Structured Products on Electricity

Inhaltsverzeichnis

1. Introduction

2. Electricity Market
2.1 Electricity in the Context
2.2 The Power Markets
2.3 The Power Exchanges
2.4 The Swiss Market
2.5 Electricity as an Investment

3. Characteristics of Electricity Prices and Returns
3.1 Overview
3.2 Correlation and Moment Analysis
3.3 Main Properties of Electricity Prices

4. Estimation of the Stochastic Model
4.1 One-Factor Models
4.odel with Additional Factors
4.3 Parameter Estimation Procedure
4.4 Data Set
4.5 General Calibration Theory .
4.6 Disjunction of Jumps and Mean Reverting Process.
4.7 Parameter Estimation
4.7.1 Jump Estimation
4.7.2 Mean Reversion
4.8 Recapitulation

5. Structured Products
5.1 Introduction
5.2 The Swiss Product Range
5.3 Overview of the Literature
5.4 In Practice: How Are the Structured Products Priced?
5.4.1 Reverse Convertible
5.4.2 Capital Protected Note
5.4.3 Certificate
5.5 Structured Products on Electricity
5.5.1 Overview
5.5.2 Traditional Structured Products
5.5.3 Exotic Structured Products

6. Pricing Mechanism and Results
6.1 Electricity Option Pricing
6.1.1 Challenges in the Case of Energy..
6.1.2 Two Ways to Meet the Challenge .
6.1.implified Approach .
6.2 Monte Carlo Method
6.2.1 Procedure...
6.2.2 Discretization.
6.2.3 Drawbacks .
6.2.4 Simulation Results.
6.3 Option Pricing Results .
6.4 Structured Product Pricing...
6.5 Feasibility of Structured Products on Electricity .

7. Conclusion

Table 2-1 Swiss Electricity Production .

Table 2-2 Swiss Electricity Consumption .

Table 3-1 Regression of SWEP on different Swissix indices .

Table 3-2 Key Statistics

Table 3-3 Variance Ratio Test.

Table 3-4 Rescaled Range Test

Table 3-5 Tests of Normality

Table 3-6 Regression

Table 3-7 Rescaled Range Test

Table 4-1 Jump Process Estimate

Table 4-2 Jump Size Estimation

Table 4-3 Jump Length Estimation

Table 4-4 Mean Reversion Estimation

Table 5-1 Structured Products in Switzerland.

Table 6-1 Simulation Characteristics

Table 6-2 Option Pricing Results in %

List of Figures

Figure 3-1 Swiss Electricity Price Indices

Figure 3-2 Daily Electricity Price Variation

Figure 3-3 Monthly Electricity Price Variation

Figure 3-4 Daily Log Returns

Figure 3-5 Return Histogram

Figure 3-6 SWEP Price without Trend

Figure 4-1 Jump Elimination Procedure.

Figure 4-2 Jump Analysis

Figure 4-3 Seasonal Patterns

Figure 4-4 Jump Size Distributions

Figure 4-5 Jump Length Distributions

Figure 6-1 Monte Carlo Sample Paths

Figure A-1 Swiss Derivative Map

Abbildung in dieser Leseprobe nicht enthalten

1. Introduction

Electricity is essential for modern society, which is why a centralized regulation of the electricity supply has always been considered cogent to guarantee a secure and stable supply. Traditionally, the power industry has been characterized by vertically integrated companies. However, for the past 15 years, electricity markets in Europe have been undergoing a phase of deregulation (Weron, 2006), and have now evolved to liberalized markets where consumers can choose their electricity provider (Vattenfall, 2006). Power suppliers, networks, and end- customers have become independent from each other. In order to facilitate the interaction between these market players and to ease the trading of electricity, different markets and exchanges have been founded across Europe.

In Switzerland, the process of deregulation has just started and is currently a hot topic of debate. In 2007, new legal standards were established that have been changing the vertically integrated industry towards a more liberalized market environment where electricity is traded between the producer and the supplier. After 2008, large end-customers will be able to choose their electricity provider. In around five years, all customers will be able to choose their power producer (VSE, 2008). This deregulation of the electricity market in Switzerland has a strong impact on the power industry. Increased competition enforces price pressure, so prices for the end-customer are expected to be closely determined in the market of electricity demand and supply. This will ultimately lead to a more volatile and stochastic electricity price development. Furthermore, the electricity prices in Switzerland have been steadily rising and are expected to further grow, despite deregulation (Gerber, 2008). As a consequence, the amount of electricity price risk borne by all market participants is increasing. Due to the new price risks, the need for risk management is growing. Different hedging tools for producers and suppliers of electricity have already been developed. Futures, forwards, plain-vanilla, and exotic options are widely used in practice (James, 2008). However, most derivatives are only traded over the counter (OTC) between the producers and the networks. Since end-consumers have only limited access to OTC markets, a product is required that offers the customers and the investors the possibility to hedge their pricing risk and to profit from increasing electricity prices in a simple way.

