DIPLOMOVÁ PRÁCEquantitative.cz/wp-content/uploads/2020/02/DP_Martin_Dubravsky_201… · Vysoká ²kola ekonomická v Praze Fakulta nancí a ú£etnictví Katedra bankovnictví a

Vysoká ²kola ekonomická v Praze

Fakulta �nancí a ú£etnictví

Katedra bankovnictví a poji²´ovnictví

DIPLOMOVÁ PRÁCE

2019 Bc. Martin Dúbravský

Vysoká ²kola ekonomická v Praze

Fakulta �nancí a ú£etnictví

Katedra bankovnictví a poji²´ovnictvý

studijní obor: Finan£ní inºenýrství

Power markets and derivatives

Autor diplomové práce: Bc. Martin Dúbravský

Vedoucí diplomové práce: prof. RNDr. Ji°í Witzany, Ph.D.

Rok obhajoby: 2019

estné prohlá²ení:Prohla²uji, ºe jsem bakalárskou práci na téma "Power markets and derivatives"vypracoval

samostatn¥ a ve²kerou pouºitou literaturu a dal²í prameny jsem °ádn¥ ozna£il a uvedl

v p°iloºeném seznamu.

V .................. dne ..................

Pod¥kování:Rád bych na tomto míst¥ pod¥koval prof. RNDr. Ji°í Witzany, Ph.D. za vedení mé

diplomové práce a za podn¥tné návrhy, které ji obohatily. Rád bych také pod¥koval

Ing. Ji°í Novotný, za odbornou konzultaci a cenné rady.

AbstraktKomodity použ́ıvané v celosvětovém měř́ıtku na denńı bázi se také obchoduj́ı na svých samostatnýchtrźıch. Elektrická energie v Německu, neńı v tomto ohledu žádnou výjimkou. Kromě popisu charak-teristik elektrické energie tato práce analyzuje finančńı produkty derivované z dodávek elektřinyv Německu, obchodované na burze EEX. Ex -post futures prémie za riziko je analyzována pomoćıpř́ıstup̊u navržených v publikaćıch Bessembinder & Lemmon (2002) a Fama & French (1987).Bessembinder̊uv př́ıstup je založen na teorii zajǐtěńı. Očekává se, že riziková prémie vzroste sešikmost́ı rozděleńı spotové ceny během dodávky futures a poklesne s jej́ım rozptylem. Výsledekpoukazuje na opačnou tendenci. Důvodem může být jeden z předpoklad̊u modelu, že futurestrh poskytuje prostor pro zajǐstěńı, sṕı̌se než pro spekulace. Ukázalo se, že bez ohledu na měśıcdoručeńı, báze obsahuje informace o vývoji spotové ceny mezi dodaćım obdob́ım a současnost́ı.Nav́ıc poskytuje informace o úrovni rizikové prémie na dodávky během 5.-7. a 10.-12. měśıce.Analýza hlavńıch komponent forwardové křivky EEX ukázala, že je možné významné zmenšeńırozměr̊u pouze se strátou malého informačńıho obsahu ve forwardové křivce. Funkce rozptylu a je-jich tvary byly diskutovány v krátkodobém i dlouhodobém horizontu dodávek. Dominantńı pohybydlouhodobých dodávek futures jsou vysvětleny vytěsněńım uhelných zdroj̊u a strukturálńı změnoustruktury nab́ıdky. Rovněž, byla provedena analýza općı na dodávky elektřiny, která je obsaženave futures kontraktech s využit́ım dobře známeho modelu Black-Scholes-Merton. Byla analyzovánaimplikovaná volatilita a jej́ı časová struktura a bylo prokázáno, že vzhledem k mean-reversion po-vaze podkladového aktiva vzr̊ustá mı́ra implikované volatility općı s časem bĺıž́ıćım se datu expiraceopce. Bylo také prokázáno, že implikované sešikmeńı volatility se zvyšuje s časem expirace času.Rovněž byla prokázána sezónnost tohoto jevu. Pravděpodobným vysvětleńım sezónnosti sešikmeńıimplikované volatility je závislost struktury nab́ıdky elektřiny na počaśı a s t́ım spojena očekáváńıohledně směru cenových šok̊u, které by mohly nastat. To má vliv na změnu dynamiky poptávkya nab́ıdky pro call a put opce.Kĺıčová slova: elektrická energie, futures, opce, volatilita, sezónnost, nab́ıdka, poptávka,sešikmeńı implikované volatility

AbstractCommodities used on worldwide scale and daily basis, are also traded on their separate markets.Electric power in Germany, is no excetion in this regard. Apart from description of characteristicsof electric power, this thesis analyze derivative products on electricity in Germany traded on EEX.Ex -post futures risk premium is analyzed using approaches proposed by Bessembinder & Lemmon(2002) and Fama & French (1987). Bessembinder’s approach is build on theory of hedging pressure.Risk premium is expected to rise with skewness of spot price during delivery of futures and decreasewith increasing variance. Results show exactly opposite tendency. Reason for this might be one ofthe assumption of the model, that futures market provides insurance, rather than speculation. Itwas shown that regardless of month of delivery, basis contains information about developement ofspot price between delivery period and present. Moreover, basis provides information about level ofrisk premium for deliveries of 5th-7th month and from 10th-12th. Principal components analysisof EEX forward curve was performed and it was found, that significant dimension reduction ispossible without loss of any major information content in forward curve. Dominant componentsand their shapes were discussed in both short-term and long-term delivery horizons. Dominantmovements of long-term deliveries futures are explained by coal-phaseout and structural change ofGerman merit-order. Options on front-month futures deliveries were studied, utilizing well knownBlack-Scholes-Merton model. Implied volatility and its term structure were analyzed and it wasshown, that due to mean-reverting nature of underlying asset, level of implied volatility is increasingas time approaches exercise date. It was also shown, that implied skew of volatility is increasing astime approaches expiry date. Seasonal pattern of this phenomena was also shown to be significant.Probable explanation for seasonality of volatility skew is depenedency of merit-order structure onweather and different expectations about signs of price shocks that might occur, hence changingthe demand and supply dynamics for call and put options.Keywords: electric power, futures, options, volatility, seasonality, supply, demand,skew of implied volatility

Contents

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1 Electricity martets & German context 21.1 German regulatory framework & market organization . . . . . . . . . . . . . . . . 2

1.1.1 Energiewende . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2 Electric power as a commodity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.2.1 Non-storability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.2.2 Demand & supply . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.2.3 Cross border capacities & trading . . . . . . . . . . . . . . . . . . . . . . . 91.2.4 Explicit auctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.2.5 Implicit auctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.3 Fundamental drivers of power prices . . . . . . . . . . . . . . . . . . . . . . . . . . 101.3.1 Fuels & Carbon emission price . . . . . . . . . . . . . . . . . . . . . . . . . 111.3.2 Powerplants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Coal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Natural gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Diesel aggregates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14Carbon capture & storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.3.3 Weather conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2 Stylized facts of power prices 162.1 Mean reversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.2 Price spikes & Negative prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.3 Seasonality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.3.1 Intra-day hourly effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.3.2 Intra-week seasonality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.3.3 Intra-year seasonality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.4 Returns distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3 EEX Electricity futures 253.1 Futures contracts risk premium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.1.1 Literature overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.1.2 Bessembinder & Lemmon . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.1.3 Fama & French . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.1.4 Data & Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.1.5 Estimation Bessembinder-Lemmon model . . . . . . . . . . . . . . . . . . . 303.1.6 Estimation Fama & French model . . . . . . . . . . . . . . . . . . . . . . . 31

3.2 Principal component analysis of forward curve . . . . . . . . . . . . . . . . . . . . 333.2.1 Theoretical background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.2.2 PCA of EEX Futures prices . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

Short-term delivery horizon . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Mid-term & Long-term delivery horizon . . . . . . . . . . . . . . . . . . . . 38

3.2.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4 Options 414.1 EEX Power options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.2 Black-Scholes-Merton model & equation . . . . . . . . . . . . . . . . . . . . . . . . 424.3 Valuation of EEX power options . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.4 Volatility smile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.4.1 Term structure of level of implied volatilities . . . . . . . . . . . . . . . . . 464.4.2 Term structure of volatility skew . . . . . . . . . . . . . . . . . . . . . . . . 49

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

IntroductionCommodities used on worldwide scale and daily basis, are also traded on their separate markets.Electric power in Germany, is no excetion in this regard. What differentiate it from many othercommodities, is its neccessity of continous delivery and almost non-existent storage solutions. Thisis also one of the reasons, why electric power market is only for few decades deregulated and ex-posed to free market exchange. With growth of attention paid to environmental consequences ofcarbon dioxide emission levels, inclusion of carbon pricing, and general effort of Germany to re-shape the structure of its power generation mix, new challanges and opportunities are present in theindustry. These motives include massive increase of renewables share in the power generation mix,coal-phaseout alongside with nuclear phase-out. Motive of this master’s thesis is to understandelectricity’s originality as a commodity, discover fundamental drivers of its price, discuss possibledangers of proposed regulation framework and perform analysis of behaviour of derivatives marketand its products (mainly futures and options).

