sumbpos:200-sumbneg))).^2); RSQUARED((z-1)/200+1,:) = RSS/TSS; DsimSupply = polyval(polyfitesupply((z-1)/200+1,:),P(1+sumbpos:200-sumbneg)); RSSSupply = sum((DsimSupply-mean(S(1+sumbpos:200-sumbneg))).^2); TSSSupply = sum((S(1+sumbpos:200-sumbneg)-mean(S(1+sumbpos:200-sumbneg))).^2); RSQUAREDSUPPLY((z-1)/200+1,:) = RSSSupply/TSSSupply; end
Empirical Analysis of Price-Curves at the EEX
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2. Point elasticity computation using MATLAB
clear clc %we start from the data "Curvestudy" and "Price_Quantity" assets = xlsread('Curvestudy.xlsx'); assets2 = xlsread('Price_Quantity.xlsx'); %Market Clearing Price (MCP) and Market Clearing Quantity (MCQ) MCP = assets2(2:1513,1); MCQ = assets2(2:1513,2); for i = 1:3:192 price(:,(i-1)/3+1) = assets(4802:9601,i); demand(:,(i-1)/3+1) = assets(4802:9601,i+1); supply(:,(i-1)/3+1) = assets(4802:9601,i+2); end Price = 1; Demand = 1; Supply = 1; for i = 1:63 Price = [Price ; price(:,i)]; Demand = [Demand ; demand(:,i)]; Supply = [Supply ; supply(:,i)]; end Price = Price(2:end); Demand = Demand(2:end); Supply = Supply(2:end); for z = 1:200:302400 for t=1:200 P(t,1)=[price(z+t-1)]; D(t,1)=[demand(z+t-1)]; S(t,1)=[supply(z+t-1)]; bpos = P>-450; %lower value considered sumbpos = sum(bpos==0); bneg = P<450; %upper value considered sumbneg = sum(bneg==0); end %computation of the polynomial of order x (here 12) for the demand (polyfite) and supply (polyfitesupply) polyfite((z-1)/200+1,:) = polyfit(P(1+sumbpos:200-sumbneg),D(1+sumbpos:200-sumbneg),12); polyfitesupply((z-1)/200+1,:) = polyfit(P(1+sumbpos:200-sumbneg),S(1+sumbpos:200-sumbneg),12); %First derivative of each function is taken diffequation((z-1)/200+1,:) = polyder(polyfite((z-1)/200+1,:)); diffequationsupply((z-1)/200+1,:) = polyder(polyfitesupply((z-1)/200+1,:)); end %Computation of the point elasticity of demand (ElasticityD) and of the %point elasticiy of supply (ElasticityS) for i =1:1512 Upperpart = MCP(i)*polyval(diffequation(i,:),MCP(i)); Lowerpart = polyval(polyfite(i,:),MCP(i)); ElasticityD(i,:) = Upperpart/Lowerpart; end for i =1:1512 Upperpart = MCP(i)*polyval(diffequationsupply(i,:),MCP(i)); Lowerpart = polyval(polyfitesupply(i,:),MCP(i)); ElasticityS(i,:) = Upperpart/Lowerpart; end
Empirical Analysis of Price-Curves at the EEX
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3. Arc elasticity computation using MATLAB
clear clc %we start from the data "Curvestudy" and "Price_Quantity" assets = xlsread('Curvestudy.xlsx'); assets2 = xlsread('Price_Quantity.xlsx'); %Market Clearing Price (MCP) and Market Clearing Quantity (MCQ) MCP = assets2(2:1513,1); MCQ = assets2(2:1513,2); for i = 1:3:192 price(:,(i-1)/3+1) = assets(4802:9601,i); demand(:,(i-1)/3+1) = assets(4802:9601,i+1); supply(:,(i-1)/3+1) = assets(4802:9601,i+2); end Price = 1; Demand = 1; Supply = 1; for i = 1:63 Price = [Price ; price(:,i)]; Demand = [Demand ; demand(:,i)]; Supply = [Supply ; supply(:,i)]; end Price = Price(2:end); Demand = Demand(2:end); Supply = Supply(2:end); for z = 1:200:302400 for t=1:200 P(t,1)=[Price(z+t-1)]; D(t,1)=[Demand(z+t-1)]; S(t,1)=[Supply(z+t-1)]; bpos = P>MCP((z-1)/200+1); sumP = [sum(bpos==0)]; bneg = D<MCQ((z-1)/200+1); sumV = [sum(bneg==0)]; end %determination of the individual numbers needed Q1 = D(1+sumV); Q2 = D(sumV-1); P1 = P(1+sumP); P2 = P(sumP-1); QS1 = S(1+sumV); QS2 = S(sumV-1); %computation of the arc elasticity of demand (AEOD) and of the arc %elasticity of supply (AEOS) AEOD((z-1)/200+1,:) = ((Q1-Q2)/((Q1+Q2)/2)) / ((P1-P2)/((P1+P2)/2)); AEOS((z-1)/200+1,:) =((QS1-QS2)/((QS1+QS2)/2)) / ((P1-P2)/((P1+P2)/2)); end Output = [AEOD AEOS];
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4. Daily volatility computation using MATLAB