The purpose of this paper is to create financial products that meet these requirements. This paper will focus on the creation of structured products as they seem to be favourable investment tools for various market players. Structured products are financial products that include options and other financial products and can be tailor made to the customer’s needs.

Creating a structured product provides the most flexibility to the customer, and may therefore be an attractive hedging tool.

This paper will focus on the Swiss electricity market, for which the structured products shall be priced. The challenging part of the valuation of the structured products is to price the embedded derivative contracts. The stochastic process of electricity shows unique characteristics so that the pricing of electricity derivatives cannot rely on traditional option pricing formulas. Rather, a method of electricity pricing has to be developed that is able to take particular characteristics into account. Since the electricity markets differ around the world in their observed price movements (Escribano, Pena & Villaplana, 2002), each market has to be examined separately. In this paper, the unique characteristics of the Swiss market are identified. The features of this market require the use of a different pricing methodology than would be applied to other markets.

This paper is structured as follows. In chapter 2, the special characteristics of the electricity market are explained. In particular, the unique nature of the Swiss electricity market is reviewed and analyzed in a way that is possible to see the implication on its price dynamic. Chapter 3 will give a thorough statistical analysis of the Swiss electricity indices, on which the structured products shall be priced. In particular, different statistical tests are applied to investigate various hypotheses of characteristics that have been observed in international electricity markets. Chapter 4 proposes a multi-factor stochastic model that is able to reproduce the Swiss electricity price dynamic. A two step procedure is applied to estimate the parameter of the model efficiently. Chapter 5 presents an overview of the structured product market and discusses new types of products that are superior in order to manage electricity price risk. Thereby, this paper introduces a new way of how to analyze the structured products. Chapter 6 performs the pricing of these derivatives on the findings of the previous chapters. A Monte Carlo simulation is used as a pricing tool since no closed-form solutions are available for the analyzed price dynamic. Furthermore, this chapter addresses the challenge of the risk neutral valuation of derivatives. At the end of the chapter, the pricing results for various structured products are presented and analyzed for their feasibility and attractiveness. Chapter 7 concludes this paper with final remarks and a presentation of issues for further research.

2. Electricity Market

2.1 Electricity in the Context

Commodity markets have become very popular topics of most financial and other media in recent years as there have been significant movements in many of the commodity markets (Kleinmann, 2005). Only a limited number of other asset classes have generated comparable returns in recent years (UBS, 2006).¹ In particular, the oil market and the agricultural market have been in the spot light due to their strong price increases that can be observed in the financial markets². The upswings are explained by an increasing consumption and a stable or decreasing supply. The prices of commodities correlate highly with the business cycle as economic growth measures an increase in demand (CS, 2008)³. Not only the high returns but also other characteristics, such as the low correlation with other asset classes and the presumed protection against inflation, make commodities so popular among investors (Gorton & Rouwenhorst, 2004). Due to these reasons, commodities are suggested to be part of any diversified portfolio.

Electrical power must be examined against the background of the commodity markets since electricity is generated from different types of energy sources and some of them are traded on the commodity markets. Coal, gas, oil, and uranium are commodities that are often used in the production of electrical power. The prices of electricity therefore depend strongly on their market mechanics. Other energy sources, such as wind energy, solar energy, or water energy are not yet directly traded and depend therefore on other factors. In order to understand the development of the electricity prices, the behaviour of the input factors have to be understood.