This thesis can be separated into general market and derivatives market blocks. In the blockdedicated to general market, German regulatory framework is presented alongside with its targetsand motives. Secondly, unique properties of electricity as a commodity are discussed. In the nextsections this thesis contains overview of main supply and demand drivers alongside with stylizedfacts of its prices. Regarding supply side of the power market, brief overview of thermal officienciesand flexibility measures are provided for powerplants categorized by fuel used in their thermody-namic cycle. Calculation of clean spark spread and clean dark spread is also shown and usedas the main relationhip in discussion about powerplant’s desision making process. Various levelsof seasonality of electricity prices are discussed in the greater detail. Analysis of drivers behindoccurence of extremely high and negative prices is shown in the same section of this thesis. Formultiple reasons stated in this section and in the sections before that, high seasonal reliance onwind generation could be the reason for price spikes as well as for negative prices.

In the other part of this thesis, dedicated to German electricity derivative products traded onEEX, I perform multiple analyses and tests for validity of various hypotheses analyzed by manyauthors in markets for different commodities. Futures market risk premiums are studied and mod-els proposed by Bessembinder & Lemmon (2002) and Fama & French (1987) are estimated. Inframework proposed by Bessembinder, build on theory of hedging pressure, risk premium is ex-pected to rise with skewness of spot price during delivery of futures and decrease with increasingvariance. Next, I test for information content present in the difference between futures price at timet with delivery during T and spot price at time t. Two models are estimated to test whether thisdifference, also known as basis, provides market with information about spot price developementbetween t and T and also, if the basis observed has explanatory power to predict levels of ex-postrisk premium observed during delivery period T . Principal components anaylisis of EEX forwardcurve of German power futures was deseasonalised and examined. Significant dimension reductionwas possible with lost of merely 5% of explained variance. Discussion of results and implicationsfor both short-term and long-term delivery horizons is provided in respective sections.

Regarding options, comparison between market prices and prices obtained using Black-Scholes-Merton model, is shown and analysed. Due to liquidity of this product, only options on front-monthfutures delivery are contained in this part. Hypotheses regarding term structure of implied volatil-ities and their skew are formulated and verified. Specifically, term structure of implied volatilityand its skew tested. Because of mean-reverting nature of futures prices, it is expected that withtime t approaching expiry of an option, implied volatility should increase. Metric for measurementof implied skew is proposed, and similarly to previous one, hypothesis about its increasing tendencywith time t approaching expiry of an option is tested. Both of these hypotheses were found to betrue and discussion about economic reasons behind their existence is provided in respective sectionof this thesis.

Every calculation, model estimation and visualisation provided by me, was obtained usingPython programming language. As data source, EEX database served as the main source. Forresults of day-ahead auctions as well as forward step-curves, I used my employer’s data, for whichI am grateful to them.

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Chapter 1

Electricity martets & Germancontext

1.1 German regulatory framework & market organizationElectric power prices are nowadays subject to competitive market forces in majority of developedcountries. Deregulation of power markets during 1990s was preceeded by deregulation of othercommodity markets, namely natural gas and oil. Before the deregulation of a power market,regulator had power to set the prices accounting for generation, distribution and transmissioncosts. These deregulation movements usually consist of three steps. Thorough description of thosecan be found in Stender (2009).

1. Abolishment of hurdles that impede the entrance of new parties into market

2. Unbundling of vertically integrated companies in the market

3. Enhanced transparency from previous steps enables cost reduction of natural monopolies

European Union initiated this process, enacting EU directive1 in December 1996. Purpose ofthis directive was to lower electricity and gas costs for end customers by regulating existing mo-nopolies as well as promotion of market competition. This directive was in 1998 transformed intoa new German energy law2. Afterwards, eight companies, which at the time practically governedthe industry, participated on series of mergers and strategic partnership agreements. The resultof this restructuring was oligopoly formed by RWE, E.ON, Vattenfall and EnBW. These partiescombined, were in posession of 80% of domestic power generating capacity at the time.

In 2003 EU decided to enact another directive3, as they were not satisfied with the speed ofliberalisation of the industry. Target of this regulatory decision, was to enforce demerging of verti-cally integrated parties with more than 100,000 clients. These companies were required to legallyand operationally separate divisions of production, operation and distribution.

Results of the regulatory actions and their defined targets were, and still are, subject of interestamong academia as well as industry players. Regarding the first directive, it is rather questionablewhether the results met with the targets, since power generation facilites are still owned by smallamount of companies. When it comes to lowering energy costs of the end customers, results arequite straightforward and easy to check, by looking at the figure 1.1.

1Directive 96/92/EC2Energiewirtschaftsgesetz, EnWG for short3Directive 2003/54/EC

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Figure 1.1: German electricity retail prices

The most significant outcome of this deregulation was allowing spot markets to host tradingof physical electricity. Electricity is one of the most versatile forms of energy. It can be used toproduce light, heat and mechanical power in an efficient way. Utility privided by electric poweris dependent on its continous flow. For this reason, all power contracts are structured to providepower over time period rather than delivery at fixed point in time. This means that in our powersystem generation and consumption have to equal one another at every moment in time. In Scan-dinavian countries4 and Germany5, developement of liquid spot market prices was utilized andderivative contracts indexed to spot prices were introduced. Vehvilainen (2002)

Physically settled contracts provided by spot market appears in two forms. Day-ahead marketand real-time market. Both of them are supervised by state sponsored party6, called Transmissionsystem operator (TSO). Prices on Day-ahead market observed during day d are obtained via auctionrealised during d− 1, while real-time market7 serves as upward and downward regulation, in casethe quantity auctioned on day-ahead market will during day d provide either shortage or surplusof power to the grid. In reality, the day-ahead demand forecast will never be completely accurate.Also supply will differ from what was expected, due to different wind conditions, solar insulationor unexpected plant outages. Therefore, the role of real-time market is very important. Esentially,it serves as balancing mechanism in case that demand (or supply8) during day d will exceed orlack the quantity at which spot market was cleared the day before. From now on, I will adressDay-ahead market as ’spot market’ because these prices serves as a reference for financially settledproducts i.e. derivatives.

4Nordpool5EEX6Due to the cost of establishing a transmission infrastructure, the institution is likely to be natural monopoly.

Combined with the importance of services provided, it is state-owned enterprise more often than not.7Also known as ’Intra-day’ market8With share of renewables in generation mix increasing, the possibility of sudden , unpredictible weaher events

can severely affect supply side as well

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Figure 1.2: EEX Spot market organization

Price mechanism on EEX spot market is build on auction, where suppliers and consumersplace their respective bids and offers. For every predefined period of 1 hour, the generation bidsare aggregated to one supply curve. Since the bids are ranked according to increasing price, thiscurve is referred to as the merit order curve. Renewables have a very low marginal cost 9 and arefound at the bottom of the curve. Nuclear has also a low running cost and follows the renewablesin the ranking. For low (or non-existing) carbon permit prices, the running costs of a coal plantare typically lower than those of a combined cycle gas plant (CCGT, also known as STAG plant).Peak plants, which are meant to cover rare peaks in demand (for example on an exceptionally coldwinter day) are often diesel or gasoline fueled and therefore have the highest running cost. Anillustration of the merit order curve is given in the figure 1.8. It is natural for each commodityto have unique set of properties influencing their trading. This is true statement, especially forelectric power. Before adressing these properties, I would like to pay a closer attention to one moreregulatory movement presented in recent history.

1.1.1 EnergiewendeWorldwide concerns, regarding climate change and global warming, has changed power generationsector10. In Germany, set of policies, most of which are in a broader sense aimed at reducing carbondioxide emissions, were included in a framework called Energiewende, in English, energy transition.

Legislative support for the Energiewende was passed in late 2010. There is no official start-ing date for the Energiewende, but rather it is a continuous and gradual process of transition ofthe energy system. Among the first initiatives, German coalition passed the Renewable EnergyAct (EEG) promoting investments on renewable power generation, and the first law on nuclearphaseout in agreement with the energy utilities. The nuclear phase-out plan, however, did notset an exact timetable for the closure of the nuclear plants, but allocated electricity productionlimitations for each plant. The EEG implemented a fixed feed-in tariff for renewables, paid bymeans of a surcharge on consumption, creating a reliable market to support greater investmentand participation in renewable energy generation. Expansion of power generation with close tozero marginal costs was directly paid for, by consumers.

In 2010, the newly-elected conservative government led by Chancellor Angela Merkel adoptedthe Energiekonzept, a long-term energy strategy calling for a renewable based economy by 2050.It included:

• Rather ambitious mid and long-term targets for the development of renewable energy

• Enhancement of energy efficiency

• Reduction of carbon dioxide emissions9Since there are no costs neccessary to make the sun shine and the wind flow.

10Globally, but in European Union especially.

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The strategy, however, extended the lifetime of existing nuclear powerplants, thus delaying thenuclear phase-out until 2036. This postponement of nuclear phase out was pulled back to 2022,right after Fukushima accident in Japan, which occured in 2011.

