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Liberalization of electricity markets has increasingly created the need for understanding the volatility and correlation structure between electricity, financial and energy commodity markets. This work reveals the existence of structural changes in correlation patterns among these markets and links the changes to both fundamentals and regulatory conditions prevailing in the markets, as well as the current European financial crisis. We apply a Dynamic Conditional Correlation (DCC) GARCH model to a set of market’s fundamental variables, related commodity markets and Greece’s financial market and microeconomic indexes to study their interaction. Emphasis is given on the period of severe financial crisis of the Country to understand “contagion” and volatility spillover between these markets. This approach enables us to capture the changing co-movement of assets within and between markets (financial, commodity, electricity) as market conditions change. The main results are that there is strong evidence of volatility spillover (or co-volatility) between financial and commodity market, while the Greek electricity market seems to be almost “isolated” from these two markets.

In the financial and Commodity markets, conditional volatility models have found an extensive application. However the studies focusing on modeling the spillover of price conditional volatility between financial, energy (commodity) and wholesale electricity markets in Europe are very few. We provide first a brief literature review.

The transmission of price volatilities between two natural gas markets, the British and Belgium ones, is investigated by Bermejo-Apricio et al., (2008) [

The interaction between gas spot prices at Zeebrugge, one month-ahead Brent Oil Prices and temperature, for period 2000-2005, is examined in the work of Regnard and Zokoian (2011) [

The interaction between Brent Oil and NBP spot price returns is estimated by Asche et al. (2009) [

The volatility spillovers between the CO_{2}, Brent Oil and gas markets in Europe, is the main theme of the paper by Chevallier (2012) [_{2} price series daily futures for the December 2008 contract are used. Daily NYMEX Crude Oil futures and Zeebrugge next month contract prices are used in Chevallier (2012) [_{2} is from −0.2 to over 0.1.

Commodity prices i.e. gas, oil, coal as well as electricity have a strong effect in the determination of Carbon prices, in Phase I of the EU ETS, as shown in the papers of Mansanet-Bataller et al. (2011) [

Yearly compliance events combined with Regulatory (institutional) and the macroeconomic uncertainties in EUA market have a strong influence on dynamic development of EUA price volatility (Chevallier, 2011a) [

Bredin and Muckley (2011) [

Phase II the Carbon-energy Co-movement is reinforced, in parallel with a structural increase in correlation patterns.

Another group of literature is concentrated on the mutual interactions between Carbon and Energy market, considering the bi-directional influence. By using a cointegrated VAR method, Bunn and Fezzi (2009) [

Granger causality tests were performed by Keppler and Mansanet-Bataller (2010) [

Volatility spillover between Carbon and Energy was examined by Mansanet-Bataller and Soriano (2009) [

Moreover, Koch, N. (2014) [

The linkage between EUA and Financial markets as described in Koch’s [

We share Koch’s [

We must note that in this study, we refer as “financial crisis” to the Subprime mortgage crisis, which spans from 2008 to late 2009 in our sample, and as “Greek debt crisis” to the European sovereign debt crisis of late 2009.

The rest of the paper is organized as follows. In Section 2 we describe the macroeconomic risk factors and stretch the significance of volatility spillover or co-movement, between 3 different markets: financial, energy commodity and Power (electricity) markets. The used data sets and a short description of the Greek electricity market and financial market are given in Section 3. Section 4 provides all necessary information on the methodology (DCC, CCC etc) used in this work and finally the empirical findings are presented in Section 5 followed by Conclusions in Section 6.

The importance of macroeconomic risk factors in shaping the expectations of the equity, bond and commodity markets, has been “stressed” by Fama and French (1989) [

The operational behavior that links fuel and EUA is the generator’s fuel-switching. This is so because a higher gas (coal) price ends up to a higher (lower) eua:

ngasUK ↑ theneua ↑ coal ↑ theneua ↑

This observation is a good theoretical basis for explaining the co-movement or the Dynamic Conditional Correlation between input fuel prices and eua. A producer of electric power uses hydrocarbon fuels and eua as production inputs, so he depends on these “assets”. This situation is not the same as in a financial market in which a portfolio manager can diversify his assets portfolio by altering the (percentage) share of the assets, in order to protect the value of the portfolio from price changes (hedging). The power producer is exposed to changes in prices in electricity, energy (commodity) and EUA markets. Therefore, the risk-averse Power Plant Owner (producer) has to operate in forward (futures) markets for hedging his profits against the risk of unpredictable and unfavorable price volatility. In other words he tries to lock in a given profit based on a given (assumed) marginal generation cost.