2.2 The Power Markets

Electrical power is an invention that has changed human existence: it is not only essential for improving the private life but also for the economy as a whole. Due in large part to its central role in economic and social welfare, the electricity market has traditionally always been strongly regulated. Around the world, vertically integrated companies controlled primarily by

the government have been traditionally responsible for the supply of electricity to industry and households alike. Governments have overall been cautious in leaving such an important sector to market forces. The power outage in California in 2000 and 2001 showed that defective deregulation of the power market can lead to severe consequences (Pilipovic, 2007).⁴ Nevertheless, governments have recognized in recent years that liberalization of the power markets could introduce market forces, lead to potential efficiency gains, stimulate technical innovations, and support economic investments (Geman, 2005; Weron, 2006). After the pioneering liberalization of Chile in 1982, the European countries started their own deregulation process (Weron, 2006). In 1990, the United Kingdom began to reform its electricity market, and in 1992 the Nordic markets followed a similar path. The number of liberalized markets in Europe has since been increasing as the European Union has been pushing towards deregulation.

This large wave of liberalizations across Europe and around the world has led to both positive and negative impacts in terms of price and investment behaviour. According to Weron (2008), the deregulation of electricity markets has generally decreased the price level (the increased taxes reversed the effect). However, according to Geman (2005), the price effect is ambiguous. For example, the UK and the French markets belong to the electricity markets with the lowest production costs. Interesting is however, while the UK has one of the most deregulated market, the French market is strongly regulated. Mixed effects have also been observed in the investment behaviour after the liberalization. On the one hand, the liberalization wave resulted in a reduction of overcapacities and increased efficiencies (Weron, 2008). Before the liberalization, the producers were able to pass the production costs directly to the end-consumers (Deng & Oren, 2006). Since in this framework, the producers had no incentive to keep low production costs, over-investments and inefficiencies occurred. In a deregulated market, the competitive environment puts pressure on the supplier to produce efficiently. This shifts the investment risk from the consumer to the producer (Deng & Oren, 2006). On the other hand, the competitive environment that came along with the liberalization lured companies to invest in facilities that could be built in a short time (e.g. gas-fuelled plants) despite the unfavourable energy source (Weron, 2008).

In the hope to profit from the benefits, Switzerland has joined the liberalization trend and is currently deregulating the market. The process of deregulation started in 2003, when the federal court claimed the regulated system to contradict antitrust laws (VGE, 2008). The plan is to have an open market in 2014. The deregulation is taking place in two phases. In a first step, large power consumers with a consumption of over 100 GWh can change their power supplier by the end of 2008. Smaller clients will benefit from improved price transparency. In

a second step, the smaller clients will similarly be able to select their power supplier by 2014. Similar to other countries, Switzerland will keep certain regulations and only introduce restricted market forces. Since electricity is a basic necessity for everyday living, its provision will not be completely left to the market forces.⁵

Another effect of the global deregulation trend was the creation of electricity exchanges where electricity can be traded⁶. According to Weron (2008), these exchanges represent a common factor for all successful markets, as they provide a formal price quotation mechanism. In contrast to other countries, Switzerland is not likely to have its own power exchange. However, the EEX in Germany and the EXAA in Austria have launched a Swiss

segment, where most of the Swiss suppliers and distributors are trading (EEX, 2008, EXAA, 2008). As a measurement of the market prices of the Swiss electricity prices, there are two main indices. Since 1999, there exists a price index for Swiss energy prices (SWEP), which is calculated by Dow Jones indices services (BKW, 2008). Since 2006, the European Energy Exchange (EEX) is also calculating a price index (Swissix) (EEX, 2008). This index shows the spot market clearing price every day.

2.3 The Power Exchanges

The above mentioned electricity markets differ significantly from other financial markets due to particular characteristics of power as a tradable good (Pilipovic, 2007). Similar to other commodities, electricity does not generate future cash flows in the form of interest or dividend payments. According to Geman (2005), the pricing of commodities does therefore not depend on discounted cash flows, but only on the interaction of demand and supply⁷. However, in contrast to other commodities, electricity is a non-storable good (except for

electricity based on hydro energy), and therefore driven by immediate supply and demand (Geman, 2005). Electricity supply has to meet demand at every moment⁸. The electricity that is produced in one hour has to be consumed in the same hour. This supports the already steep

supply and demand curves. Supply can only be increased by either switching on a new production unit (if it is already running at full capacity) or by creating a new power plant. In the short run, supply is therefore very steep. Demand is very inelastic and similarly steep.