In 2014, the new Renewable Energy Act EEG 2.0 introduces measures to manage the growthand competitiveness of renewable energy. Among those, the most significant were:

• Reduction of fixed tariffs

• Inclusion of most solar producers in power auctions

• Recalculated surcharges included in retail price to assist large industry

• Enforcement of surcharge from self-suppliers connected to grid

The amendment made in 2017 to the Renewable Energy Act moves from fixed feed-in tariffs toauction-based determination of renewable electricity prices. It also aims to ensure that the pace atwhich renewable capacity is added corresponds to the pace at which the grids are developed andit restricts the expansion of onshore wind power in certain areas of northern Germany that suffergrid congestion.

An overview of main drivers and obstacles of this regulatory framework can be seen in figure1.3.

Figure 1.3: Energiewnde goals and obstacles

Source: Kuittinen & Velte (2018)

Kuittinen & Velte (2018).

Result of all of these legislative arrangements, resulted into massive increase of share of renew-ables in German power generation mix.

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Figure 1.4: Renewables pushing off nuclear

Source: Kuittinen & Velte (2018)

Since majority of the renewables generation investments was stimulated either by state’s invest-ment subsidies or by guaranteed fixed price of power for these generators, additional funds wererequired to be raised. In the previous part of the text, describing Energiewende evolution, multiplementions of surcharges can be seen. I also mentioned that going down this path, divergence of thewholesale prices and retail prices was more or less expected. Figure 1.5 is providing a very specificbreakdown of retail power price.

Figure 1.5: Retail power price breakdown

Source: https://1-stromvergleich.com/strom-report/

Moving back to the wholesale electricity power market and looking beyond effect of renewableson nuclear, the effect of renewables expansion on the power generation mix, as a whole, can beinspected by looking at the shift of the merit order. Citing abstract of Roldan-Fernandez et al.(2016).”The integration of certain amount of renewable generation in the wholesale market right-shiftedthe merit-order generation curve, which produces a noticeable reduction of the clearing price whileslightly increases the traded energy (almost inelastic demand curve). The downward pressure on

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the clearing price is mainly due to the fact that the introduction of renewable generation bids withvery low (even null) marginal cost, displaces to the right all kinds of conventional technologies(with higher marginal cost), including the technology which would otherwise have set the clearingmarket price. This right-shifted displacement of the merit-order generation curve leads to a lowerwholesale clearing price, a small increment of the traded energy and a reduction of the total costof the traded energy in the wholesale market. This is the key mechanism and its main effects onthe market of the very well-known meritorder effect of the renewables.”

Figure 1.6: Merit order effect of renewables

Source: https://www.cleanenergywire.org/factsheets/setting-power-price-merit-order-effect

In their work, Benhmad & Percebois (2017) examine the effect of renewables generators pen-etration of power generation mix, by modelling of volatility of electric power spot market prices.They used feed-in tarrifs provided to photovoltaic and wind turbines generators as explanatoryvariables. In their analysis they came to conclusions that feed-in tarrifs provided to photovoltaicpowerplants decreased the wholesale price. On the other hand, wind turbines generation seems toexacerbate the volatility of these prices, while photovoltaics’ tarrifs tends to decrease it.

1.2 Electric power as a commodityWhile talking about electricity as a commodity which is globally consumed on a daily basis, belowis an overview of every relevant power exchange around the world.

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Figure 1.7: Power exchanges around the globe

Source: Barouti & Hoang (2011)

In the section designated to German regulatory framework, I mentioned that each commodityhas its unique set of properties which influence its trading. Electricity is no exception to this ruleand in the following subsection I will describe the main characteristics of electric power.

1.2.1 Non-storabilityIt is impossible to store significant volumes of electric power. With exception of hydro powerplants,nowadays there is not a feasible way how to buy electric power on a spot market, store it and sellit afterwards, for example on futures market. This feature has a set of important consequences.

1. Arbitrage arguments based on storage possibility shown for example, in Witzany (2013), cannot be used to derive relationship between spot and futures prices.

2. Spot price is extremely vulnerable to severe shocks, caused by either supply or demand sideof the market.

3. Seasonal deviation of region’s power consumption is directly transferred into seasonality ofprices of power deliveries.

Consequence number 1 is a complication, however there is an alternative approach to dealingwith interconnection of spot and futures prices. This approach is discussed in section ”Futurescontracts risk premium” of this thesis.

Empirical evidence of consequence number 2 is provided in section ”Stylized facts of powerprices” and its subsection ”Price spikes % negative prices”.

Regarding the seasonality, its analysis is also provided and discussed in to section dealing withStylized facts of power prices.

1.2.2 Demand & supplyDue to non-storability of electric power, generated amount of electricity must always match de-manded quantity during delivery period. As I already mentioned, spot market prices are obtainedin auctions. In the short-term future horizon, demand for electricity is very price-inelastic. In orderto satisfy their needs, agents participating as demand side of the power market, do not possess vastportfolio of energy substitutes to electricity power. It is fair to assume, that in any given point intime, majority of demand side of the market, can be characterized by this description, thereforedemand curve as such is broadly understood to be inelastic. In reality, consumers within category

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of big industry companies, possess certain maneuver space, where optimisation of their activitiescan be subject to electricity power intra-day or intra-week seasonality11. As a consequence of thismarket behaviour, bidding side of auction will bid for the quantity demanded by its customer,at virtually any price. Additional research on electricity market demand low price-elasticity wasconducted by Bye & Hansen (2008) and Johnsen (2001).

Because electricity cannot be stored, it is likely that the spot price is strongly driven by funda-mentals connected to supply and demand (see Geman & Roncoroni (2006)). While it is true, thatdemand shocks occur on power markets, it is generally a market where day-to-day dynamics aredriven by supply side. Not occasionally, an occurence of negative supply side shock, for examplesudden shut-down of coal fired powerplant, a substantial positive price jump is often observed 1.8.Analogically, in case of positive supply side shock, more often then not provided by renewablesproduction, can cause.

Figure 1.8: Illustration of power supply and demand

Source: https://www.next-kraftwerke.be/en/knowledge-hub/merit-order-curve/

1.2.3 Cross border capacities & tradingGenerally, power transmission infrastructure, or power grids, are constructed on national level.Flow of electricity in between these regional infrastructures is subject to special chapter of elec-tric power trading. Until recently, electric power generation, transimission and distribution wasvertically integrated into state monopolies. For this reason, the capacities, that are currentlypresent on borders and capable of power transmission are not sufficiently big to ensure a singleprice within continent. This absence of sufficient power transmitting border capacity is calledcongestion. However, there are solutions to this problem:

1. Explicit auctions

2. Implicit auctions - can be present in form of either market splitting or market coupling

1.2.4 Explicit auctionsCiting a document published by Nordpool on this link12 ”Explicit auction is when the transmissioncapacity on an interconnector is auctioned to the market separately and independently from themarketplaces where electrical energy is auctioned. Explicit auction is considered as a simple methodof handling the capacity on the international interconnections in Europe. The capacity is normally

11Estimation of these seasonal effects will be discussed in the following part of this thesis12https://www.nordpoolgroup.com/globalassets/download-center/pcr/how-does-it-work explicit-and-implicit-

capacity-auction.pdf

9

auctioned in portions through annual, monthly and daily auctions. Since the two commodities,transmission capacity and electrical energy are traded at two separate auctions, there is a lackof information about the prices of the other commodity. This lack of information can result inan inefficient utilization of interconnectors, i.e. less social welfare, less price convergence andmore frequent adverse flows.” In practice, this means that market participants place their bids onauctioned capacity between two power grids. Conditional on amount of transmission capacity thatis left after the auction one of two scenarios take place:

1. If there is none capacity left without a bids, offers are satisfied from the highest bid to thelowest one, until available capacity is depleted

2. Offers are satisfied from the highest bid to the lowest one placed in auction

In each of these scenarios, the result is a single price for all successful bidders. In case of depletedcapacity, last accepted bid is paid by all participants13. Alternatively, if there is capacity availableeven after all bids are placed, the price paid by participants is zero.

1.2.5 Implicit auctionsWith implicit auction system, day-ahead transmission capacity is used to integrate day-aheadmarkets in different areas of bidding. Flow of electric power assigned to particular interconnectingpoint, is not subject to aution of its own. Auctions of these capacities are implicitly included inauction of electricity on different markets. In implicit auctions, the transmission capacity betweenbidding areas14 is made available to the spot price mechanism in addition to bid/offers per area,thus the resulting prices per area reflect both the cost of energy in each internal bidding area (pricearea) and the cost of congestion. Implicit auctions ensure that electrical energy flows from thesurplus areas (low price areas) towards the deficit areas (high price areas) thus also leading to priceconvergence.

This idea of implicit auctions is based on idea, that in a particular market M there is unex-ercised offered volume of electric power, while in a particular market P there is a bid volume ofelectricity. Contidional, on capacity available between markets M and P , complete interconnectionis possible. If this situation occurs, the market participants are not required to purchase trasn-mission capacity, no trasmission costs occur and both markets M and P have the same price ofelectricity. As I mentioned above, this type of auction can evolve either into market splitting ormarket coupling.

