Stochastic EUA Price Forecasting

(1)

International Economics & Business Msc. Thesis

Stochastic EUA Price Forecasting

University of Groningen

May 29th, 2010

A.J. Mulder

Supervisors: Prof. C.J. Jepma Ir. C.F.M. Bos (TNO)

Abstract

To assess the effectiveness of the EU ETS, a stochastic market model has been constructed with the main goal to forecast the long-term EUA price. The model includes institutional, political and economical factors and provides a more comprehensive analysis of the EUA price fundamentals than is typically found in the available literature. The model shows that the current design of the EU ETS is unlikely to lead to an EUA price anywhere above €25 before 2030, while it is equally unlikely that the EU will achieve its emission reduction goal for 2020. Various policy alternatives are proposed to improve the chances of meeting the emission reduction goal. Also, the analysis shows that the EUA price is unstable, which is primarily caused by systemic uncertainty in the demand for allowances. As a result, it is unlikely that the EU ETS will be able to create the conditions required for the commercial roll-out of CCS. Other supporting mechanisms, such as subsidies or mandatory CCS as part of licensing procedures for new installations, will be required. Finally, the simulations show that combining the EU ETS market mechanism with regulation mandating CCS on newly built coal fired power plants is counter-productive in achieving further emission reductions.

(2)

List Of Figures

FIGURE 2.1:DISTRIBUTION OF INSTALLATIONS UNDER THE EUETS ... 8

FIGURE 2.2:EUAFUTURES CONTRACTS WITH VARIOUS EXPIRATION DATES... 9

FIGURE 2.3:EUEMISSION REDUCTION TARGET UNTIL 2020... 11

FIGURE 4.1:FLOWCHART OF DEMAND, SUPPLY AND BANKING... 19

FIGURE 4.2:FROM CARBON ABATEMENT TO AN ALLOWANCE PRICE... 21

FIGURE 4.3:THE COMPLETE DETERMINISTIC FUNDAMENTAL EUA PRICE MODEL... 26

FIGURE 5.1:THE GLOBAL GHG ABATEMENT COST CURVE BEYOND BAU-2030... 33

FIGURE 5.2:GLOBAL AVERAGE ABATEMENT COSTS,POWER... 36

FIGURE 5.3:CUMULATIVE ABATEMENT POTENTIAL,POWER... 36

FIGURE 5.4:GLOBAL AVERAGE ABATEMENT COSTS,IRON STEEL... 37

FIGURE 5.5:CUMULATIVE ABATEMENT POTENTIAL,IRON STEEL... 37

FIGURE 5.6:GLOBAL AVERAGE ABATEMENT COSTS,PETRO GAS... 38

FIGURE 5.7:CUMULATIVE ABATEMENT POTENTIAL,PETRO GAS... 38

FIGURE 5.8:GLOBAL AVERAGE ABATEMENT COSTS,CEMENT... 38

FIGURE 5.9:CUMULATIVE ABATEMENT POTENTIAL,CEMENT... 38

FIGURE 5.10:GLOBAL AVERAGE ABATEMENT COSTS,CHEMICALS... 39

FIGURE 5.11:CUMULATIVE ABATEMENT POTENTIAL,CHEMICALS... 39

FIGURE 6.1:EUAPRICE FORECAST UNDER THE BAU SCENARIO... 41

FIGURE 6.2:ALLOWANCE SCARCITY UNDER THE BAU SCENARIO... 41

FIGURE 6.3:CARBON EMISSION REDUCTION COMPARED TO 2008 UNDER THE BAU SCENARIO... 42

FIGURE 6.4:SCENARIO 2:STOCK OF BANKED ALLOWANCES... 44

FIGURE 6.5:SCENARIO 3:ALLOWANCE SCARCITY... 45

FIGURE 6.6:SCENARIO 4.1:ALLOWANCE SCARCITY... 46

FIGURE 6.7:THE CUMULATIVE DISTRIBUTION FUNCTION OF THE GROSS ALLOWANCE BALANCE IN 2020 ... 48

FIGURE 6.8:CUMULATIVE DISTRIBUTION FUNCTION OF CUMULATIVE ABATEMENT IN 2020... 48

FIGURE 6.9:SCENARIO 4.1ORIGINAL EUA PRICE FORECAST... 49

FIGURE 6.10:SCENARIO 4.1 PRICE FORECAST UNDER Α=0.3 ... 49

FIGURE 6.11:SCENARIO 5-ALLOWANCE SCARCITY AND THE EUA PRICE IN 4 RANDOM TRIALS... 49

FIGURE 10.1:GLOBAL GHG ABATEMENT COST CURVE FOR THE POWER SECTOR UNDER MAXIMUM GROWTH OF RENEWABLES AND NUCLEAR ENERGY... 63

FIGURE 10.2:GLOBAL GHG ABATEMENT COST CURVE FOR THE IRON AND STEEL SECTOR... 63

FIGURE 10.3:GLOBAL GHG ABATEMENT COST CURVE FOR THE PETROLEUM &GAS SECTOR... 64

FIGURE 10.4:GLOBAL GHG ABATEMENT COST CURVE FOR THE CEMENT SECTOR... 64

FIGURE 10.5:GLOBAL GHG ABATEMENT COST CURVE FOR THE CHEMICALS SECTOR... 65

FIGURE 10.6:HISTORICAL OIL PRICE 1860-2007... 65

FIGURE 10.7:SCENARIO 1:EUAPRICE FORECAST... 66

FIGURE 10.9:SCENARIO 1:EMISSION REDUCTION SINCE 2008... 66

FIGURE 10.10:SCENARIO 1:ABSOLUTE LEVEL OF EMISSIONS... 66

FIGURE 10.12:SCENARIO 1:PROB. TO ACHIEVE 2020 TARGET... 66

FIGURE 10.15:SCENARIO 2:EMISSION REDUCTION SINCE 2008... 67

FIGURE 10.16:SCENARIO 2:ABSOLUTE LEVEL OF EMISSIONS... 67

FIGURE 10.21:SCENARIO 3:EMISSION REDUCTION SINCE 2008 ... 68

FIGURE 10.22SCENARIO 3:ABSOLUTE LEVEL OF EMISSIONS... 68

(4)