However, the key variables in a futures market are the price volatility of an “asset” (input fuel, eua etc.) and its co-movement with other relevant asset’s price. This co-movement is measured by its conditional covariance or correlation price volatility is usually expressed as conditional variance.

Following Koening, P. (2011) [_{i}, in €/GJ_{e} of generating a given unit of power, by using as input fuel i:

M C i = F C i n i + E F i n i E C (1)

where F C i is the fuel cost in €/GJ, n i is the power plant net thermal efficiency in GJ_{e}/GJ (GJ_{e} is the power output in gigajoule of electricity, GJ the power input in gigajoule of fuel), E F i the Green House Gas (GHG) emission factor in kg CO_{2}/GJ and EC is the GHG emission cost in €/kg CO_{2}. Equation (1) is actually a simplification and M C i is primarily estimated by the variable costs of fuel and CO_{2}.

The variance of M C i is given by (Koening, P., 2011) [

σ M C i 2 = 1 n i 2 σ F C i 2 + E F i 2 n i 2 σ E C 2 + 2 1 n i E F i n i ρ F C i , E C σ F C i σ E C (2)

where ρ F C i , E C is the correlation of input fuels and eua and σ i 2 are variances. Equation (2) is a risk measure, related to M C i . In this paper will show that the pairwise correlations between electricity, fuel and eua are time-varying and also will examine how the volatility in Energy commodity markets in combination with volatility in financial markets affect the above conditional correlations.

The optimal merit order of power generation is affected by changes in the relative price of input fuels. These changes ultimately result in a fuel-switch, by the power generator which tries to maximize its profit. Fuel-switching is not an observable operational variable and has to be inferred from changes occurred in the relative marginal costs.

From the above we conclude that the unobserved fuel-switching behavior by generators is the main factor of “producing” the correlation between input fuels (brent, ngasUK) and carbon emission allowances (eua). The empirical Carbon price moves between two extreme values, the upper bound theoretical switch price SP_{u} defined as the price of CO_{2} above which natural gas is the preferred input fuel (technology), no matter what the thermal characteristics of the generation mix (or plant portfolio) (Koening, P., 2011) [

S P u = n c o a l E F C g a s − n g a s I F C c o a l n g a s I E F c o a l E − n c o a l E E F g a s I (3)

where n c o a l E and E F c o a l E are the thermal efficiency and emission factor of the most efficient coal fired power plant in a Country’s generation mix (plant portfolio). The thermal efficiency and emission factor of the most inefficient gas fired power plant are n g a s I , E F g a s I respectively. Therefore, if the price of carbon increases then it will motivate generators to switch input fuels from Coal (Lignite) to gas. As soon as CO_{2} price has attained SP_{u}, even generators that have a choice between the most inefficient gas and most efficient Coal plant, will have, at the end, to “move” to natural gas generation. So, there is no other technology feasible generation mix which prefers coal over gas generation. An electricity producer, a profit maximizing “rational” market player, will switch generation from using Coal (lignite) to using natural gas, just in the case of the empirical emission price exceeds the SP_{u}.

The lower bound theoretical switch price, SP_{l}, is the price of Carbon below which Coal is the preferred input fuel, irrespective of the thermal characteristics of the generation mix (Koening, P., 2011) [

S P l = n c o a l I F C g a s − n g a s E F C c o a l n g a s E E F c o a l I − n c o a l I E F g a s E (4)

where n c o a l I , E F c o a l I the thermal efficiency and emission factor, respectively, of the most inefficient coal fired plant in a Country’s generation mix. n g a s E and E F g a s E are the thermal efficiency and emission factor, respectively, of the most efficient natural gas fired plant in the Country’s generation mix.

Thus, if the Carbon price decreases it will give the motivation to generator to switch input fuels from natural gas to Coal power generation. When carbon price reaches SP_{l}, all generation “players” will have to switch to Coal, even though they have the choice between the most inefficient Coal and the most efficient natural gas plant.

From the above, the main conclusion is that a higher share of Coal production (Lignite in the case of Greece), rationally, will increase the demand for Carbon emission allowances (eua) and its price will go upwards again.