Market splitting mechanism was firstly formed in Scandinavian region. It is managed by oneexchange, Nordpool. The exchange accepts bid and offers from all participating businesess, re-gardless of location where they operate. All bids and offers are in the first step managed as if theywere no transmission capacity constraints. If the result of this evaluation falls between limits ofinterconnection limits, one price is formed for all participating regions managed by the exchange.In case of transmission capacity, required to set a single price, is not sufficient, multiple prices areformed in order to adjust clearing volume in particular markets.

Market coupling mechanism is on the other hand aranged in such a way, that each region isevaluated by national electric power exchange. The number of cooperating exhanges is given bynumber of countries that agree to create a common electric power market area. Czech Republic,Slovakia, Hungary and Romania formed one common market area, with all members joining indifferent times15. This process was completed by connection of Romania in 2014. Participants aredealing only with national power exchange of the country they are operating in.

1.3 Fundamental drivers of power pricesElectricity power prices generally discount various factors and variables. The most common ofthem are the cost to building a powerplant, finance costs, maintenance, and operational costs

13Marginal price14in most cases these areas represent countries, even though in German case, there are 4 bidding areas present.15Czech Republic and Slovak Republic formed market-coupling area in 2009, Hungary joined them in 2012.

10

of powerplants and the electricity grid16. Some for-profit utilities also include a financial returnfor owners and shareholders in their electricity prices. Several key factors influence the price ofelectricity:

• Fuels: Fuel costs can vary, especially during periods of high demand. High electricity demandcan increase demand for fuel, such as natural gas, which can result in higher prices for thefuel and, in turn, higher costs to generate electricity.

• Carbon emission allowance17 price: In order to be compliant with environmental regulation,EUA price per one metric tonne of emissions of carbon dioxide, is especially crucial forthermal generation such as coal or natural gas.

• Powerplants: Each powerplant has construction, maintenance, and operating costs. Trans-mission and distribution system: The electricity transmission and distribution systems thatdeliver electricity have maintenance costs, which include repairing damage to the systemsfrom accidents or extreme weather conditions.

• Weather conditions: Rain and snow provide water for low-cost hydropower generation.18Wind can provide low-cost electricity generation from wind turbines when wind speeds arefavorable. However, extreme temperatures can increase the demand for electricity, especiallyfor cooling, and demand can drive prices up.

• Regulations: In some states, public service/utility commissions fully regulate prices, whileother states have a combination of unregulated prices for generators and regulated prices19for transmission and distribution.

Following map shows an overview of principal determinants of electric power prices and theirinterconnections. Some of the these factors will be adressed separately and in greater detail infollowing subsections.

Figure 1.9: Price evolution for each scenario

Source: Yilmaz (2016)

1.3.1 Fuels & Carbon emission priceSince power generation, especially from coal and gas, is both capital intensive and the fuels (as wellas carbon allowances required to operate in power generation) are highly volatile, producers tendto hedge both their revenues and costs for a reasonably distant future. To calculate the margin forwhich a producer can generate megawatt hour of electricity two (resp. four) spreads are important.

• Clean Spark spread (CSSEUR/MW h(e)) - EUR margin from 1 MWh of production fromnatural gas fired generation.

CSSEUR/MW h(e) = P [E]EUR/MW h(e) −P [NG]EUR/MW h(t)

eg− P [EUA]EUR/TCO2

efgeg

(1.1)16Complex system of power transmission and distribution lines17European Union Allowance, or EUA for short18High hydrogenerating power capacities are installed in countries such as Norway and Austria.19Recently, Poland has moved towards freezing of electricity power prices for households.

11

– P [E]EUR/MW h(e) - price of 1 MWh of electricity– P [NG]EUR/MW h(t) - price of 1 thermal MWh of natural gas– P [EUA]EUR/TCO2 - price of 1 metric tonne of carbon dioxide emission– eg - natural gas thermal efficiency20 of natural gas fired powerplant facility– efg - natural gas emission factor21 of natural gas fired powerplant facility

• Clean Dark spread (CDS) - margin from 1 MWh of production from coal fired generation.

CDSEUR/MW h(e) = P [E]EUR/MW h(e) −P [C]USD/TSREUR/USD

ec6 ∗ 1.163 − P [EUA]EUR/TCO2

efcec(1.2)

– P [E]EUR/MW h(e) - price of 1 MWh of electricity– P [C]EUR/MW h(t) - price of 1 thermal metric tonne of coal– P [EUA]EUR/TCO2 - price of 1 metric tonne of carbon dioxide emission– SREUR/USD - spot price of EUR/USD– ec - natural gas thermal efficiency22 of coal fired powerplant facility– efc - natural gas emission factor23 of coal fired powerplant facility– constant 6 ∗ 1.163 - Physical constant used to obtain thermal energy contained in one

metric tonne of API2 (ATW - Rotterdam) coal

Figure 1.10 shows both of these spreads calculated for one hour of delivery during whole calendaryear 2020. It is important to realize, that these values are conditional mainly on efficiency ofpowerplant so each powerplant will have different value of spread despite taking same price offuels. Speaking of fuels, prices of futures contracts traded on Intercontinental exchange (ICE forshort). German NBP natural gas with delivery period of calendar year 2020 and Rotterdam coalfutures ATW with same delivery period. Emission allowance price was taken also from futurescontract traded on ICE with delivery in December 2019.

1.3.2 PowerplantsIrrespective of technology, all electric power generators share the following characteristics whichinfluence the plant’s operations:

• Ramp rate - how quickly the plant can increase or decrease power output, in [MW/h]

• Ramp time - the amount of time it takes from the moment a generator is turned on to themoment it can start providing energy to the grid at its lower operating limit

• Capacity - maximum potential output of powerplant [MW]

• Lower operating limit - minimum amount of power a plant can generate once it is turned on[MW]

• Minimum run time - shortest amount of time a plant can operate once it is turned on [h]

• No-load cost - cost incurred by the generator that is independent of the amount of energygenerated Start-up & Shut-down costs - costs involved in turning the plant on and off, in[Euro/MWh]

Figure 1.11, provides overview with aformentioned constraints for different powerplants. Figure1.12 illustrates different powerplants and shows the relaionhips between fuel type, operational costsand operational flexibility.

20Amount of MWh of electricity (MWh(e)) produced from one thermal MWh (MWh(t)) of natural gas21Amount of metric tonnes of carbon dioxide produced from burning one thermal MWh (MWh(t)) of natural gas22Amount of MWh of electricity (MWh(e)) produced from one thermal MWh (MWh(t)) of coal23Amount of metric tonnes of carbon dioxide produced from burning one thermal MWh (MWh(t)) of coal

12

Figure 1.10: CSS and CDS

Powerplants efficiences and fuels emission factors eg = 0.52,ec = 0.42,efg = 0.2,efc = 0.96Source: Author’s calculation

Figure 1.11: Ramp and run times for powerplants

Source: Penn state university - EME 801; Energy markets, policy and Regulation study materialshttps://www.e-education.psu.edu/eme801/node/530

Calculation of clean dark spread and clean spark spread provided in previous subsection ofthis thesis, is shedding a light into factors that determine willingness of powerplant to operate.Efficiency of powerplant is conditional on engineering solution of power generation. In recent eraof carbon emission policy compliance, additional dimension in form of emission factors and carboncapturing mechanisms installed in powerplants, have significant role.

Coal

Coal based power accounts for almost 41% of the world’s electricity generation. Thermal efficiencyis dictated by the parameters of its thermodynamic cycle. The overall coal plant efficiency rangesfrom 32% to 42%. Most of the large coal powerplants operate at technology that allows themto convert 35% to 38% of thermal energy content into electric power. However, coal powerplantsusing super critical pressure, can reach thermal efficiencies ranging from 45% to 48%.

Natural gas

Natural Gas (including LNG fired) power generation facilities account for almost 20% of the world’selectricity generation. Technology used by these powerplants makes use of Gas Turbines or Gas

13

Figure 1.12: Comparison of operating cost and operational flexibility

Source: Penn state university - EME 801; Energy markets, policy and Regulation study materialshttps://www.e-education.psu.edu/eme801/node/530

Turbine based combined cycles24. Gas turbines in the simple cycle mode, only Gas turbinesrunning, have an efficiency of 32% to 38%. The most important parameter that dictates the thermalefficiency is the maximum gas temperature possible. The latest Gas Turbines with technologicaladvancement in place has efficiencies upto 38%. In the combined cycle mode, the new “H class”Gas turbines with a triple pressure HRSG and steam turbine can run at 60% efficiency at ISOconditions25. This is by far the highest efficiency in the thermal power field.

Diesel aggregates

Nowadays, diesel aggregates serve only if the prices of electricity soar to the highest levels. Marginalcosts of these powerplants are very high, rulling the out of merit-order. Even though their thermalefficiency is comparable to their coal counterparts, ranging from 35% 42%, fuel costs and emissionfactors are high enough to justify running this powerplants only when prices are very high.

Incorporation of carbon dioxide capture technology is logically conditional on price of one tonneof carbon dioxide. With prices of EUA Futures contracts with delivery during December 2019,soaring and currently trading at 25 Euros per metric tonne of carbon dioxide, this topic will attractmore attention from field as well as from academia. At this time, this topic is to a greater detailanalyzed in publications David & Herzog (2000) and Rubin et al. (2015).