FIGURE 10.27:SCENARIO 4.1:EMISSION REDUCTION SINCE 2008 ... 69

FIGURE 10.28SCENARIO 4.1:ABSOLUTE LEVEL OF EMISSIONS... 69

FIGURE 10.29:SCENARIO 4.1:STOCK OF BANKED ALLOWANCES... 69

FIGURE 10.31:SCENARIO 4.2:EUAPRICE FORECAST... 70

FIGURE 10.33:SCENARIO 4.2:EMISSION REDUCTION SINCE 2008... 70

FIGURE 10.39:SCENARIO 5:EMISSION REDUCTION SINCE 2008 ... 71

FIGURE 10.40SCENARIO 5:ABSOLUTE LEVEL OF EMISSIONS... 71

FIGURE 10.43:SCENARIO 6:INSTALLED CAPACITY OF CCS IN EU POWER SECTOR... 71

FIGURE 10.49:SCENARIO 6.1:PROB. TO ACHIEVE 2020 TARGET... 72

FIGURE 10.55:SCENARIO 6.2:PROB. TO ACHIEVE 2020 TARGET... 73

List Of Tables

TABLE 4.1:THE NER IN MTCO2E DURING PHASE II AND III ... 16

TABLE 4.2:EXPLANATORY TABLE TO FIGURE 4.1... 20

TABLE 4.3:EXPLANATORY TABLE TO FIGURE 4.3 ... 27

TABLE 4.4:OVERVIEW OF TERMS VARIABLES INTRODUCED IN SECTION 4.6 ... 30

TABLE 5.1:GLOBAL AVERAGE COSTS AND ABATEMENT POTENTIAL IN THE POWER SECTOR... 35

TABLE 5.2:GLOBAL AVERAGE COSTS AND ABATEMENT POTENTIAL IN THE IRON AND STEEL SECTOR... 36

TABLE 5.3:GLOBAL AVERAGE COSTS AND ABATEMENT POTENTIAL IN THE PETROLEUM AND GAS SECTOR... 37

TABLE 5.4:GLOBAL AVERAGE COSTS AND ABATEMENT POTENTIAL IN THE CEMENT SECTOR... 38

TABLE 5.5:GLOBAL AVERAGE COSTS AND ABATEMENT POTENTIAL IN THE CHEMICALS SECTOR... 39

TABLE 6.1:OUTPUT STATISTICS EXPLAINED... 40

TABLE 6.2:OUTPUT STATISTICS UNDER THE BAU SCENARIO... 42

TABLE 6.3:SCENARIO 2:OUTPUT STATISTICS... 43

TABLE 6.5:SCENARIO 4.1:OUTPUT STATISTICS... 45

TABLE 10.1:SCENARIO 1:‘BUSINESS AS USUAL (BAU)’INPUT PARAMETERS... 58

TABLE 10.2:SCENARIO 2:‘NO RECESSION’INPUT PARAMETERS... 58

TABLE 10.3:SCENARIO 3:‘FASTER REDUCTION OF THE CAP’INPUT PARAMETERS... 59

TABLE 10.4:SCENARIO 4.1:‘ABANDONMENT OF THE LINKING DIRECTIVE’INPUT PARAMETERS... 59

TABLE 10.5:SCENARIO 4.2:‘ABANDONMENT OF THE LINKING DIRECTIVE’INPUT PARAMETERS... 60

TABLE 10.6:SCENARIO 5:‘HIGHER CAP REDUCTION & LIMITED LINKING DIR.’INPUT PARAMETERS... 60

TABLE 10.7:SCENARIO 6.1:‘STRICT ETS POLICY & MANDATORY INST. OF CCS’INPUT PARAMETERS... 61

(5)

1. Introduction

1.1. EU Emissions Trading Scheme

Ever since the EU Emissions Trading Scheme (EU ETS) came into effect on January 1st 2005, it has been surrounded by uncertainty. Although the scheme could potentially become a powerful weapon in the effort to reduce European carbon emissions, doubts with respect to the scheme’s effectiveness and practical feasibility have remained. In theory, “the ETS should

allow the European Union to achieve its emission reduction target under the Kyoto Protocol at a cost of below 0.1% of GDP, significantly less than would otherwise be the case”(EC,

2008). In practice, however, the efficiency and effectiveness of the ETS still remain questionable.

If given enough time, political alignment and decisiveness, the EU can possibly have a fully functioning emissions trading scheme, covering all major polluting sectors and leading to a substantial cutback in carbon emissions. However, time is limited, as the EU is committed to cutting carbon emissions by 20% by 2020 compared to 1990 levels (EC, 2008). Secondly, the EU has stressed the importance of CCS as a bridging technology1 in order to achieve the EU’s long term emission reduction goals beyond 2020. Therefore the EU aims to make CCS an economically viable abatement technology by 2020. Generally, the EU ETS, which is seen as the flagship of European carbon policy, is expected to provide a strong and stable price incentive to the industry. But whether the EU ETS will result in an EUA (European Union Allowance) price that will support the timely commercial roll-out of CCS is being questioned. McKinsey & Company (2008) estimate that fitting a single 900 MW coal plant with CCS (Carbon Capture and Storage) equipment would raise the required capital investment by approximately 50%, to almost € 2.25 billion. Although CCS and other technologies provide enormous abatement potential, the current political and, hence, CO2 price uncertainties, imply a required rate of return for such projects that is well beyond what it currently feasible. Therefore, to realize large-scale abatement investments the ETS should ideally provide a strong and stable price incentive.

Until 2008, the ETS has primarily been in a testing phase. As a result of over-allocation of allowances, the ETS has not led to significant cutbacks yet (Grubb and Ferrario, 2006). Any step towards achieving the EU’s emission goals will therefore have to be made in the years to come. While time is running out, important obstacles are still in the way of large-scale investments, which are indispensable to meet the climate targets. As Hoffmann (2007) noted,

“policy makers should reflect their long-term reduction intentions in the scarcity of allowances, provide more incentives to increase efficiency, and reduce regulatory uncertainty.”

The scarcity of allowances is instrumental in driving investments. However, as a result of the recent economic turmoil the demand for allowances has dropped significantly. This drove down the price for allowances to a level which is simply “too low to provide sufficient

incentive to change behaviour in a more climate-friendly direction” (Kolk and Pinkse, 2009).

Although the recession does bring the EU closer to its emission reduction target for 2020, it seems a risky policy to rely on economic downturns to achieve the emission reduction target. Indeed, a stock of allowances builds up as firms bank excess allowances during the recession, allowing firms to postpone carbon abatement once the economy rebounds. To increase the probability of achieving the 2020 reduction target it is imperative that investments in carbon

1

(6)

abatement be not postponed for too long, as achieving the target requires a fundamental change in the way we produce and consume across many sectors. European legislators have introduced the EU ETS with the objective to provide the incentive to kick-start this structural change. However, as long as allowances are in abundant supply the incentive to invest in carbon abatement is removed. Prolonged oversupply of allowances could therefore turn out to be a serious obstacle to achieving the long-term emission reduction goal.