In a deregulated market environment, these special characteristics result in a need for derivative trading. A power supplier tries to forecast the power demand of its customers in order to be able to provide the right amount of energy at the right moment. However, since this is only possible to a certain degree, the producer must either buy electricity from other producers in case of under-production, or sell electricity in the case of over-production. When there is a large uncertainty about future demand, the producer might try to use hedging instruments in order to manage the sales risk. Mork (2001) believes therefore that the market for electricity will in the near future be the largest commodity market in the world, where physical trading will be only a small part of the total market turnover and derivative trading will have a major role. According to Deng, Johnson and Sogomonian (2001), the electricity derivative market is one of the fastest growing derivative markets.

The special pricing mechanism of electricity leads to the fact that its trading activities differ compared to other financial markets. Firstly, the delivery of the electricity financial contract is determined in a different way. For both the spot and the futures markets, the delivery time must be specified in a more restrictive fashion than in other markets, since electricity is not storable. For example, a futures contract for the delivery of one MWh for a peak hour will cost more than for a base hour. Secondly, the electricity market shows a wide range of financial products that are frequently traded among the electricity market participants: i. e. forwards, futures, swaps, plain vanilla options, and exotic options (Deng & Oren, 2006). In particular, there are exotic derivatives traded that are typical for the electricity market (Pilipovic, 2007; Clewlow & Strickland, 2000). Swing options and spark spread options are examples that are often named in the literature⁹. Thirdly, compared to other financial markets,

most contracts are traded OTC. There is only a limited choice of standardized contracts as most contracts require a specifically tailored payoff or delivery (James, 2008). In the US, the standardized option market turned less liquid when there were huge price jumps in 1998 and after the Enron disaster. For the German market, there are options traded on the Phelix at the EEX. For the Swiss market there are at the moment no standardized derivatives traded. However, the annual reports of Axpo (2007) and other electricity companies show that there must be a significant Swiss OTC market. Energy markets in general rely much more on OTC derivatives as they allow for customized transactions (James, 2008). Finally, according to Pilipovic (2007) most derivative contracts are relatively complex to price and require more sophisticated pricing tools and models.

2.4 The Swiss Market

The Swiss electricity market differs from many other power markets in a significant way. Whereas other European countries rely mostly on coal and nuclear energy, Switzerland produces over 50% of its electricity with hydro energy (IEA, 2008). The other significant share is supplied from nuclear power. Together these sources account for about 95% of total production so that the Swiss production mix resembles that of the Nordic countries (Mork, 2001). In the future, the dependency on gas is very likely to increase (IEA, 2008).

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In Switzerland, an average 31,996 GWh from the total production are exported and another 38,346 GWh are imported (IEA, 2008). This leads to a total amount of electricity of 65,962 GWh, which is consumed according to Table 2-2. The industry is the largest consumer of electricity, while the residential and commercial (servicecompanies) sectors are ranked second and third, respectively.

In order to understand the pricing behaviour of the electricity market, the different drivers of consumption and production have to be examined. On the production side, the market conditions of the two main energy sources, hydro and nuclear energy, shall be briefly

explained. Nuclear energy was not fashionable during the last decades due to the problem of the final storage of the radioactive waste and due to the possibility of severe accidents, such as in Chernobyl (CS, 2006). In 2005, only 16% of energy stemmed from nuclear power, which is a reduction compared with 19% in 1990 (IEA, 2008). However, nuclear power shows the convincing advantage of no CO2 emissions, which has turned this energy form into an attractive alternative to CO2 emitting energy forms, such as coal. According to Hanke (2008), over 96 nuclear power plants are globally planned at present. Analysts of Credit Suisse (2006) expect therefore an increase in the uranium demand and price. The production cost of power produced with nuclear energy is expected to increase.

Hydro power is a very good electricity source as it is environmentally friendly and can be stored. The disadvantage of hydro power is that it depends on the amount of water that comes down in the Alps. According to Hanke (2008), global warming could reduce this amount and decrease the amount of hydro electricity being produced. Furthermore, there is only limited potential to build new plants in Switzerland as almost all appropriate locations for hydro power stations are already in use (Hanke, 2008).

Other energy sources, such as solar and wind energy, cannot add significantly to the Swiss electricity production capacity. Coal shall not be used as Switzerland is trying to reduce its CO2 contribution. One alternative is to build more gas power plants; however, the construction of a gas-fuel power plant takes several years and can therefore not increase the supply in the immediate future. One concern for Switzerland is that energy contracts with France are expiring in the next year, and these contracts have to date been very favourable for Switzerland (Gerber, 2008).