Carbon capture & storage

In the second one, of the aformentioned publications, authors provide an overview, in which theycompare efficiencies of coal and gas fired power generating facilities with and without carboncapture technology in place. They also analyze transport and storage costs of captured carbondioxide. Both of these powerplant types are amenable to post-combustion carbon capture. Theyconcluded26 that on top of increased 18% - 49% of capital costs increase linked to powerplant con-struction between periods 2005 and 2015, incorporating of carbon capture and storage technology

24Commonly referred to by abbreviation ’CCGT’25The same technology will perform differently under various atmospheric conditions, surrounding power gener-

ating facility. ISO conditions are involve ambient temperature of 15 degrees Celsius , 60% relative air humidity andambient pressure at sea level.

26This analysis was performed in the US market, hence the results are not directly convertible into Germanenvironment.

14

would inflate these values by 9 - 14 %27. Also, the constant dollar levelized costs of electricity(LCOE)28 calculated as a sum of fuel costs, variable non-fuel costs and fixed operating and initialcosts29 saw only small increase. They also conclude , that further incentive to invest in such tech-nology could be provided by use of captured carbon dioxide in enhanced oil recovery. Moreover,one of the final thoughts mentioned in this paper, is that there is no obvious tehnological winnerthat is best suited for low-carbon fossil power generation.

1.3.3 Weather conditionsEffects of weather could be devided into those affecting demand side and those affecting supplyside. Demand side is affected through temperature and consquently demand for heating and airconditioning. Cloud cover is affectting demand through neccessity to use light. Intra-year sea-sonality of demand is also connected to an amount of hours of sunlight during a day. Naturally,business hours during a day and business hours, during a week, also provide electricity demandwith intra-day and intra-week seasonality.

Regarding supply side, figure 1.13 shows that share of renewables in German power generationmix is consistently growing. For this reason, exposure of supply side of the market is growing withit.

Figure 1.13: Power generation mix evoution in Germany

Source: https://www.energy-charts.de/power inst.htm

Nonetheless, weather and atmospheric conditions have an impact on powerplants as well.González-Dı́az et al. (2017) in their work, provide empirical measurements and analysis of airtemperature and atmospheric pressure on efficiencies of gas fired powerplants.

27Coal fired plants would require the higher investment28Average price per unit of output needed for the plant to break even over its operating lifetime.29Units of dollars per megawatt hour of electricity.

15

Chapter 2

Stylized facts of power prices

Following sections are dedicated to description of dominant characteristics of power market data,namely prices and returns. For each of these Stylized facts, comparison between spot and futuresmarket behaviour will be shown.

2.1 Mean reversionMean reversion1 is another noticeable feature of electricity prices. This characteristic has beendescribed by many authors (Cartea and Flgueroa (2005), Geman Roncoroni (2007) among others).In periods of extremely high prices, supply tends to squash the price down. On the other hand,in periods of extremely low prices, powerplants often prefer not to run and consequently sell theelectric power, since their marginal cost are higher than the price of delivery during given period.Combined, the electricity price time series is mean reversion toward a level that represents slowlychanging marginal costs.

Existence of mean reversion in both spot and front-month futures prices was investigated byAugmented Dickey-Fuller test, which is in great detail described in Tsay (2005). In both cases,existence of mean-reversion was not declined using significance level α = 0.05.

2.2 Price spikes & Negative pricesDue to storage impossibility and requirement of continuous delivery of electricity, occurence ofeither positive or negative price shocks is frequent. In previous part of thesis I presented the maindemand and supply side reasons for their existence. Figure 2.1 presents developement of hourlyday-ahead spot prices on EEX. As you can see, that presence of negative prices is really nothingoccasional in Germany’s power market.

Price spikes are useful for a few reasons (Eydeland & Wolyniec (2003)):

1. On the demand side, they help to signal shortages and encourage customers to reduce theirusage in times of stress

2. On the supply side, they signal shortages and help bring in more supply/ additional entry

Analyzing occurence of extremely positive and negative values I came to the following results. Inbetween begining of the year 2012 and March 2018, 746 hours with negative prices occured. Thataccounts for 1.185% of all hours within this period of time. Figures 2.2, 2.3 and 2.4 are providingan insight into seasonality of negative prices and extremely negative (and also positive) prices. Inthis regard, January and February are months that seems to be most likely to bring extremelyhigh power prices. Decemeber is the month when most, nearly 50, of extremely negative priceswere observed. Months of October, January and May seems to have similar amount of extremelynegative hourly prices, each of them approximately 23.

1Sometimes described as anti-persistence

16

Figure 2.1: EEX Hourly spot price

Source: Author’s calculation

Figure 2.2: Negative hourly prices


Figure 2.3: Extremely negative hourly prices

Source: Author’s calculationSource: Values negative at least mean - 4 standard deviations of hourly day-ahead prices. See legend in figure 2.1

Histograms for extreme values of daily prices are not necessary, since their shapes are similar,when compared to hourly ones. Although it is true, that reneweables increase in power generationmix is partly responsible for increasing occurence of negative prices, low flexibility and adjustmentof conventional powerplants also has its share of responsibility. It is also important to realize thatnegative prices are not neccessarily bad. From economic point of view, they provide incentives toutilities to make their power stations more responsive to changing conditions on the power market,and offer companies new business opportunities by adapting demand. At times of high production,producers should be stimulated to take capacity offline, while large-scale consumers can ramp up

17

Figure 2.4: Extremely positive hourly prices

Source: Author’s calculationSource: Values positive at least mean + 2 standard deviations of hourly day-ahead prices. See legend in figure 2.1

Figure 2.5: EEX Daily spot price


demand when prices are low.

Extremely high power prices observed mainly during first half of 1st quarter and second halfof 2nd quarter, could provide a more alarming information. Figure 2.7, is meant to show longerhistory of price developement of long-term contracts for physical delivery of electric power. Sinceheavier involvement of renewables, prices of power in Germany tends to decrease, which is bothunderstandable and already mentioned in this thesis in section ”Energiewende”. Nature of thesegeneration capacities is, however, very sensitive to weather conditions which are for a certainhorizon in the future reliably predictible and also seasonal. By lowering price of generated power,many conventional generation projects that were starting to show signs of errors and were seekingcapital for reconstruction were hit by one of two main obstacles2:

1. Regulatory requirements, to use state of the art technology in order to get permission tocontinue and enhance conventional generation3

2. Negative net present value of investment of any kind

Regulatory requirements often require usage of best available technology, in green-house gas emit-ting generation facilities. Lowering prices of electricity has proven as insufficient for this kind ofinvestment, causing net present value of these investments to be low or even negative. Hencelowering investment in these powerplants.

Keeping in mind previously mentioned obstacles of investing into conventional power genera-tion, and looking once again at figure 2.4, a possible explanation could be the following one. During

2Both of these also holds for starting a green-field project in power-generation3By conventional generation I generally mean coal powerplants, natural gas powerplants and nuclear powerplants

18

January and February4, where vast majority of hourly price spikes occurs, photovoltaic generationis understandably lower then during other periods of a year. In work published by Heide et al.(2010), and also in figure 2.8 it is shown that wind generation is higher during winter in Germany.In case of sudden change in wind conditions, high reliability of grid on wind generation combinedwith impossibility to kick-start coal generation immidiately can produce negative supply shocksthat were described above.

Figure 2.6 shows daily average of wind speed in german wind power generating facilities. Day-ahead prices are formed one day in advance of actual delivery. Because of that, I highlighted withred dashed lines dates ti−1, during which an exremely expensive hourly delivery price was formedat the market. It turned out, that price spikes on the day-ahead power market occured during 2018only when Germany’s average daily wind speed fell below last two months average wind speed.Moreover, when average daily wind speed during this period of year 2018 fell below 4.21 km/h,probability of observing at least one spike hourly price during the next day was more than 0.21.

Figure 2.6: Exremely high prices and daily wind speed during 2018

Source of data https://www.energy-charts.de/climate/month wind 2018 01.jsonReason for subset of only last two months of the year is that extremely high prices of hourly delivery were not

observed during other months

Figure 2.7: EEX Front-Cal futures developement

Source:https://www.carbonbrief.org/the-energiewende-and-energy-prices-public-support-and-germanys-long-term-vision

For every given day during year Y , price of futures contract with delivery period throughout year Y + 1 is selectedto create this time series

Needless to say, price spikes can occur also by positive demand shock. Considering results andinformation provided in this subchapter so far, expectations are that this shock would be causedby cold weather and sudden demand for heat by households and industries.