Now, almost five years after its introduction, it is time for the ETS to show that it will be capable of delivering to its promises. The extent to which the EU ETS, under the current political climate, will be able to provide a sufficiently strong incentive to the industry to meet the EU’s emission reduction target in time is the subject of this research.

1.2. EU ETS Model

To assess the effectiveness of the EU ETS a market model has been constructed. The main goal of the model is to forecast the fundamental EUA price for the mid- and long-term. We define the fundamental EUA price as follows:

• The fundamental EUA price reflects the marginal abatement cost of the last tonne of CO2 abated, given the level of scarcity of allowances in that year.

Fundamentally, there is no price tag on carbon dioxide as long as allowances are in abundant supply. Firms are only willing to pay for allowances if they have a short position and are faced with a non-compliance penalty2. The maximum price an individual firm is willing to pay for an allowance is equal to the cost of the cheapest abatement opportunity available to that firm. On economic principle, if the market is short, the firm with the lowest cost abatement opportunity will abate carbon emissions first. As the price increases, more firms will choose to abate CO2 and this process continues until demand and supply are back in

equilibrium. As a result, the fundamental allowance price equals the costs of the last tonne of CO2 abated. In this analysis, the expansion of the EU ETS across more sectors is left out of

the analysis. Also, market mechanisms such as arbitrage and speculation are not taken into account while calculating the fundamental EUA price. As a result, future expectations are not accounted for in the price. Instead, the fundamental EUA price is a direct reflection of the price of the available abatement potential, given the need for abatement in any given year. The level of the allowance price depends on both the controllable political and institutional environment as well as the uncontrollable worldwide economy (i.e. uncontrollable from a European policy-makers perspective). The main problem statement is therefore:

What is the fundamental EUA price given various controllable and non-controllable assumptions?

From this central question, three research questions can be derived, viz.

1. Given the development of the EUA price, which abatement opportunities will be

grasped? More specifically, when will CCS become economically viable?

2_{Firms are fined €100 (the non-compliance penalty) for each tonne of CO}

2 emitted in excess of the number of

(7)

2. How likely is the EU to achieve its emission reduction goals given the current implementation policy of the EU ETS?

3. Which measures are most effective in terms of improving the probability of

meeting the emission reduction goals?

(8)

2. A Short History of the EU ETS

As mentioned in the introduction, the EU ETS became operational on January 1st 2005. That date marked the birth of the biggest cap-and-trade scheme in the world as no such scheme had been launched on an international scale before. With the latest countries Iceland, Liechtenstein and Norway joining the scheme in 2008, the ETS currently comprises 30 countries and talks with other countries to join the scheme are ongoing. The EU ETS is not the only CO2 emission trading scheme in the world; similar schemes have been set-up in for

example Japan and Australia.

The popularity of cap-and-trade schemes can be explained by its straightforward concept: by issuing a limited number of allowances to emit waste gases into the atmosphere, the industries to which the scheme is applicable are forced to contain their emissions. The ability to trade allowances between individual companies furthermore ensures that reductions are achieved in the most efficient way: low-cost carbon abatement opportunities are used first, while the most expensive opportunities are exploited last, minimizing the program’s overall cost to society. While alternatives, like a tax or simply more stringent regulation, are probably more straightforward, the presumed efficiency of a market-based instrument like the ETS is fuelling its popularity.

Currently, more than 11.000 heavy energy-consuming installations in power generation and manufacturing are covered by the ETS. More specifically the ETS covers the power sector, refineries, coke ovens, metallic ore, iron and steel plants, cement, glass, ceramics and the pulp and paper sector (EC, 2008). The prime reason for covering these sectors lies in a common characteristic: these sectors mainly consist of large and stationary carbon sources. Carbon abatement in these sectors is relatively easy and effective. Among these stationary sources, however, large differences in scale exist. While three quarters of all installations contribute around 5% of all emissions, the biggest 1.8% of all installations contributes 50% of the emissions under the EU ETS. A distribution of all installations under the EU ETS is shown in Figure 2.1 (Kettner et al., 2007).

How allowances are distributed across all installations is determined by National Allocation Plans (NAPs), as drafted by the national government of each member state. After verification and approval by the European Commission, allowances are issued to the firms under the EU ETS on an annual basis. Currently almost all allowances are being issued for free, as governments are allowed to auction only 10% of all allowances until 2012 (Hepburn et al., 2006). However, this rate will increase substantially in the future as the revenues can be used to “finance general socioeconomic purposes” (Sijm et al., 2007) in particular those related to energy transition and carbon reduction.

Allowances are traded on the carbon exchange using futures contracts, which give the buyer the right and the obligation to buy allowances against a certain price on a pre-determined date.

Figure 2.1: Distribution of installations under the EU ETS

(9)

The historic price development of futures contracts with various expiry dates are shown in Figure 2.2.

Whilst the ETS is slowly expanding across more countries, the EU is also working on expansion across more sectors. The aviation industry is the most prominent candidate to be included in the scheme, while the maritime and transportation sector are also being looked at. As these carbon sources are mainly mobile as opposed to the stationary sources already in the ETS, including these sectors may still prove to be challenging.

The development of the ETS is divided into different phases. Phase I (2005-2007) was mainly a period of trial and error. Fifteen months after its introduction it turned out that an excessive amount of allowances had been distributed. As a result, the supply of allowances exceeded demand by far, causing the market price to plummet immediately after the news reached the market. An important reason for the over-allocation of allowances could be found in the way the allowance cap was determined. Grubb and Ferrario (2006) concluded that in general there is a “systematic upward bias in industrial energy and emissions forecasts, particularly when

these form the basis of setting sector emissions targets or caps.” In fact, by setting the cap on

the basis of forecasts a perverse incentive was generated for all covered industries: by simply reporting overly high emission forecasts, too many allowances were allocated (Grubb and Neuhoff, 2008).

To correct for the fact that the cap was set too high in Phase I, the cap was set 6.5% below reported 2005 emissions at the start of Phase II, which started in 2008 and will last until the end of 2012 (EC, 2008). Unexpectedly, however, demand for allowances decreased quickly in the second half of 2008 as a result of the financial crisis which led to a global reduction in production levels and demand for energy. These developments are reflected in the volatile development of the EUA price over time, as shown in Figure 2.2. The initial crash in April 2006, when the market was informed about the oversupply of allowances, led to an immediate fall in the EUA price. In subsequent years the EUA price slowly recovered to €30. However, as the financial crisis unfolded around August of 2008, the EUA price plummeted once again.