On the demand side, it can be assumed that the electricity consumption is going to stay stable or to slightly increase. This can be explained by economic and population growth. The electricity prices are therefore likely to increase for Switzerland. According to statistics of the Energy Information Administration (EIA, 2008), Switzerland has significantly lower energy prices than its neighbouring countries¹⁰.

2.5 Electricity as an Investment

The recent sections presented the main characteristics and trends in the electricity markets and explained the peculiarities of the Swiss power situation. Based on these observations, the

following section gives the motivation for this paper. The following two paragraphs provide an answer to the question why electricity is an interesting investment possibility in Switzerland. Then, chapter 2 is concluded with the motive of this paper to create new financial products.

One key reason for investing in electricity is that its price is expected to increase in Switzerland, and this is occurring despite the current liberalization that leads to downwards price pressure (Gerber, 2008). According to a study of PricewaterhouseCoopers (PWC, 2008), 92% of the energy supply companies expect an increase in the electricity price in Switzerland for the next four to five years. 41% of these firms believe an increase of at least 20% will take place. This increase in price can be at least partially explained by the above price drivers for uranium and other energy sources. Past price developments have mirrored expectations.¹¹

A second reason for investing in electricity is that in the process of liberalization, the pricing mechanism of electricity is changing. Before liberalization, the prices for the end-customer were fixed in long term contracts. The price calculation was not transparent and based on the production cost. The deregulation of the electricity market changes this situation in two ways. First, the vertically integrated companies split up into producers and distributors so that an active electricity exchange market is required as a transaction mechanism. Second, the electricity market becomes more competitive and more transparent. This leads to price pressure as it has been observed in other countries (Weron, 2006). These two effects imply that the prices charged to the end-customer will be determined by actual market prices of electricity and not only its production costs. Vischer (2002) cuts right to the chase of the matter: “We cannot regulate the energy price for the long term as the prices orientate themselves on the daily traded energy price.” Prices for the end-customer depend more on the fundamental rule of supply and demand (Geman & Roncoroni, 2003); in other words, the end- customer bears the whole price risk. Therefore, if there are increasing electricity prices or large jumps in the price, the end-customer will be directly charged. Since the prices are built on the market where there is a steep demand and a steep supply curve, large price movements are possible (Deng & Oren, 2006; Geman & Roncoroni, 2006).

In the described environment with increasing and volatile prices, the end-customer bears a large electricity price risk; this leads to a demand for risk management tools. Especially for industrial companies, with a strong dependency on electricity it is favourable to hedge electricity price risk. According to Deng and Oren (2006), electricity price risk hedging can increase the firm’s value and must therefore be in the interest of the company’s management. James (2008) claims as well that risk management is important in the power markets.

According to Deng, Johnson and Sogomonian (2001), the risk management tools that are appropriate for other asset classes are not useful for electricity due to unique characteristics of this market. In particular, the fact that electricity cannot be stored means that the traditional arbitrage approach cannot be used in the valuation of electricity contracts. In this paper the aforementioned challenges will be addressed in the following by first modelling the stochastic behaviour of the Swiss electricity prices and then introducing products that could be appealing for customers to reduce their electricity price risk.

3. Characteristics of Electricity Prices and Returns

3.1 Overview

In order to price a structured product, the stochastic price process of its underlying has to be analyzed. As already mentioned in the introduction, electricity is an asset that has specific characteristics and therefore exhibits a particular price behaviour that differs to those of other assets. This chapter will address the specific characteristics of the general electricity prices and returns and in particular test them for the Swiss electricity market.

There is a large literature about the price dynamics of the American and the Nordic electricity markets. Different models have been suggested in order to describe their price behaviours¹². However, most of the electricity markets are rather new and their price behaviour is not entirely understood by the market participants (Barlow, 2002). In particular, the Swiss power market is very young as it is still in the process of deregulation. The Swiss segment at the

EEX has been active since 2006 (Swissix). The SWEP has been calculated since 1998 (Dow Jones, 2008)¹³. To the knowledge of the author, this paper is the first that examines the Swiss electricity prices and creates a model to describe its price dynamic.