2.3 SeasonalityElectric power spot prices are determined by many various leveles of seasonality. Main reasons forthis seasonality is the fact, that demand for electric power is tightly connected to economic activity

4In more recent history, specifically during year 2018, these extreme values are observed during months of october

19

Figure 2.8: German weekly breakdown of power mix during 2018

Source: https://www.energy-charts.de/energy.htm?source=solar-wind&period=weekly&year=2018Breakdown also on level of transmission system operators - in German case 50Hertz, Tennet, Amprion and BW

of its consumers. In this subsection of this thesis I will provide estimations of this seasonal effectson different levels. Those discussed here will be:

• Intra-day hourly effects - base-load, peak-laod and off-load

• Intra-week seasonality - day of week effects and business day vs. weekend

• Intra-year monthly seasonality

• Intra-year quarterly seasonality

2.3.1 Intra-day hourly effectsIn concordance with expectations, significant intraday seasonality is present among day-aheadelectric power prices. To calculate these effects following regression was estimated

Pt,T,h = κ0 +23∑

i=1κihi,B + �t,h (2.1)

where Pt,T,h stands for day-ahead electric power price auctioned at date t with date of deliveryT 5 and hour of delivery h. hi,B6 is binary variable representing hour of delivery h of price Pt,T,h.All estimates are statistically significant on significance level of α = 0.01 and their values can beobserved in table 2.1 as well as their visualisation in the figure 2.9. It is important to state, that

Table 2.1: Estimates of average hourly effects

i 0 1 2 3 4 5 6 7κ̂i 29.25 -2.33 -3.92 -4.89 -4.46 -2.19 4.44 12.05

i 8 9 10 11 12 13 14 15κ̂i 14.69 13.51 11.61 10.93 8.32 6.39 5.35 6.22

i 16 17 18 19 20 21 22 23κ̂i 7.99 13.68 17.92 18.4 14.19 10.02 8.18 2.42

this intra-day seasonality did get attention of electric power exchanges. For this particular kindof seasonality, so called block orders were introduced. They allow market participants to buy setsof particular hours during day. Most frequently mentioned ones are peak-load and off-peak-load

5In this particular case, T = t+ 16B stands for binary

20

Figure 2.9: Intraday mean hourly prices

Source:

blocks. As their names suggest they cover hours with demand implied by their name. Completelist of these block products designed for German electric power and their description, can be seenin the following link7

2.3.2 Intra-week seasonalityFor the same reasons, as in case of intraday hour dependence of mean price, daily seasonality onintraweek level of prices could be expected. Regression 2.2 and table 2.2 provides formulation andestimation results of this seasonality.

Pt,T,h = θ0 +6∑

i=1θidowi,B + �t,h (2.2)

where Pt,T,h stands for exatcly same variable as it was in the regression 2.1. dowi,B is binary vari-able representing weekday8 of delivery with price Pt,T,h. All estimates are statistically significanton significance level of α = 0.01.

Table 2.2: Estimates of average daily effects

const 1 2 3 4 5 6Estimate 25.19 12.82 14.77 14.88 14.65 13.87 6.53

Similarly to the regression 2.2 I decided to estimate the ceteris-paribus effect of business-dayon price of hourly delivery of electricity. This effect is visible in the table 2.3

7https://www.epexspot.com/en/product-info/auction/germany-luxembourg81 stands for Monday and 6 for Saturday

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Table 2.3: Results: OLS weekend/business day intraweek seasonality

Model: OLS Adj. R-squared: 0.102Dependent Variable: value AIC: 57829.7041Date: 2019-04-06 22:42 BIC: 57843.3655No. Observations: 6841 Log-Likelihood: -28913.Df Model: 1 F-statistic: 778.4Df Residuals: 6839 Prob (F-statistic): 2.48e-162R-squared: 0.102 Scale: 274.58

Coef. Std.Err. t P>|t| [0.025 0.975]const 29.0811 0.3749 77.5785 0.0000 28.3462 29.8159bd 12.3741 0.4435 27.9001 0.0000 11.5047 13.2435

Omnibus: 3699.367 Durbin-Watson: 0.404Prob(Omnibus): 0.000 Jarque-Bera (JB): 97110.274Skew: 2.063 Prob(JB): 0.000Kurtosis: 20.991 Condition No.: 4Source: Author’s calculation’bd’ stands for business-day dummy variable

From the results of both intra-week seasonality regressions discussed above, several interestingconclusions can be made. Price of one megawatthour of electricity during weekend, is on aver-age cheaper by approximately 33% of business-day price. Analysis has also shown, that amongbusiness-days, wednesdays tend to be most expensive daily baseload indices, traded on average onapproximately 40 Euro/MWh, during period of time since 2012 until the first quarter of this year.

2.3.3 Intra-year seasonalityCentral European region is characteristic by typically higher power consumption during the wintermonths while in the summer months, power consumption tended to be lower and this subsequentlyaffects the power price. While heating is required during winter, air conditioning in the summeris usually less demanding when it comes to power consumption. This statement is supported byestimation of intra-year quarterly effects, as well as monthly ones. Regression equations used inthis regard, are 2.3 and 2.4.

Pt,T,h = ω0 +11∑

i=1ωiQi,B + �t,h (2.3)

Pt,T,h = π0 +3∑

i=1πiMi,B + �t,h (2.4)

2.4 Returns distributionThis subsection will provide reader, with insight into distributional properties of prices and returnsof German Day-ahead prices and EEX Front-month futures contracts. This topic was previouslyanalyzed by Mugele et al. (2005). In this work, authors are trying to capture distributional char-acteristics of day-ahead prices on three different markets, namely Germany, Poland and Nordicregion. Differences between these regions were striking and related to level of their deregulationstage. Their conclusion is that the departure from Gaussian distribution is growing with marketenvironment getting less regulated. Figure 2.11 shows, that there is enormous volatility presentamong day-ahead hourly prices. Standard deviation of hourly volatility during period 26970% inbetween years 2012 and first quarter of 2019 is quite convincing, in this matter. Excess kurtosis of8131.24 shows that the distribution is extremely concentrated around its mean value of -0.13 and

22

Figure 2.10: Intra-year quarterly and monthly seasonality


also that it has heavy tails. Negative value -20 of third central moment indicates, that left tailof distribution is heavier compared to the right one9. This implies, that negative price shocks aremore likely to occur than positive ones.

There is a striking difference, when we compare these results of prices of hourly deliveries withdaily ones10. They still exhibit high level of excess kurtosis and negative skewness but measuresof variability are considerably lower.

Returns of futures contracts with different maturities, tend to be closest to normal distribution,but still very mean-concentrated and positively skewed.

Figure 2.11: EEX Hourly spot returns histogram


9It is neccessary to keep in mind, that unlike majority of assets, negative prices of electricity, especially on hourlybasis, are nothing unusual to observe. Hence, certain proportion of negative returns are not declinings of price, butrather switch from a negative price to a positive one.

10They are average of hourly deliveries during a day.

23

Figure 2.12: EEX Daily spot returns histogram


Figure 2.13: EEX Daily futures returns histogram


24

Chapter 3

EEX Electricity futures

3.1 Futures contracts risk premiumIn this part of the thesis I will try to find term structure, seasonality and possible drivers of riskpremiums included in EEX electricity futures contracts. First subsection is summary of literaturededicated to the topic. In the second part I describe my findings about risk premiums, provideillustrations of results and discuss the possible sources of observed risk premiums.

While performing analyses I use two main timeframes. Either it is whole sample of data (datingback to 2009) or the period beginning in January 2017 and ending in March 2019. The reasonfor this approach is to catch the latest behaviour of market and compare it with the broader timehorizon.

3.1.1 Literature overviewAmong research community, there are two dominant streams when it comes to spot and forwardrate connections. The theory of storage discussed among others by Kaldor (1976), Brennan (1958),Telser (1958) and Working (1948) explains difference between spot prices and their futures deriva-tives, by storage costs, foregone interest and convenience yield. Since there is no feasible way tostore electric power1, this branch of theory will be of limited use.

Alternative approach2, commonly reffered to as risk-premium approach, is based on decomposi-tion of forward price into two elements. See for example Hazuka (1984), Breeden (1980). Accordingto Marckhoff & Wimschulte (2009), futures price with delivery at time T observed at time t3 canbe decomposed into two parts:

Ft,T = Et[ST |Ωt] + πFt,T (3.1)

First of them is expectation about value of spot price that will occure at time T , given theinformation available at time t and the second one is risk-premium associated with the contract.Presence of risk premium in futures prices is usually explained, as a result of one of two followingfactors.

First of them is systematic risk defined as existence of covariance between returns of futurescontract price and market portfolio. In this thesis I will not cover this topic to a great detail butBessembinder (1992) studied this approach on wide basket of commodities.

Second of them is hedging pressure approach. Theoretical background extends back to Keynes(1930) and to the topic of normal backwardation. Not too long after that, general hedging pressuretheory was introduced. Even though empirical results, regarding applicability of this theory on

1Hydro powerplants serve as an exception to this, however there needs to be significant proportion of this plantsin generation mix to justify storage argument in power markets.

2This approach is free of any storage possibility assumptions3If there is no explicit definition, time t serves as an index of present time

25

commodities, are mixed, I decided to investigate this approach, and see if it could be justified onpower market, for the sake of electricity’s unique properties.

Following equation 3.1, πFt,T is price paid by a risk-averse party as a compensation for eliminationof spot price risk. The value of πFt,T can be both positive and negative. Motives that drives marketparticipants into entering a futures contract positions, are discussed in the next part of this section.Equation 3.1 is showing an ex-ante risk premium. Main difficulty arising from this specificationis the unobservable term Et[ST |Ωt]. For this reason an ex post specification is shown below inequation 3.2.