Figure 2.2: EUA Futures Contracts with various expiration dates

0,00 5,00 10,00 15,00 20,00 25,00 30,00 35,00 Ja n-06 Mar -06 May -06 Jul-0 6 Sep -06 Nov -06 Ja n-07 Mar -07 May -07 Jul-0 7 Sep -07 Nov -07 Ja n-08 Mar -08 May -08 Jul-0 8 Sep -08 Nov -08 Ja n-09 Mar -09 May -09 Jul-0 9 Sep -09 € dec-06 dec-07 dec-08 dec-09 dec-10

The black vertical line marks the start of Phase II of the trading scheme. Source: European Climate Exchange, www.ecx.eu

(10)

of allowances was not yet allowed during Phase I. As a result, futures contracts which expired before the 1st of January 2008 lost their value as the expiration date neared. Starting in Phase II, however, the European Commission did allow firms to bank their allowances. Although this meant that allowances would now hold their value over time, the banking facility also implied that any surplus of allowances could now be banked and used to offset emissions in any other year. Consequently, emissions covered by the scheme are not strictly bound by the overall annual cap anymore if firms hold previously banked allowances.

Next to banking, a second provision was introduced at the start of Phase II: the linking directive. Whereas the EU ETS cap was set more or less equal to the level of emissions in 2008, the linking directive allows individual firms to use Kyoto credits (CERs and ERUs3) on top of the original cap to offset their emissions. The potential to use Kyoto offsets is different for each participating country under EU ETS, but the weighted average of all countries is 13.3% on top of the EU ETS cap. Effectively this means that companies can potentially increase the supply of allowances by 13.3% on top of the original cap.

CERs and ERUs originate from two separate programs: Joint Implementation (JI) and the Clean Development Mechanism (CDM). Both programs were designed to promote carbon abatement in third countries. As these third countries are predominantly developing countries in the case of CDM, ample low-cost abatement opportunities have become available for investors. Such opportunities consist of, for example, programs to improve energy efficiency in the industry or investments in renewable energy. Once a project is completed and the carbon abatement has been verified, the CDM Executive Board issues credits (CERs) to the investor (Point Carbon, 2007).

Similarly, an investor can earn ERUs through the Joint Implementation project. Although the idea is similar, there is one main difference between CDM and JI. Whereas the host country for a CDM investment is always a developing country, JI investments only occur between Annex 1 countries4 (Point Carbon, 2007). Directive 2004/101/EC states that, when CERs and ERUs are in the hands of companies covered by EU ETS, these credits are exactly equivalent to an EUA (1 EUA = 1 CER = 1 ERU) (EC, 2008).

Analogous to the potential effect of banking, the linking directive implies that emissions are not bound to decrease once the EU ETS cap is lowered. Instead, firms could rely on Kyoto credits. In 2008 alone, more than 81 MtCO2e worth of Kyoto credits were used to offset

emissions. Given the enormous potential to use Kyoto offsets under EU ETS (up to around 277 MtCO2e annually in Phase II), the linking directive provides the EU industry with a

potentially cheaper alternative to carbon abatement at home.

As mentioned above, the cap will be reduced for the first time in 2013, at the start of Phase III (2013 – 2020). The cap will be reduced by 1.74% annually “until 2020 and beyond” (EC, 2008). The reduction has been set such that the EU ETS cap is 21% below the 2005 level. The 21% reduction in these sectors is part of the European goal to reduce the overall level of emissions by 20% compared to 2020. In order to achieve this target the burden of abatement is divided between the sectors covered by the EU ETS and those which are not under the

3

Certified Emission Reductions and Emission Reduction Units

4_{Annex 1 Countries: Parties include the industrialized countries that were members of the OECD (Organization}

(11)

scheme. Because the costs of abatement are generally higher in sectors outside the EU ETS, a higher reduction is demanded from the sectors covered by the scheme. An overview of the 2020 targets is shown in Figure 2.3.

Compared to 2005, non EU ETS sectors are expected to reduce their emissions by 10% while sectors under the EU ETS are forced to reduce their emissions by 21%. Based on the annual cap reduction of 1.74% starting in 2013, a reduction of 14% is needed compared to 2008 in order to meet the 2020 target. Because most of the abatement burden is put on the sectors under EU ETS it is unlikely that the EU will be able to achieveits overallreduction target if the EU ETS is incapable of driving emissions 14% below the 2008 level. The success of the EU’s carbon policy is therefore critically dependent on the success of the EU ETS.

Figure 2.3: EU Emission reduction target until 2020

(12)

3. Literature Review

Various studies have been conducted to forecast both the scarcity of allowances and the allowance price. An early report by Ecofys (Reece, Phylipsen, Rathmann, Horstink and Angelini, 2006) estimated the expected shortage of allowances for nine member states. Using BAU emission estimates, these states account for around 80% of all emissions under EU ETS. The Ecofys estimates are based on CO2 projections for 2010 from the fourth National

Communication, submitted to the UNFCCC in October 2006. The countries included in the study were Germany, the UK, Poland, Ireland, France, Spain, Italy, Portugal and the Netherlands. Reece et al. (2006) estimated the scarcity of allowances in Phase II (2008-2012) to be around 118 MtCO2/yr. They raised their doubts however “on the accuracy of some of the official BAU estimates from Member States, i.e. some BAU projections may be over-optimistic in their growth assumptions.” Also the potential effect of the linking directive was

highlighted: “companies who are short of allowances may tend towards purchasing JI/CDM

credits before they would choose to buy EUAs.” This process could completely nullify the

shortage, as the potential to use JI/CDM credits far surpasses the expected shortage.

Whereas the Ecofys report only gave a forecast with respect to the scarcity of allowances, Deutsche Bank also predicts a long-term price level for EUAs. Based on a long-term oil price forecast of $85/bbl and a long-term coal price of $125/t, Deutsche Bank estimates a carbon price of €30/t today, gradually going up in coming years. With a cost of carry5 of 4%, a carbon price of €48 is estimated for 2020, reaching €71 in 2030 (Lewis, 2009a). Between 2008 and 2020 the Deutsche Bank expects an average residual abatement of 86 MtCO2/yr.

Until October 2008, a scarcity of allowances of 125 MtCO2/yr was estimated, much closer to

the Ecofys estimate. Before the financial crisis in 2008, Deutsche Bank estimated a current long term price of €40, increasing to €67 in 2020 (Lewis, 2009b). The theory behind these price estimates rests on the idea that the EUA price will eventually converge with the long-run marginal-cost curve for CCS. “The price implied today by the long-run abatement-supply

curve represents a floor price; in a rational market the EUA price should never fall below this level”(Lewis, 2009a). The need for abatement “implies a significant need for new low-carbon power-generation capacity, and hence a carbon price high enough to incentivise new gas and/or carbon-capture and storage (CCS) coal plant to be built ahead of conventional coal”

(Deutsche Bank, 2008).