Combining all the above the empirically observed EUA (eua time series) is expected to move between the two time-varying extreme values, SP_{l} and SP_{u}. From the definitions given by (3) and (4), two correlation regimes are possible between eua and other commodities (ngasUK, Brent, Coal, Lignite). The first is when eua (empirical carbon price) either exceeds SP_{u} or falls below SP_{l}, a situation referred as Static merit order. In this case either natural gas or Coal is clearly the preferred input fuels and small changes in their prices do not change the merit order. In this case there is no financial motivation to switch input fuels, which results in an unchanged demand for eua and eua therefore fuel prices are decoupled. The second correlation regime is when eua is between SP_{l} and SP_{u}.

Here we have a mixed merit order in which there is no clear ranking of the input fuels in the merit order and the crucial now factor in choosing one of the two fuels is their thermal efficiencies. This is a situation where small fuel price changes have a strong influence in the merit order, which in turn result in changes of demand for eua. This fuel and eua prices are coupled (or co-move). The coupling and decoupling of eua and fuel prices have been studied in depth by Koening P. (Koening, P., 2011 [

In theory, the equilibrium allowance price is equal to the marginal abatement costs incurred to reduce one ton of pollutant (Springer, 2003) [

A rational abatement method is the fuel switching (Delarue, E. et al., 2008) [

Koch, N. (2014) [

It is well known that macroeconomic conditions (economic growth) affect heavily both EUA and financial markets. An increased demand and raised industrial production is the result of high economic activity, which in turn increases Carbon emissions therefore increases EUA (Ellerman and Buchner, 2008) [

The Carbon market, therefore, can be characterized as a peculiar market, not influenced heavily be macroeconomic variables, and that the supply and demand of allowances is the main mechanism setting the equilibrium prices.

On the other hand, Borak et al. (2006) [

The Stock market effect of the EU ETS is examined also by Veith et al. (2009) [

The way with which the inclusion of EUAs in an assets portfolio improves the investment opportunity is examined by Mansanet-Bataller (2011) [

Low electricity prices encourage higher electricity consumption, resulting in higher CO_{2} emissions. Therefore the demand for allowances may increase in case electricity utilities are not in compliance with their initial allocation, a fact that in turn exerts strong pressure of the EUA markets. A further consequence is that the increase in CO_{2} prices and generation costs may increase electricity prices creating the need for a demand adjustment, which of course implies some level of price elasticity.

Observed power and CO_{2} prices are influenced also by fuel prices. If the prices of natural gas are increased then there is a strong incentive for generating base-load electricity by using more Coal―or Lignite fired-Plants, driving up, in turn, the demand for CO_{2} allowances. It is worth to mention here that Coal-fired generating units emit almost twice as much CO_{2} as natural gas generating units. If the situation just described is sustained and the supply of allowances is not adequate, CO_{2} prices may increase at a level that result in a fuel switch i.e. natural gas, a cleaner fuel. This “cause and effect” relationship has predicted a lot of the early CO_{2} price volatility due to the switching from Coal (Lignite) to gas. Using the cointegration approach, Bunn and Fezzi (2007) [

In this paper we consider daily data covering the period for April, 2008 to March 2014, a total of 2160 observations. The analysis period is divided into 2 periods: a) the Subprime Crisis period (from April 2008 until the end of 2009) and b) the Greek Government Debt Crisis (early 2010 until April 4, 2011). The two periods correspond to the two shaded areas in the DCC plots (Section 5.2). The chosen sampling frequency produce sufficient number of data required to measure the dynamics of correlations which may vary due to periods of financial turmoil of differing durations. The price data are denominated in the local currency of each market. To enhance our choice of data frequency, we point out that from an EU ETS participant point of view, caring for his risk management, high frequency (here daily) correlations are more useful that long-term correlations. The data sets are obtained from various resources, Athens Stock Exchange (ASE), Independent Power Transmission Operator (IPTO), Intercontinental Exchange (ICE) Futures Europe, Energy Information Administration (EIA) and Bloomberg.

The three phases of the EU ETS, corresponding to the three compliance periods are Phase I: 2005-2007, Phase II: 2008-2012 and Phase III: 2013-2020. The pilot period of the EU ETS is the well-known to market participants Phase I. The National Allocation Plans (NAPs) determine the overall emission cap for Phase I and Phase II. Each member state determines its NAP, defining actually the total permits and the allocation mode. NAPs are approved by European Commission (EC), which settles the overall cap. Because neither borrowing nor banking of EUA (EU Allowances) were allowed between Phase I and Phase II, the price for EUAs (series eua in this paper) issued for Phase I collapsed. The first information regarding the actual EUAs released in April 2006, however the market participants considered that the total emission cap for Phase I was not restrictive. Phases II and III are linked by banking, where the transactions of spare EUAs enlarges the time period considered by the agents when they shape their expectations about the overall shortage of EUAs. The Banking involvement reduces, therefore, the risk of an extreme collapse of the EUA price. But, if shocks happen they still can generate strong price and volatility fluctuations. Highly efficient EUA spot and derivative markets have evolved since 2005 and the most liquid derivative market is the European Climate Exchange (ICE/ECX, London), where 90% of the futures contracts are traded.