clear clc %we start from the data "Price_Quantity" assets = xlsread('Price_Quantity.xlsx'); prices = assets(2:end-24,1); quantity = assets(2:end-24,2); oldprices = assets(1:168,8); fullprice = [oldprices ; prices]; %computation for sigma(t = 1h, T = 24h), denote H1 for i = 169:1680 logreturnH1(i-168,1) = log(fullprice(i)/fullprice(i-1)); end %transform logreturns into real numbers logreturnH1 = real(logreturnH1); for i = 1:24:1512 meanlogreturnH1((i-1)/24+1,1) = mean(logreturnH1(i:i+23,1)); for H = 0:23 summ1H1(H+1,1) = (logreturnH1(i+H,1)-meanlogreturnH1((i-1)/24+1,1)).^2; end summ2H1((i-1)/24+1,1) = sum(summ1H1); volaH1((i-1)/24+1,1) = sqrt(summ2H1((i-1)/24+1,1)/23); end %computation for sigma(t = 24h, T = 24h), denote H2 for i = 169:1680 logreturnH2(i-168,1) = log(fullprice(i)/fullprice(i-24)); end %transform logreturns into real numbers logreturnH2 = real(logreturnH2); for i = 1:24:1512 meanlogreturnH2((i-1)/24+1,1) = mean(logreturnH2(i:i+23,1)); for H = 0:23 summ1H2(H+1,1) = (logreturnH2(i+H,1)-meanlogreturnH2((i-1)/24+1,1)).^2; end summ2H2((i-1)/24+1,1) = sum(summ1H2); volaH2((i-1)/24+1,1) = sqrt(summ2H2((i-1)/24+1,1)/23); end %computation for sigma(t = 168h, T = 24h), denote H3 for i = 169:1680 logreturnH3(i-168,1) = log(fullprice(i)/fullprice(i-168)); end %transform logreturns into real numbers logreturnH3 = real(logreturnH3); for i = 1:24:1512 meanlogreturnH3((i-1)/24+1,1) = mean(logreturnH3(i:i+23,1)); for H = 0:23 summ1H3(H+1,1) = (logreturnH3(i+H,1)-meanlogreturnH3((i-1)/24+1,1)).^2; end summ2H3((i-1)/24+1,1) = sum(summ1H3); volaH3((i-1)/24+1,1) = sqrt(summ2H3((i-1)/24+1,1)/23); end
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5. Hourly volatility computation using MATLAB
clear clc %we start from the data "Price-Quantity" assets = xlsread('Price_Quantity.xlsx'); prices = assets(2:end-24,1); quantity = assets(2:end-24,2); oldprices = assets(1:168,8); fullprice = [oldprices ; prices]; %computation for sigma(t = 24h, T = 168h), denote H4 for i = 169:1680 logreturnH4(i-168,1) = log(fullprice(i)/fullprice(i-24)); end %transform logreturns into real numbers logreturnH4 = real(logreturnH4); for i = 1:168:1512 for d = 1:7 for h = 1:24 hourperweek((i-1)/168*24+h,d) = logreturnH4((i-1)+(d*24)-24+h); end end end for i = 1:216 meanhourperweekH4(i,1) = mean(hourperweek(i,:)); end for i = 1:216 summ1H4(i,:) = (hourperweek(i,:)-meanhourperweekH4(i,1)).^2; summ2H4(i,1) = sum(summ1H4(i,:)); volaH4(i,1) = sqrt(summ2H4(i,1)/6); end
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6. Hourly volatility (rolling window) computation using MATLAB
clear clc %we start from the data "Prices_+" assets = xlsread('Prices_+.xlsx'); prices = assets(1:end,1); %computation for sigma(t = 168h, T = 1512h), denote H5 for i = 169:3048 logreturnH5(i-168,1) = log(prices(i)/prices(i-168)); end %transform logreturns into real numbers logreturnH5 = real(logreturnH5); for i = 1:17 for h = 1:168 hourperweek2(h,i) = logreturnH5(h+(i-1)*168); end end for d = 1:9 for i = 1:168 meanhourperweekH5(i+(d-1)*168,1) = mean(hourperweek2(i,(d-1)+1:(d-1)+9)); end end for d=1:9 for i = 1:168 summ1H5(i+(d-1)*168,:) = (hourperweek2(i,(d-1)+1:(d-1)+9)-meanhourperweekH5(i+(d-1)*168,1)).^2; summ2H5(i+(d-1)*168,1) = sum(summ1H5(i+(d-1)*168,:)); volaH5(i+(d-1)*168,1) = sqrt(summ2H5(i+(d-1)*168,1)/8); end end
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Declaration of Authorship
“I hereby declare
- that I have written this thesis without any help from others and without the use of docu-
ments and aids other than those stated above,
- that I have mentioned all used sources and that I have cited them correctly according to
established academic citation rules,
- that I shall not pass on any copies of this thesis to any third parties without the president’s
consent, with the exception of fellow students or persons who have provided me with es-
sential information for this thesis, to whom I max pass on copies of this thesis after the
procedure has been concluded.”
St. Gallen, 5th
November 2010
Nicolas Samyn
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