New Carbon Finance (2009) expects an average price of €51 for Phase III (2013-2020) of the EU ETS. Such a price level would be mainly driven by the fact that new sectors will enter the scheme in Phase III. The inclusion of these sectors creates a higher level of demand for allowances, while the abatement potential in these new sectors is expected to be limited. Various scholars have used regression analysis in an attempt to identify the fundamentals of the allowance price (Bunn & Fezzi, 2007; Convery & Redmond, 2007). Alberola, Chevallier and Chèze (2008) related the carbon price in the first two years of the EU ETS to the price of oil, coal, gas and energy, temperature fluctuations and the clean dark and clean spark spread6 of power operators. The authors found a significant relationship to the carbon price for all energy inputs, when analysed over the full time period. The results changed substantially

5_{The cost of holding a position. For an investment this generally refers to the risk free interest rate}

6_{The clean dark spread is the profit margin from selling one unit of electricity produced by a coal-fired power}

(13)

however, when differentiated between various periods. “The first break that occurred on

April 2006 following the disclosure of 2005 verified emissions emphasizes that carbon price changes react to different fundamentals as a consequence of the revelation of institutional information. These results suggest that before the disclosure of the net short/long emission position by installations on April 2006 allowance trading was based on heterogeneous anticipations since EUA prices do react to some, but not all, mechanisms that have been highlighted during the full period. The presence of a second structural break on October 2006 as a consequence of EC announcements regarding the restriction of 2008–2012 allocation confirms this agents’ behavioural change.” These results seem to indicate that there was a

lack of consensus among carbon traders with respect to the drivers of the allowance price and an overall lack of transparency in the market regarding the supply of allowances. On a more general note, the authors mention that “Some factors are missing in the recent empirical

literature of carbon price fundamentals. Political and institutional decisions on the overall cap stringency, which is a function of initial allocation, may have an impact on the carbon price discovery” (Alberola et al, 2008).

Although this final point should not be surprising, it does highlight an important but underexposed element in the available literature: the relevance of the dynamics of allowance supply and demand. In some studies substantial and continuous levels of allowance scarcity are assumed; scarcity of allowances is sometimes assumed to be the natural state of the market. However, recent developments such as the economic crisis or the potential threat of CDM credits once more underline the volatile and unpredictable manner in which allowance supply and demand behave. Consequently, any attempt to identify the fundamentals of the allowance price, or any attempt to forecast the allowance price should start with an analysis of the dynamics of allowance supply and demand. In the end, the price of an allowance is a function of the necessary amount of abatement. This holds because theoretically, the rate of abatement will never exceed the reduction of the cap over the long-term: if this happens, the market would immediately turn into surplus, which would reduce the need for abatement. In turn, this would be reflected by a lower allowance price.

(14)

The first year of Phase II, 2008, is used as a base year for the model and fluctuations in the demand for allowances are modelled on a year-to-year basis, because detailed information on the volatility of demand and supply within a certain year is unavailable and difficult to estimate. Therefore, some factors that potentially influence allowance demand are not included in the analysis, such as unexpected drops in the temperature. Alternatively, the focus lies on structural macro-economic forces which are estimated on a year-to-year basis. The basic deterministic model, outlined in section four, is built in Excel while volatile time-series are added by using Crystal Ball. Crystall Ball is a plug-in that allows to perform probabilistic modelling and forecasting in Excel. Forecasts are generated by running a user-defined number of trials (i.e. stochastically sampled model runs). For each trial a random sample is drawn from a specified distribution. This method is also known as the Monte Carlo method.

(15)

4. Methodology

This section will outline the basic building blocks of the EUA-price model. Paragraph 4.1 and 4.2 will touch on the different drivers for supply and demand of allowances. Subsequently, paragraph 4.3 concerns the effect of banking behaviour. In paragraph 4.4, the link between allowance scarcity and the marginal cost of abatement will be made. Paragraph 4.5 will cover the last part of the deterministic model to determine the fundamental EUA price. Finally, paragraph 4.6 covers the methodology for probabilistic modelling. The setup of the model is designed such that it reflects the current policies within the EU ETS as much as possible.

4.1. Allowance Supply

Mathematically, the supply of allowances of all EU ETS countries at time t during Phase II can be expressed as:

[

]

∑

= − + + ∗ = 30 1 1 (1 ) i t i t t i t t CAP LP INER NCAP θ (1)

Where CAP is the official cap assigned to country i at t-1 (t=0 is 2008) within EU ETS. LP_ti

represents the maximum linking potential as a fraction of the cap for country i at t, the theta (θ) is the fraction of the linking potential that is actually used at t, and INERtrepresents the allowances issued to new entrants from the New Entrants Reserve.

Firms could decide not to utilize the linking directive completely, especially when the EUA cap is more than sufficient by itself. For example, in 2008 81.7 MtCO2e worth of ‘Kyoto

credits’ were used to offset emissions under EU ETS (EC, 2009). This represents around 30% of the total linking potential. To allow for variable usage of the linking directive the theta (θ) is included as an input parameter and set to 0.3 for 2008, based on the emissions data by the EU (EC, 2009).

A New Entrants Reserve (NER) was introduced to distribute allowances to new installations and new entrants to the EU ETS. Five percent of all allowances over Phase II and III are reserved in the NER. For Phase II this amounts to around 104 MtCO2 worth of allowances on

an annual basis. Essentially the introduction of the NER implies that only 95% of the original cap can be freely traded. When allowances are issued from the NER to new installations, more allowances become available to the market. Assuming that installations are added to the scheme in the beginning of the year, the full 5% is still in the reserve at the beginning of either Phase II or Phase III. The reserve is then distributed equally over the remaining years in each of the Phases, until the reserve is depleted in the last year. An overview of the assumed development of the NER is given in Table 4.1. Here NER represents the number of allowances that are still in the reserve at the beginning of year t. The annual growth in the number of allowances issued from the NER (INERt) is shown in the third row. Finally, the growth in emissions (NEt) is shown in the last row and is assumed to be equal to one third of INERt, based on estimations by the Deutsche Bank (2008). Installations that are replaced or

(16)

exercise”, it is assumed here that indeed two thirds of all NER allowances are distributed for

the purpose of replacement.