Description of the DataDaily settlement prices of EUA futures contracts (€/ton) traded on the ICE ECX are used to form a continuous price time series that combines a number of contracts expiring in Phase II and III (2008-2012 and 2013-2020), following the approach of Koch, N. (2014) [

We use daily spot price of Brent Oil traded in Euro/barrel. For natural gas historical 1 month ahead futures prices, traded at the National Balancing Point NBP Hub UK, expressed in €/MWh, are considered, obtained from ICE. Since the late 1990s, UK NBP Hub gas market is Europe’s longest established wholesale (spot-traded) market in operation (

and winters (October to March), as well as annual contracts.

Normally, contracts at NBP Hub are in pence sterling per therm. In this paper we convert the prices of all the time series to Euro per megawatt-hour (€/MWh), the standard in Europe, allowing us for a better understanding of co-variations

of prices. The appropriate conversion is 1 therm per 0.0293 MWh ICIS^{1}, and the conversion of pence sterling to Euro is according to the daily exchange rate published by the ECB (European Central Bank)^{2}.

There is no indigenous gas production in Greece and also there are no storage facilities (the LNG storage tanks are used exclusively for temporary LNG storage, the three entry points of natural gas to the National Natural Gas System (NNGS) of Greece are located at Sidirocastro, Greek Bulgarian pipeline, for the Russian gas, at Kipi, Greek-Turkish pipeline (BOTAS gas) and at the Revithoussa LNG terminal station. In Greece, the gas market is still organized on the basis of bilateral contracts between suppliers and eligible customers, so there is not any wholesale market yet. The Regulator (Regulatory Agency for Energy, RAE) of Greece published for the first time in 2011, the Weighted-Average Import Price (WAIP) of natural gas, on a monthly basis. This data on WAIP, considered together with the publication of data on daily prices of balancing gas, Daily Price of Balancing Gas (DPBG) or HTAE in Greek, on the Natural Gas TSO’s (DESFA) internet site, has greatly facilitate current and potential market participants in understanding the prevailing gas price dynamics. The

shows the monthly average System Marginal Price (SMP) of Greek Electricity Market (GEM), WAIP against the daily HTAE price for the same month (the daily HTAE price is kept constant over the entire month considered). Data

are published on RAE’s website^{3} and updated on a regular basis.

However we emphasize that our modeling is based on National’s Balancing Point Spot prices as we have mentioned before, since (

Greece’s liberalized electricity market was established according to the European Directive 96/92/EC and consists of two separate markets: 1) the Wholesale Energy and Ancillary Services Market and 2) the Capacity Assurance Market. The Greek wholesale electricity market (GEM) is currently in a transitional period, during which the market structure evolves towards its final design, namely the European Target Model. The wholesale electricity market is a day ahead mandatory pool which is subject to inter-zonal transmission constraints, unit technical constraints, reserve requirements, the interconnection Net Transfer Capacities (NTCs) and in general all system constraints. More specifically, based on forecasted demand, generators’ offers, suppliers’ bids, power stations’ availabilities, unpriced or must-run production (e.g., hydro power mandatory generation, cogeneration and RES outputs), schedules for interconnection as well as a

number of transmission system’s and power station’s technical constraints, an optimization process is followed in order to dispatch the power plant with the lower cost, both for energy and ancillary services.

LAGIE (the independent market operator) (http://www.lagie.gr/) is responsible for the solution of the so-called Day Ahead (optimization) problem. This problem is formulated as a security constrained unit commitment problem, and its solution is considered to be the optimum state of the system at which the social welfare is maximized for all 24 h of the next day simultaneously. This is possible through matching the energy to be absorbed with the energy injected into the system, i.e., matching supply and demand (according to each unit’s separate offers). The DA solution, therefore, determines the way of operation of each unit for each hour (dispatch period) of the dispatch day as well as the clearing price of the DA market’s components (energy and reserves).