Ft,T = ST + πFT (3.2)

By equalizing expressions 3.1 and 3.2 we get:

Et[ST |Ωt] + πFt,T = ST + πFT (3.3)

expressing πFT from (3.2) we have:

Et[ST |Ωt] + πFt,T = ST + Ft,T − ST (3.4)

Allowing the assumption thatEt[ST |Ωt] = ST + �t (3.5)

where �t is forecast error, made by market participants, when making expectations about futurespot price, have mean value 0. It means that on average, market participants are able to makecorrect expectations about future spot prices during T conditional on information available at timet. Assuming this, ex-post risk premium equals to ex-ante risk premium plus forecast error.

πFT = πFt,T + �t (3.6)

For empirical purposes, following realtionships were used to calculate risk premium metrics.

πFT =1T

T∑t=1

(Ft,T − ST ) (3.7)

πFT,rel =1T

T∑t=1

(Ft,T − STST

) (3.8)

ST =1n

n∑i=1

Sit (3.9)

Where Sit result of spot auction that established price of delivery during day t for hour i. Followingwork of Pietz (2009)”A plausible economic interpretation of positive risk premium is that holdersof long positions in futures are compensating holders of short positions for the bearing of price risk.Under the assumption that prices are set by industry participants and not by outside speculators,this implies that consumers rather than producers are more interested in hedging. Since price riskis an essential risk for electricity consumers in the short run, mainly due to frequently emergingprice peaks, this explanation seems to be appropriate.” By looking at the surface shown in figurefigure 3.1, risk premium tends to rise with decreasing time to delivery of contract. Secondly, thelevels towards which the risk premium tends to increase shortly before expiry, tends be higherduring winter months.

If we assume that electricity consumers are primarily interested in hedging their short-termprice exposure, risk premium could be a function of time to delivery of futures contract. Elec-tricity consumers (as natural shorts) use long positions in short-term futures for hedging purposeswhile producers (as natural longs) hedge their exposures with shorting of long-term futures.

The economic rationale behind the need of a producer to hedge himself with long-term futuresmay be the long-term, capital intensive nature of investments in the energy industry. This wouldadd up into demand for long-term futures to hedge cash flows in the longer future horizon in orderto get a more reliable image of rentability of investment. In consequence, the behaviour of both

26

consumers and producers may result in market segmentation which translates into positive riskpremium in short-term and negative risk premium in long-term futures.

Keynes assumed that futures market’s primary goal is to provide insurance against spot pricerisk to the hedgers on hand, and reward those willing to undertake this risk with return. Powerproducer seeks an assurance about the price at which he will deliver produced power. Enteringinto short futures positions, someone has to be willing to enter into the long position. It could beeither speculator4, or consumer of power who has exactly opposite hedging motive.

Following subsections will provide theoretical background into two models that will be analyzedalso in empirical part of the thesis.

3.1.2 Bessembinder & LemmonRelating to the previously described reasoning, risk premium should reflect the risk aversion oflong and short participants at the market. Bessembinder & Lemmon (2002) states, that followingregression should explain observed risk premium as a function of skewness and variance of spotprices during delivery period T :

πFT = α0 + α1V ar(ST ) + α2Skew(ST ) + ρt (3.10)

Logic behind this relationship is that increasing skewness of distribution of spot price, resultsto the increased likelihood of spot price being higher. This situation incentivize the consumers ofpower to be more risk averse than producers, since the increase in spot prices will cause propor-tional increase of their costs. Consumers of power are natural shorts and they hedge themselveswith entering into a long position on futures, hence the risk premium should increase due to in-creased demand for futures.

When demand variability increases5, power producers may need to generate enough power tosatisfy the demand on one hand, on the other in case of a sudden drop in demand, excess supply ofpower would cause decrease in spot price, posing problems to producers. This is the reason, whysevere demand variabilty encourage producers to entering into short positions in futures, hencedecrease the risk premium due to increase supply of futures.

3.1.3 Fama & FrenchIn their work, Fama & French (1987) provide 21 commodities wide analysis of two approaches torelationship between spot and futures prices. In their own words: ”The theory of storage is notcontroversial. In contrast, there is little agreement on whether futures prices contain expectedpremiums or have power to forecast spot prices.”

The fundamental and obvious difference between commodities of their interest and electricity,is the multiple times stated non-storability property of electric power. That is why I will occupymyself only with the controversial part of their work. In their work, there were multiple timesemphasized the fact that the theory of storage and risk premium approaches are alternative butnot competing views of the basis.

Foundation of this approach is described in following equations:

Ft,T − St = Et[πFt,T ] + Et[ST − St] (3.11)

Where Et[πFt,T ] is expressed in their work using already described equation 3.1.I test for time varying expected premiums and price forecasts in futures prices with the regression

4Since I assume that only producers and consumer participate on this market, this group is not considered inthe furher analysis

5Since demand variability is translated into variability of spot prices, variance of spot power prices is used insteadof demand.

27

approach in Fama (1984a) and Fama (1984b).

ST − St = α1 + β1[Ft,T − St] + ut,T (3.12)

Ft,T − ST = α2 + β2[Ft,T − St] + zt,T (3.13)

In case of positive β1, basis6 observed at time t contain information about developement of spotprice from time t to T . If positive value of β2 will be observed, then the the basis observed at timet provide information about risk premium realized during delivery period T .However, these relations are subject to constraints described below:

α1 + α2 = 0 (3.14)

β1 + β2 = 1 (3.15)

ut,T + zt,T = 0 (3.16)

3.1.4 Data & MethodologyPrices of EEX futures contracts7 and EEX Spot auctions results served as data inputs for thispart of the thesis. Calculation of ST is based on average of daily spot baseload indecies8 duringparticular month of delivery T . EEX provides results of daily auctions as well as futures contractson their website. The sample included in this thesis consists of futures contracts with monthlydelivery period, ranging from January 2009 to March 2019. Descriptive statistics of the data isprovided below.

In figure 3.1, relationship of risk premium for monthly futures contracts from whole sample isvisualized.

Figure 3.1: Risk premium surface


Surface plot shown in figure 3.1 does not appear to provide much information regarding relationof risk premium and days to delivery. However, seasonality seems to be present during deliver-ies ranging from October to February. Absolute risk premium appear to be higher during thesemonths. Explanation for this could be two-fold.

6Difference between futures price observed at time t and spot price at the same time.7Monthly delivery period8Simple average of prices of hourly power delivery during particular day

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Figure 3.2: Average relative risk-premiums


Based on equations 3.7 and 3.8 I performed calculation of average risk premiums for a particu-lar contract, during all of its possible trading dates. Contrary to figure 3.1, in this part I analyzecontracts with wider range of deliveries, as shown on the following pictures. Figure 3.3 depictsaverage risk premiums for contracts, calculated via equations 3.7 and 3.8 . Figure 3.4 shows sta-tistical significance of relative and absolute average risk premiums9. Red horizontal lines serve asindicator of critical values of student’s t-distribution with given degrees of freedom10 for two-tailedalternative of test on significance level of 10%.

Figure 3.3: Average absolute and relative risk-premiums


For the majority of the deliveries, it appears that estimated averages of risk premium arestatistically significant.

9t-ratios of average risk premiums and their standard deviations10120 degrees of freedom, two tailed alternative of test

29

Figure 3.4: T-ratios of relative risk-premiums


3.1.5 Estimation Bessembinder-Lemmon modelNext, I will estimate the the linear regression, shown in the equation 3.10. As explained in theprevious part of this thesis, the hypothesis being tested by this model is that risk premium duringdelivery period T is an increasing function of skewness of spot prices during T and decreasingfunction of variance of spot prices during the same period. However, results presented in the table3.1 suggests quite the contrary. Not only that both parameters have exactly opposite signs11, theyare also both statistically significant.

Table 3.1: Results: OLS Bessembinder-Lemmon model

Model: OLS Adj. R-squared: 0.231Dependent Variable: risk premium% AIC: -126.7673Date: 2019-03-18 13:02 BIC: -121.1429No. Observations: 123 Log-Likelihood: 65.384Df Model: 2 F-statistic: 19.49Df Residuals: 121 Prob (F-statistic): 4.61e-08R-squared: 0.244 Scale: 0.020555

Coef. Std.Err. t P>|t| [0.025 0.975]var 0.0011 0.0002 6.2425 0.0000 0.0007 0.0014skew -0.0303 0.0147 -2.0579 0.0418 -0.0594 -0.0011

Omnibus: 20.420 Durbin-Watson: 0.993Prob(Omnibus): 0.000 Jarque-Bera (JB): 30.331Skew: 0.821 Prob(JB): 0.000Kurtosis: 4.794 Condition No.: 91Source: Author’s calculation

Looking at the figure 3.5, it is apparent that specification of the model proposed by Bessem-binder & Lemmon (2002) does not suit12 the EEX power market. One of possible reasons forthis result might be in not realistic assumption of futures market being place of hedging ratherthan speculation. With liberalisation of electricity markets, institutional investors and outsidespeculation were attracted. This holds especially for financially settled products such as futures.