Table 4.1:The NER in MtCO2e during Phase II and III

Phase II Phase III

Year 2008 2009 2010 2011 2012 2013* 2014 2015 2016 2017 2018 2019 2020

NER 104.0 83.2 62.4 41.6 20.8 96.0 84.0 72.0 60.0 48.0 36.0 24.0 12.0

INERt 0.0 20.8 20.8 20.8 20.8 20.8 12.0 12.0 12.0 12.0 12.0 12.0 12.0

NEt 0.0 6.9 6.9 6.9 6.9 6.9 4.0 4.0 4.0 4.0 4.0 4.0 4.0

*A new NER is formed. The average annual cap over Phase III is 1921 MtCO2; the NER is 5% of the cap

The NER will presumably suffice to supply allowances to individual installations. However, considering the EU’s ambition to increase the coverage of the scheme by including e.g. the aviation sector, it is hard to believe that the NER will continue to be the sole provider of allowances to new entrants. Most likely, new NER allowances will be made available and issued. In our model, however, the potential effects of the expansion of the EU ETS across more sectors is not taken into account.

Finally, the annual reduction of the cap with 1.74 percentage points during Phase III (2013-2020) should be considered. Therefore, the formula looks slightly different as of 2013 as the cap starts to decline:

[

]

t t i i t i t t CAP LP PC INER NCAP =

∑

∗ + ∗ − + = − ) 1 ( ) 1 ( 30 1 1 θ (2)

Here, PC is the annual decline in the cap as a fraction of the previous year in year t.

4.2. Allowance Demand

Because the supply of allowances is mainly politically driven, this is taken as a controllable assumption. The story is entirely different for the demand for allowances as it is mainly driven by market forces, which makes demand more volatile by nature than allowance supply. Total demand for allowances can be written as:

t t t t t GCO EG CI NE GCO = ₋1*(1+ )*(1− )+ (3)

Where GCO represents the gross carbon output in year t. The gross carbon output is _t

dependent on the gross carbon output in the previous year and economic growth (EG ), the _t

change in the carbon intensity of the economy (CI ) and new entrants (_t NE ) in year t. _t

The natural starting point is the level of CO2 emissions in the base year, the Gross Carbon

Output (GCO ). In 2008, CO2t emissions within the EU ETS (excluding Iceland) totalled around 2,118 Mt/CO2 (European Commission, 2009).

(17)

economies to cleaner and more energy efficient service economies over the last decades. Consequently, the carbon intensity7 of the economy decreased significantly. Other factors, such as rising fuel prices, increased environmental awareness and technological progress, have also contributed to the decreasing carbon intensity in Western Europe. As these factors continue to play an important role, the carbon intensity is expected to decline further along its current path, even if we control for the potential effects of the EU ETS. Therefore, a distinction is made in the model between the carbon reduction that is incentivised by the EU ETS and reduction that is incentivised by other factors. In the model we assume that the latter type of abatement is independent of the scarcity of allowances under the EU ETS. Therefore it is termed ‘autonomous abatement’ and treated as an input for the model.

It is important to make a distinction between carbon reduction that is incentivised by the EU ETS and the carbon reduction that is not, because both types have opposing effects on the EUA price. While reductions that are incentivised by the EU ETS are the result of allowance scarcity and therefore support the price of EUAs, autonomous reductions merely reduce allowance demand and put downward pressure on the EUA price.

Based on historical data, the autonomous decline in the carbon intensity can be analysed using the Kaya equation. The Kaya equation allows to separate the carbon intensity into multiple factors. Mathematically, the carbon intensity at t can be written as follows:

t t t t t t t GDP TOE TOE CO GDP CO CI = 2 = 2 × (4)

Where CO2 is the level of CO_t 2 emissions, TOE is the use of energy (denoted in Tonne of t Oil Equivalent) and GDP is national, or in this case European, income at t. The first term _t

essentially denotes the development of the carbon intensity of energy usage (CE ), while the _t

second term denotes the energy intensity of the economy (EI ): _t

t t t TOE CO CE = 2 (5) t t t GDP TOE EI = (6)

A one percent decrease in the carbon intensity from one year to the next would effectively mean that for every euro earned, one percent less CO2 is emitted. This is equivalent to a one

percent decrease in emissions under the EU ETS, assuming that the decrease in carbon intensity is evenly distributed throughout all sectors of the economy.

Finally, the last term of equation (3) represents the growth in demand for allowances from new entrants. See Table 4.1 for the estimated magnitude of NE over time. t

7

(18)

4.3. The Allowance Balance

After developing an identity for both supply and demand, we arrive at a measure of scarcity of allowances in the market in year t, termed the Gross Allowance Balance (GAB ): _t

t t

t NCAP GCO

GAB = − (7)

If the net cap at t is larger than the gross carbon output, the market for allowances is long, while the market is short if the net cap is smaller than the gross carbon output. The GAB can be defined as the scarcity of allowances in the market as determined by macro-economic and political forces at t. The next step is to look at banking behaviour by firms under the scheme. If the market is long in year t the banking behaviour is straightforward: all allowances in excess over those used immediately are banked and stored for later use. However, if the market is short, incumbents are faced with an inevitable choice: either some firms will have to rely on banked allowances, or carbon will have to be abated. The Net Allowance Balance

(NAB ) can therefore be defined as: _t

t t t GAB

NAB =

α

(8)

where

α

_t represents the extent to which companies choose to abate carbon emissions over using banked allowances. The exact level of

α

_t is dependent on the price of EUAs. Although individual banking behaviour is essentially a micro-economic optimization problem, a simplified approach will be used here as it is hard to accurately model the banking behaviour of all individual actors. The simplified approach rests on a few basic rules that the market will follow.

For example, consider a market price for allowances that is equal to the non-compliance penalty (NCP ) of €100. Now companies will rely as much as possible on banked allowances. t Individual actors will do this because each used banked allowance will save them the full opportunity cost of €100. Alternatively, if the price is €0, using banked allowances represents the highest opportunity cost. Therefore, using banked allowances is completely avoided when the price drops to €0. In the model, we assume that usage of banked allowances in year t depends on the price of allowances, and that usage increases linearly as the price goes up. Therefore, usage of banked allowances can be defined as:

t t t NCP P₋₁ =

α

(9)

To avoid a circular reference,

α

t is a function of the EUA price at t-1 instead of the EUA price at t.8 For example, if the price of an allowance is €40 in 2012, 40% of the GAB in 2013 t will be fulfilled by using banked allowances, while 60% of the GAB needs to be abated. t

8_{Ideally, α}

t is a function of bothP_t and future expectations. Unfortunately, Excel does not allow performing

(19)

Of course, banked allowances can only be used to the extent to which they are available. Therefore, more specifically, if sufficient banked allowances are available:

t t t GAB UBA =(1−

α

) (10) t t t GAB NAB =

α

(11) t t t BA UBA BA = ₋₁− (12)

Where UBA represents the Used Banked Allowances, and t BA is the stock of banked t allowances at t. If banked allowances are not sufficiently available, the following formulas hold: 1 − = t t BA UBA (13) 1 − − = t t t GAB BA NAB (14) 0 = t BA (15)

This concludes the first part of the model, covering demand and supply of allowances and banking behaviour. Figure 4.1 shows a schematic overview of the model as is explained up to this point.