The SWEP and the Swissix are different concepts. While the SWEP is calculated by Dow Jones in a way that is not transparent, the Swissix represents the market transaction prices at the EEX for the Swiss segment and its calculation is very transparent. The SWEP is a single index and represents the prices in the spot market for the Swiss-European power transactions. It maps the prices of the short term daily business of three large Swiss power suppliers. Prices are calculated only for weekdays and apply for the hour 11.00 – 12.00 a.m. The EEX publishes different indices: 24 indices for every single hour of the day, 9 different indices for blocks of hours (night, morning, business hours, etc.), and two for the day base and the day peak. (BKW, 2008; EEX, 2008)

At the EEX, there are futures and options traded for the German segment called Phelix (EEX, 2008). For the Swiss segment there are no standardized derivatives yet being traded. However, it can be expected that in the future there will be a market at the Swissix. Due to low transparency, there will not be a standardized market for the SWEP. However, according to Mork (2001), there has been a growing number of OTC contracts traded on the SWEP. On the one hand, it could make sense to use the Swissix as an underlying for this paper’s

structured product analysis. On the other hand, the available data from the Swissix is too short upon which to make reliable estimates for its stochastic process. The SWEP with a time series of around 9 years is more reasonable to estimate. The limited data of the Swissix presents a dilemma for the purpose of this paper, which is to price a structured product on one of these two Swiss electricity price indices. One solution to this dilemma is if the SWEP and the Swissix are very highly correlated. In this case, one could use the estimates of the SWEP to price options on the Swissix. This will be examined in the next sections.

3.2 Correlation and Moment Analysis

Figure 3-1 shows the development of the SWEP, the Swissix day base index and the Swissix peak base index for two different time periods. The first graph compares the Swissix day base index with the SWEP index over the complete time period of the SWEP. The second and the third graphs compare the Swissix day base and the Swissix day peak indices with the SWEP since the launch of the Swissix.

On the first examination, these two indices move very closely together. The SWEP has larger reactions than the Swissix day base but lower than the Swissix peak base. Further insight into how close the Swissix moves with the SWEP can be gained by using a regression analysis. The following table shows the adjusted R2 of different regressions. It can be seen that the Swissix and the SWEP move very closely together. Based on this result it can be assume that if the stochastic process of the SWEP is identified, the results can be used to price options on the SWEP as well as on the Swissix.

3-1 Regression of SWEP on different Swissix indices

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Note: Calculations based on spot prices of EEX (2008), BKW (2008). Regressions made without a constant as much higher R2 received .

The differences between the SWEP and the Swissix behaviour can also be shown by an analysis of the key statistics. Table 3-2 presents the moments of the log returns of the three indices, revealing large differences between the time series. The SWEP returns for the time period 06-08 show a lower volatility than both Swissix indices. This discrepancy can partially be explained by the fact that the Swissix indices contain prices for the weekends where the prices for energy are lower.

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Figure 3-1 Swiss Electricity Price Indices

Note: Data from EEX (2008), BKW (2008). * SWEP calculated in EUR. ** Swissix Base load. *** Swissix Peak load. Starting point adjusted. Shows only weekday data.

Since the SWEP is negatively skewed, there are more large negative returns than positive ones (Jondeau, Poon & Rockinger, 2007). The log returns of the Swissix are instead positively skewed. The kurtosis statistics of the returns show that the SWEP has larger fat tails than the returns of the Swissix. The higher kurtosis of the SWEP can be explained by the large jumps that occurred over the nine years period. A distribution with a kurtosis higher than the normal value of three is called leptokurtic (Hanson, 2007).

Table 3-2 Key Statistics

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Note: Calculations based on data of EEX (2008), BKW (2008). Calculated on log returns.

3.3 Main Properties of Electricity Prices

This section will examine two different issues regarding the stochastic process of the Swiss electricity prices. Firstly, from the above statistics and figures, one can see that the stochastic process of the electricity indices differ from stock indices or single stocks. Electricity has general characteristics that differ from other assets and that makes the analysis more sophisticated (Pilipovic, 2007; Geman, 2005). These features will be explained in the following section. Secondly, the Swiss electricity price process deviates significantly from international electricity price behaviour. Switzerland’s electricity production is mainly driven by hydro power, which accounts for over 50% of total electricity production. Only few other European countries rely that strongly on the only storable form of energy (EIA, 2008)¹⁴. Due

to these characteristics, it can be expected that the Swiss electricity prices differentiate from other countries power prices.

According to Pilipovic (2007), the electricity markets are the most complex of all energy markets since the stochastic price behaviour shows particular characteristics: seasonality, spikes¹⁵, rather large volatilities, and mean reversion. In the following section, these characteristics shall be explained and tested for the Swiss price indices.