11Bessembinder & Lemmon assumed positive sign of parameter for skewness and negative for variance12See the scales of axes

30

Figure 3.5: Bessembinder-Lemmon


3.1.6 Estimation Fama & French modelIn order to estimate equations 3.12 and 3.13, the calculation of relevant variables had to be done.I calculated risk-premiums, bases and difference between average spot price during delivery periodand spot price at time t during trading of particalar contract13. These values were calculated foreach and every one of more than 120 futures contracts with monthly delivery period. Afterwardsthe two regressions were estimated for every futures contract.

The presentation of results of these models, will make use of figures and plots. Figure 3.6 (resp.figure 3.7) shows the distribution of β̂1 and β̂2 respectively. Regarding statistical significance ofestimates, in case of β̂1, null hypothesis of β̂1 = 0 was rejected for all futures contracts on confidencelevel α = 0, 05. Moreover, all β̂1 turned out to be positive. As a consequence of this results, itcan be stated that the level of basis14 observed at time t provide information about the differencebetween average spot price during delivery period and spot price observed at time t.

Figure 3.6: Histogram of β̂1 estimates from equation 3.12

Source: Author’s calculation13Variable ST − St14Ft − St

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Figure 3.7: Histogram of β̂2 estimates from equation 3.13


For estimates of β̂2, statistical significance was as not homogenous as in case of β̂1. As Ialready mentioned in the previous part of this thesis, positive and statistically significant β̂2, wouldimply that the basis observed in time t provide information about risk premium. The overviewof deliveries, for which this parameter was both significant and positive, is available below in thefigure 3.8.

Figure 3.8: Delivery months with positive and significant β̂2 estimates from equation3.13

Red horizonatal represents mean of positive and significant β̂2 during a month Source: Author’s calculation

From this estimation and analysis of Fama & French model, following could be summarized:

• Regardless of delivery month or year, Ft − St provides information about developement ofspot price of power delivery on EEX between T and t

• For contracts with monthly delivery periods of May - July and October - December, basisprovides information about risk premium in EEX power futures contracts

32

3.2 Principal component analysis of forward curveIn the following part of the thesis, I would like to present a principal component analysis15, decom-position of forward curve. PCA is general name for numerical operation, that is used to transforma set of correlated variables into a smaller set of variables called principal components16.

In general terms, PCA uses a vector space transform to reduce the dimensionality of large datasets. Using mathematical projection, the original data set, which may have involved many vari-ables, can often be interpreted in just a few variables (the principal components). It is thereforeoften the case that an examination of the reduced dimension data set will allow the the user to spottrends, patterns and outliers in the data, far more easily than would have been possible withoutperforming the PCA. Richardson (2009)

3.2.1 Theoretical backgroundThis subsection of the thesis is to a large extent citation from work of Geyer (2007). A randomvector is just a vector whose components are random variables. Its mean is the vector whosecomponents are the means of the components. If XXXX = (X1, ..., Xn) is a random vector, andµµµµ = (µ1, ..., µn) is its mean vector, then µi = E(Xi) for i = 1, ..., n, but we usually write this as avector equation

µµµµ = E(XXXX ) (3.17)We define var(XXXX ) to be a matrix whose i, j element is cov(Xi, Xj). This matrix has variousnames17. In this thesis, the matrix will be called covariance matrix. This matrix is always sym-metric, since covariance operator is symmetric function of its arguments.

cov(Xi, Xj) = cov(Xj , Xi) (3.18)

If XXXX and YYYY are random variables and YYYY is a linear function of XXXX , that is, YYYY = aXXXX + b for someconstants a and b, then

E(YYYY ) = aE(XXXX ) + b (3.19)var(YYYY ) = a2var(XXXX ) (3.20)sd(YYYY ) = |a|sd(XXXX ) (3.21)

Equations 3.19 and 3.20 can be rewritten as formulas of vector-to-vector transformation:

E(YYYY ) = AAAAE(XXXX ) + bbbb (3.22)

var(YYYY ) = AAAAvar(XXXX )AAAAT (3.23)Considering the case where Y = AAAAXXXX is scalar, meaning that AAAA is a row vector and XXXX is a columnvector, then 3.23 becomes

0 ≤ var(YYYY ) = aaaaT var(XXXX )aaaa (3.24)The inequality comes from the fact that variance is always non-negative. It means, that covariancematrix is symmetric and positive semi-definite.

Any symmetric matrix AAAA has a spectral decomposition

AAAA = OOOODDDDOOOOT (3.25)

where OOOO is orthogonal, meaning that OOOOT = OOOO−1 and DDDD is diagonal matrix. OOOO is orthogonalbeacause it’s vectors wwwwi are orthogonal18 If we denote wwwwi as i-th column of OOOO, then wwwwTi wwwwj is thei, j-th element of OOOOTOOOO = OOOO−1OOOO = IIII , which is just another way of saying that columns of OOOO areorthogonal to each other, with unit length. OOOO is then change of coordinate system.Multiplying 3.25 by OOOO from the right hand side, we get

AAAAOOOO = OOOODDDDOOOOTOOOO (3.26)15Going forward, it will be adressed as ’PCA’16This operation is also called reduction of dimensionality17Variance matrix, disperssion matrix, variance-covariance matrix18Scalar product of vectors is equal to 0.

33

Since OOOOTOOOO = IIIIAAAAOOOO = OOOODDDD (3.27)

This can be rewritten in terms of wwwwi, which stands for orthogonal, column vector of OOOO as

AAAAwwwwi = λiwwwwi (3.28)

Where λi stands for i-th diagonal element of DDDD. If this equation holds for a matrix AAAA, non-zero vector wwwwi and scalar value λi, we call the vector wwwwi eigenvector and λi eigenvalue. It alsomeans that after spectral decomposition of AAAA, columns of OOOO are its eigenvectors and alementsof diagonal matrix DDDD are its eigenvalues. It is also worth mentioning that eigenvectors are notuniquely identified by their eigenvalues.

(AAAA − λIIII )wwww = 0 (3.29)

Since characteristic equation shown above always has multiple solutions, any non-zero multipleof an eigenvector is also an eigenvector. Keeping in mind everything stated above, we can moveforward to final derivation of principal components. If random vector X has finite variance, we canwrite

var(XXXX ) = OOOODDDDOOOOT (3.30)

as spectral decomposition of its covariance matrix. Considering YYYY being equal to YYYY = OOOOTXXXX then

var(YYYY ) = OOOOT var(XXXX )OOOO (3.31)

where we can substitute var(XXXX ) from equation 3.30

var(YYYY ) = OOOOTOOOODDDDOOOOTOOOO (3.32)

Using properties OOOOTOOOO = IIII and OOOOT = OOOO−1 once again

var(YYYY ) = DDDD (3.33)

From this, following can be concluded.

• Random vector YYYY has diagonal covariance matrix. Since the off-diagonal elements of var(YYYY )are equal to zero, components of YYYY are uncorrelated.

• Variances of elements of YYYY are eigenvalues of covariance matrix of X

In Koekebakker (2001), authors applied PCA on Nordpool19 power futures prices. In their workthey provide two alternative underlying models used for the analysis. First of them, presented inequation 3.34 explains changes of futures prices observed during day t for power deliveries on Tvia sum of K-elements large set of variance functions σAi (20) multiplied by independent Brownianmotions.

dft,T =K∑

i=1σAi (t, T )dWi(t) (3.34)

Second model, explains relative changes of futures prices with respect to the level of prices.dft,Tft,T

=K∑

i=1σBi (t, T )dWi(t) (3.35)

These variance functions are derived using PCA. From covariance matrix Σ 21 we collect orthogonalvectors wwwwi . As I already described above, these vectors are columns of matrix OOOO used in spectraldecomposition. In our case, for MxM covariance matrix Σ

ΣΣΣΣ = OOOOΛΛΛΛOOOOT (3.36)19Scandinavian power trading hub20These are functions of time to delivery only.21This notation of covariance matrix will be used throughout this thesis

34

ΛΛΛΛ is diagonal matrix with diagonal elements Λ[i,i] representing i-th eigenvalue. Matrix of principalcomponenents is defined as

ZZZZ = XXXXOOOO (3.37)

Where XXXX stands for matrix of data22. i-th column of ZZZZ corresponds to i-th principal componentzzzz i defined as a linear combination of i-th row of data matrix XXXX and i-th eigenvector wwww

zzzz i = XXXXwwwwi = xxxx1p1i + xxxx2p2i + ...+ xxxxKpKi (3.38)

To select appropriate number M of principal components, we use a convenient property of eigen-values which allows us to calculate cumulative contribution of first M factors towards varianceexplanation. ”Rule of thumb” value of required explained variance is around 0.95, which will beused as a target value in this analysis.

0.95 ≤∑K

i=1 Λi∑Mi=1 Λi

(3.39)

After selecting number of eigenvalues required to satisfy inequalit above, we can define volatilityi-th function as

σ̂i(t, Tm) = pmi√λi (3.40)

3.2.2 PCA of EEX Futures

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