Figure 4.1: Flowchart of demand, supply and banking

Yes No Yes No t t t NCAP GCO GAB = − Shortage ? 0 < t GAB t PC i t LP

θ

t t BA t t t

NCP

P

₋₁

=

α

Sufficient Banked Allowances

(20)

Table 4.2: Explanatory table to Figure 4.1

Variable Units Description Page

t

BA MtCO2 Banked Allowances at t 19

i t

CAP −1 MtCO2 Emissions cap for country i in year t-1 15

t

CE %/100 The carbon intensity of energy usage in year t 17

t

CI %/100 The Carbon Intensity in year t 16

t

EG %/100 Economic growth in year t 16

t

EI %/100 The energy intensity of the economy in year t 17

t

GAB MtCO2 The gross allowance balance 18

1

−

t

GCO MtCO2 Gross carbon output in year t-1 16

t

INER MtCO2 Amount of allowance issued from the NER in year t 15

t

NAB MtCO2 The net allowance balance 19

t

NCAP MtCO2 The Net cap in year t; all allowances issued in year t 15

t

NCP € The non-compliance penalty 18

t

NE MtCO2 New Entrants at t 16

t

PC %/100 Percentage change in the cap in year t 16

i t

LP %/100 Linking (as % of the cap) for country i in year t 15

t

UBA MtCO2 Used Banked Allowances in year t 19

t

α %/100 Part of the gross shortage (GAB) which will be abated 18

t

θ %/100 Fraction of linking potential used in year t 15

Legend:

Input parameter Decision statement Direct relation

4.4. The Marginal Cost of Abatement

The model above outlined the methodology to calculate the shortage of allowances in the market. Participants, however, are not able to borrow allowances from future periods for immediate use. Therefore, any resulting shortage of allowances is in effect unsustainable. In general firms have five options when facing an immediate shortage. In order of attractiveness:

- Investing in carbon abatement;

- Paying the non-compliance penalty;

- Cutting production;

- Moving to a non-EU ETS country (carbon leakage);

- Going out of business.

(21)

However, if enough abatement opportunities are available then, on economic principle, those opportunities that are available against the lowest marginal abatement cost will be used first. Companies that have such an opportunity are only willing to pay for abatement if the market price for an allowance is equal or higher than the cost of abatement per tonne of CO2 abated.

If the market is short, bidding for allowances will therefore continue until enough abatement opportunities become economically viable to drive the market in equilibrium. If significant shortages continue to exist over multiple years, the price of allowances would consequently be expected to move upwards continuously as businesses will have to pursue ever more expensive abatement opportunities.

Figure 4.2 below clearly illustrates this principle. The graph on the right-hand side illustrates all abatement potential which is available to the trading sectors under EU ETS, ordered by the abatement costs per tonne of carbon abated. The horizontal axis can therefore be interpreted as the total cumulative abatement over time, as firms are forced to use ever more expensive technologies to reduce their carbon emissions. Note however that, for illustrative purposes, this figure is a simplified version of the actual carbon abatement cost curve that will be used in this study. If we assume that the market experienced a shortage of allowances equal to

Figure 4.2: From carbon abatement to an allowance price

100 MtCO2 (scenario A), the corresponding EUA price would therefore be around €17, while

the corresponding market price of allowances would lie around €27 when the cumulative shortage over time equals roughly 600 MtCO2 (scenario B).

The main lesson of this example is that the price of an allowance is controlled by the availability of alternatives. The more low-cost abatement opportunities are available to participants, the lower the corresponding allowance price. However, the availability and price of abatement opportunities is not static, but dependent on the various factors. Assuming that we know the price and the amount of capacity installed for each technology in the base year, the development of the price can be characterized by the following formula:

(22)

Here, MC_tk is the marginal cost of abatement per tonne of CO2 for technology k in year t. The

marginal cost of technology k at t is dependent on the marginal cost in the base year and the capacity driven learning rate for technology k, LR . The capacity driven learning rate k

determines the rate against which the marginal cost decreases with every doubling of installed capacity. Therefore we also need to know how many times the installed capacity has doubled compared to the installed capacity in the base year (µ_tk). Because,

k t k t k t

I

NI

=

₌₀

×

2

µ (17)

)

(

log

0 2 k t k t k t

I

NI

=

µ

(18)

WhereI_tk₌₀ is the already installed capacity in the base year andNI is the cumulative newly _tk

installed abatement capacity of technology k since the base year, at the beginning of year t. WhileI_tk₌₀is known beforehand, the newly installed capacity at t, NI , is a function of both _tk

the abatement effort within Europe, as well as the abatement effort in the rest of the world. If we assume free knowledge transfer, then,

k t ROW k t ETS k t

IAC

NI

=

+

(19) Here, k t ETS

IAC is the cumulative newly installed abatement capacity of technology k within the

EU ETS and k t ROW

IAC is the cumulative newly installed abatement capacity by the rest of the

world at t. Because the abatement effort by the rest of the world is not affected by EU ETS, we will treat it as an exogenously determined parameter, while k

t ETS

IAC is dependent on the

level of scarcity of allowances and the relative cost of technology k to other available technologies.

As the usage of abatement capacity grows, the total capacity installed grows. The higher the total capacity installed at t, the higher k

t

µ , leading to a lower marginal cost for technology k at t if the learning rate is positive. In some instances the learning rate could also be negative (i.e. the marginal cost of abatement increases as the installed capacity grows). Prime examples are efficiency or process improvements. In these cases, initial carbon abatement is relatively cheap because efficiency improvements are easily identified. However, as more efficiency improvements are pursued, the relative cost goes up as finding and capitalizing on these opportunities becomes increasingly difficult.

(23)

) ( ) ( ) 1 ( 0 t BAU k r BAU t k o k k t k t MC LR O O r r MC = ₌ × − µ +ε − +ε − (20)

Whereε_okis technology k’s sensitivity to a one euro increase of the oil price. O is the oil price _t

at t, andO_BAU is the oil price assumed in the McKinsey BAU (Business-As-Usual) scenario.

Likewise,

ε

rk is technology k’s sensitivity to a one percent increase of the interest rate, where t

r is the interest rate at t, and r_BAU is the interest rate in the BAU scenario.

McKinsey (2009a) notes, in its study on the abatement cost curve, that “an increase in the energy prices reduces the average cost of abatement by making energy efficiency opportunities more profitable and a switch to alternative energy sources cheaper.” In its

BAU estimates McKinsey assumes an oil price of €60 per barrel and concludes that if the oil price is increased by €10 and other energy prices increase proportionately, the average abatement cost, decreases by €4.48 per tonne of CO2 abated.