First, electricity prices show a daily, a weekly and a seasonal effect due to the fact that demand varies largely at different points in time. The daily variation depends mostly on the varying industrial and commercial demand. Thus, during the night the demand for electricity is smaller than during the day. This characteristic is apparent from the fact that there is a Swissix peak time and Swissix base time index. The weekly effect depends on a similar

reason. On Saturdays and especially on Sundays the power prices are smaller as the industry demand is lower¹⁶. This can be seen in Figure 3-2.

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Figure 3-2 Daily Electricity Price Variation

Note: Calculations based on data of EEX (2008) and BKW (2008).

The seasonal effect depends largely on climatic conditions. Switzerland experiences cold and dark winters and mild summers with shorter nights. Hence the demand and also the prices for electricity are expected to be higher in the winter months than in the summer months. The data contradict this expectation, as can be seen in Figure 3-3. Different factors are causing this

observation. The main reason is explained in the following paragraph¹⁷. In other parts of the

world, e.g. in California, the situation is different. Air conditioners in the hot summers consume a higher amount of electricity than the heating systems in the mild winters (Barlow, 2002).

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Figure 3-3 Monthly Electricity Price Variation

Note: Calculations based on data of EEX (2008) and BKW (2008).

Compared to other countries or regions, the seasonal variation in Switzerland is relatively small (compare e.g. Lucia & Schwartz, 2002). This can be partially explained due to the fact that Switzerland is importing a large amount of power in the winter and exporting a large amount of power in the summer months (especially in July) (SFOE, 2007). The Swiss market cannot be viewed independently from other markets and can therefore profit from the integration in the European electricity network.

Second, electricity prices experience large price spikes. The price can jump to a multiple of the average price level within days (Weron, 2008). In the period between December 2006 and April 2008, the average of the Swissix day base was 55 EUR/MWh and the maximum 180 EUR/MWh. After a few days the price usually drops back to the normal level. Compared to other electricity markets the spikes in the Swiss market are moderate. The moderate fluctuations may depend on the storability of hydro energy and the international integration of the Swiss market. Geman (2005) stated that the US market showed jumps from 30 to over 1,000 USD. According to Geman and Roncoroni (2003), German prices jumped from 25 to 500 EUR. Whereas the spikes result in a kurtosis lower than 9 for the Swiss market, Lucia and Schwartz (2002) show that the Nordic markets experience a kurtosis of over 15.

Different situations can disconnect the traded price from the production cost and cause these large jumps. Positive spikes can be explained by the high demand due to weather conditions or due to outages in the generation/ transmission process. According to de Jong and Huisman (2002), the producer cannot react immediately as there is a time lag in switching on another generator. In a similar way, negative spikes occur when it is difficult to reduce generation capacity in periods of low demand (London, 2007; Eydeland and Geman, 1999). In Switzerland, where the electricity networks have been very reliable, the upward spikes can be explained with international shocks.

Third, energy prices show a significant volatility. This can be explained by the fact that small changes in supply or demand lead to large price effects. The volatility is larger compared to stock market indices or individual stocks (Deng, 1999). In the case of Switzerland, the price indices are supposed to be less volatile than in other countries as hydro energy is storable and accounts for more than 50% of the Swiss production. That this assumption is correct can be validated by comparing EEX volatilities. Historically, the volatility for the Phelix was more

than twice as large as for Swissix index¹⁸. In the near future, Switzerland is going to increase

electricity production based on other technologies than hydro, which might increase the volatility further. Figure 3-4 shows that the volatility of the log returns is not constant over time.

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Figure 3-4 Daily Log Returns

Note: Calculations based on Data of EEX (2008), BKW (2008).

Fourth, energy prices exhibit mean reversion. The term mean reversion refers to the behaviour of a price to decline after a period of rise or to increase after a downswing. Mean reversion is considered as an alternative to the random walk hypothesis (Bodmer, 1996). The literature has showed a great interest in mean reversion of the stock markets in order to investigate the predictability of asset returns. Thereby, different test methods have been suggested to inspect

mean reversion¹⁹. An easy way to test for mean reversion is to test for stationarity²⁰, for which

different tests have been developed in the literature (Brigo et ali, 2007): the autoregression test, the Dickey-Fuller test, the Augmented Dickey-Fuller test, the Phillips and Perron test, the Variance Ratio test.