Although this rule of thumb is useful, the effect of a changing oil price can be quite different for individual abatement technologies. For example, while energy efficiency measures become more attractive under a rising oil price, CCS becomes less attractive as a result of higher capital requirements and lower power plant efficiency. However, individual correlations between abatement opportunities and the oil price are not given by McKinsey. Therefore we make a distinction between those technologies that result in a higher dependence on oil, coal and gas and those that result in equal or a lower dependence.9 Technologies that result in an equal dependence on oil, coal or gas are assumed to be uncorrelated with the oil price. For all the other technologies,

ε

_ok, has been set such that on average McKinsey’s rule of thumb holds.

More specifically, the abatement costs of technologies that are positively correlated with the price of oil increase by €8.28 for every €10 increase in the price or oil. Alternatively, the costs of technologies that are negatively correlated with the oil price decrease by €8.28 for every €10 increase in the price of oil.

ε

_ok remains constant over time.

Similar to the oil price, the costs of an abatement project are highly dependent on the project’s financing. In its BAU estimates McKinsey (2009a) takes a “societal perspective” on the cost

of abatement. In other words, the abatement costs reflect the costs to society, net of taxes and subsidies. Therefore it is assumed that all projects are financed against a fixed government bond rate of 4%. However, private companies are generally unable to borrow against the government bond rate. Therefore, we assume that all firms participating in EU ETS finance their abatement projects against an interest rate of 10%. As a rule of thumb, McKinsey (2009a) states that the “average abatement cost increases by approximately €7 per tCO2e for every 5 percentage points increase in the interest rate.´ The rule of thumb implies

that k =1.40 r

ε

. Because an interest rate of 10% is assumed in our model, the average abatement costs are €8.40 higher than the average abatement costs in the McKinsey BAU scenario.

9_{The underlying assumption is that the prices of all of these commodities are correlated to each other and that}

(24)

4.5. The Fundamental EUA Price

In sections 4.1-4.3 an algorithm was developed to calculate the scarcity of allowances. Subsequently, in section 4.4, a methodology was laid out to calculate the costs of various abatement opportunities. Therefore, the basic ingredients to determine the fundamental EUA price are known as both the necessary level of abatement and the costs of abatement are known.

An element that is still missing is a decision algorithm to determine which technology determines the price. Therefore, we need to know the readily available abatement capacity of technology k at t. Assuming that the cumulative abatement capacity of technology k in the final year of the forecast is known, the available abatement potential at t is:

k t ETS k k t k t CAC IAC AC =

δ

− (21)

WhereACtk is the available abatement capacity of technology k at t in MtCO2e. k

CAC is the cumulative abatement capacity of technology k in the final year of the forecast (2030) and δ_tk is the proportion of cumulative abatement capacity available at t. Finally, the cumulative capacity installed at the beginning of year t is subtracted. By definition, the second term is always smaller or equal than the first term, so the available abatement potential in MtCO2 at t

is either positive or zero. k

δ

versus time is essentially the growth path along which abatement capacity becomes available. For example, while considerable abatement potential is already available in the form of solar or wind energy, CCS will only become a potential abatement technology once the technology becomes available to commercial parties on a large scale. Currently the development of CCS is limited to a number of heavily subsidized demonstration projects. While awaiting the results of these projects, it is unlikely that the EU will allow any market driven installation of CCS. Therefore, it is assumed in the model that currently no CCS abatement potential is available (

δ

kis still 0%). By 2030, however, CCS abatement potential is expected to be available to the industry on a large scale (a highCACk).

As mentioned in section 4.4, the least expensive abatement opportunity is used first, and more expensive technologies will be implemented in ascending order, until the following equation holds: ) .... ( _t1 _t2 _tn t AC AC AC NAB = + + + (22)

(25)

WhereMC_tnrepresents the marginal cost of the last tonne of CO2 abated in year t.

While formula 23 is the general rule, the EUA price deviates fromMC in three cases. First of _tn

all,

IfNABt =0; Pt =0 (24)

If the market for allowances is either long or in balance at t, the price drops to €0 as there is no ground for a fundamental EUA price. Note however, that the fundamental EUA price is the price of an allowance without considering the effects of arbitrage and speculation. While these forces may prevent the price from immediately falling to €0, the fundamental price cannot be higher than €0 if allowances are not in scarce supply. Secondly,

IfMC_tn <0; P_t =0 (25)

If the market is short, but the marginal abatement cost of the last tonne of CO2 abated in year t

is negative, the price is €0. Over the lifetime of several abatement technologies the savings from technological or efficiency improvements are greater than the overall costs per tonne of CO2 abated. Therefore the marginal abatement cost per tonne of CO2 abated is negative, and

the price of an allowance will equal zero. Finally,

If ( ) 1

∑

= > k k k t t AC NAB ; P_t = NCP_t (26)

If the sum of the total abatement capacity in year t is smaller than the shortage of allowances, some companies will be forced to pay the penalty. The price will therefore equal the non-compliance penalty. The market will consequently remain short. This shortage will be transferred to the next year in which new abatement potential becomes available. This process continues until enough abatement potential is on stream to absorb the complete scarcity of allowances.

From formula 22 we know that the total abatement in year t is

) .... ( ) ( 1 2 1 n t t t k k k t used AC AC AC AC = + + +

∑

= (27) Where k t used

AC is the capacity of technology k that is used to offset the scarcity of allowances in

year t. Similarly, all abatement activity that takes place at t-1, will consequently lead to a lower level of emissions at t. Therefore, we have to add one extra term to equation 3:

∑

= − − + − + − = k k k t used t t t t t GCO EG CI NE AC GCO 1 1 1*(1 )*(1 ) ( ) (28)

(26)

Figure 4.3: The complete deterministic fundamental EUA price model No Yes No Yes No ) ( ) ( ) 1 ( 0 t BAU n r BAU t n o n n t n t MC LR O O r r MC = × − tn + − + − = µ

ε

k t ETS k k t k t

CAC

IAC

AC

=

δ

−

) ( log 0 2 k t k t k t I NI = = µ n t MC₌₀ LRn εon Ot n r

ε

rt k t I₌₀ k t

δ

k

CAC

) .... ( 1 2 n t t t t AC AC AC NAB ≡ + + + ? 0 > t NAB Yes No 0 = t P ? 0 < n t MC ? ) ( 1

∑

= > k k k t t AC NAB Yes t t NCP P = Yes n t t MC P = No t t t NCAP GCO GAB = − Shortage ? 0 < t GAB t PC i t LP

Stochastic EUA Price Forecasting