More recent literature examined mean reversion for energy and, as such, electricity prices. Pindyck (1999) examined long term energy price development and detected mean reversion²¹. Researchers agree today on the mean reversion of electricity prices as well.²² Around the mean, the energy prices exhibit random movement that represents temporary supply/demand mismatches (Geman & Ronconori, 2006). In order to know if in this paper a mean reverting

stochastic process should be applied for the Swiss electricity market, its mean reversion must be examined. Two different test methods shall be applied: The Variance Ratio test and the Rescaled Range test.

The Variance Ratio test is an appropriate test statistic for electricity data as it is more reliable than other test statistics for heteroscedastic data. Lo and MacKinlay (1988) compared the

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¹ However Gorton & Rouwenhorst (2004) claim that the performances of commodities are similar to the ones of equity and have only outperformed in recent years.

² According to an own calculation: the Wheat price rose by 280%, the soy price by 190% and the crude oil price by over 300% over the last 8 years.

³ Compare also Gorton & Rouwenhorst (2004) for additional information. However, this has to be contemplated for each commodity individually, as they have different drivers.

⁴ However, not only the deregulation, but also other factors played a major role in the California crises (Weron, 2008).

⁵ Deng an Oren (2006) show that most markets have even established price caps and other regulations in order to protect the customers.

⁶ The largest power exchanges in Europe are: Nordpool (for Norway, Sweden, Finland, Denmark), England & Wales Electricity Pool, European Energy Exchange (EEX for Germany), OMEL (Spain), Amsterdam Power Exchange, UK Power Exchange, Powernext (France), ITEX (Italy). See Weron (2008) for a list. The oldest European market for spot and futures trades (Lucia & Schwartz, 2001) is Nordpool, which is also the most successful electricity futures exchange in the world (James, 2008).

⁷ Hilpold (2006) states that there is a supply delay as exploration especially in energy markets come only when prices are high enough so that the extraction turns profitable.

⁸ For other commodities, the convenience yield is an important factor in the pricing in the futures and in the spot markets (see Kaldor (1939, cited in Geman & Rocoroni, 2003) and Working (1949, cited in Geman & Rocoroni, 2003). Holding a commodity was important to unwind forward contracts or to speculate of later upside in prices. This is not possible for electricity. The pricing of futures for electricity must therefore be treated differently than for other commodities. These comments will be important in a later chapter.

⁹ Refer to Clewlow & Strickland (2000), Deng (1999), Eydeland & Wolyniec (2003, 2008), Pilipovic (2007), Deng & Oren (2006).

¹⁰ These prices are energy end-use prices that include taxes. France shows higher prices for households but lower prices for the industry.

¹¹ This will be shown in the next chapter.

¹² Refer to most of the electricity literature mentioned in this paper.

¹³ The SWEP is published in EUR since May 99. In the following analysis, the SWEP in EUR is used as this is directly comparable to the Swissix, which is published at the EEX in EUR/MWh.

¹⁴ EIA Statistic 6.3: World Net Electricity Generation. Only Norway (98%), Austria (60%), Iceland (83%), Albania (98%) have a higher share of electricity produced by hydro energy. Most large industrial countries show a significant lower part: USA (7%), Australia (7%), Germany (4%), UK (1%), Italy (14%), France (11%), Spain (12%). Many developing countries in Africa and South America produce as well a large part with hydro power.

¹⁵ Jumps in electricity prices are often called spikes as the prices jump back to the normal level after a certain time.

¹⁶ In Switzerland, the industry is one of the largest consumers of electricity (see above).

¹⁷ An analysis of the different reasons is out of the scope of this paper.

¹⁸ Own calculation based on Bloomberg historical volatility numbers.

¹⁹ Shiller & Perron (1985), Summers (1986), Fama & French (1988) and Poterba & Summers (1988) started the broad discussion about random walk to mean reversion in stock prices. They also introduced test methods. McQueen (1992) gives a good overview of problems attached with simple regression. Daniel (2001) gives a more recent overview and comparison of different tests.

²⁰ In a later chapter, it will be shown that a discrete mean reversion model can follow an AR(1) process. For AR(1) processes testing for mean reversion is equivalent to test for stationarity (Brigo et ali, 2007).

²¹ Pindyck (1999) used a data series of 127 years for oil and coal, and a data series of 75 year for natural gas.

²² See all the mentioned literature about electricity prices cited in this paper.