More specifically in this pool, market “agents” participating in the Energy component of the day-ahead (DA) market submit offers (bids) on a daily basis. Producers and importers submit energy offers with the limitation that the weighted average of the offer should be above the unit Minimum Average Variable Cost. On the contrary exporters and load representatives submit load declarations. The bids are in the form of a 10-step stepwise monotonically increasing (decreasing) function of pairs of prices (€/MWh) and quantities (MWh) for each of the 24 h period of the next day. A single price and quantity pair for each category of reserve energy (primary, secondary and tertiary) is also submitted by generators. Deadline for offer submission is at 12.00 pm (“gate” closure time).

So, the DAS solution produces a 24 hour unit schedule and a unique price which is called the System’s Marginal Price (SMP). The Dispatch Scheduling (DS) is used to define the time period between Day Ahead Schedule (DAS) and Real Time Dispatch (RTD) where the producers have the chance to change their declarations whenever has been a problem regarding the availability of their units. In the RTD the units are re-dispatched in real time in order to meet the actual demand. Finally in the IS stage an Ex Post Imbalance Pricing (EXPIP) is produced after the dispatch day which is based on the actual demand and unit availability. The capacity assurance market is a procedure where each load representative is assigned a capacity adequacy obligation and each producer issues capacity availability tickets for its net capacity. Actually this mechanism is facing any adequacies in capacity and is in place for the partial recovery of capital costs. The most expensive unit dispatched determines the uniform pricing in the day-ahead market. In case of congestion problems and as a motive for driving new capacity investment, zonal pricing is a solution, but at the moment this approach has not been activated. Physical delivery transactions are bounded within the pool although market agents may be entering into bilateral financial contracts that are not currently in existence. The offers of the generators are capped by an upper price level of 150 €/MWh. Physical Transmission Rights (PTR) are explicitly allocated via auctions.

Not only the fundamentals but also the various Regulatory Market Reforms (RMRs), “imposed” by the Greek Regulatory for Energy (RAE), have a significant impact on the volatilities of energy and electric prices (RAE, 2009 to 2014 [

4th Reference Day (1.5.2008) (RMR5). Cost Recovery Mechanism, CRM, was considered by the Regulator a necessary step until the Imbalance Settlement Mechanism, ISM (scheduled for the 5th Reference Day). CRM states that if the SMP is lower than the marginal cost of generating Unit (plus 10%), then the Unit will receive the difference as a compensation. The Regulator expected that this Reform would have no effect on SMP. CRM was aiming to ensure that generators will be compensated at least their marginal cost, in case they were ordered to operate. The Cost Recovery Mechanism was abolished on 30th June 2014.

RMR6. Regulatory Market Reform, RMR6 (RAE’s Decision 1.1.2009), focused on the change of the ex-post SMP calculation methodology according to the unit commitment algorithm that considers all technical constraints of the units and the reserve requirements of the IPTO (ADMIE) expecting to lead to lower SMPs.

5th Reference Day (30.9.2010) (RMR7). Regulatory Market Reform, RMR7, initiated the mandatory day-ahead market model and introduced the Imbalances Settlement Mechanism retaining at the same time the SMP methodology allowing only the submission of demand declarations. RMR7 is referred to the adoption of an enhanced Unit commitment algorithm which co-optimizes energy as well as ancillary services. In this new mandatory, Day-Ahead market

model incorporating, at the same time, an Imbalance settlement mechanism^{4}, market clearance is now based on the non-priced demand declarations. Taking into account that the methodology for estimating SMP retained the same and the fact that usually the declared demands were underestimated, the effect of this reform expected to reduce SMP slightly.

RMR8. Regulatory Market Reform, RMR8 (Ministry of Finance Decision 1.9.2011), regards the decision of the Ministry of Finance (1.9.2011) to impose a new tax levy on natural gas, equal to 1.50 €/GJ (applied also to electricity generation). As SMP was set, for the majority of trading periods, by Natural Gas fired Units, the resulted increased generation cost was expected to increase SMP (see Section 6.1 for comments).

RMR9. Regulatory Market Reform, RMR9 (1.7.2013), Abolition of the “Plus 10% Rule”. This rule was embedded in Cost Recovery Mechanism (CRM) and allowed for a 10% increase of the boundary for generators to be compensated for generating costs.

RMR10. Regulatory Market Reform, RMR10 (31.12.2013), Abolition of the “30% Rule”. The “30% Rule” allows generators to offer 30% of their plant’s capacity at a price below its minimum variable cost, as long as the total weighted average of their bids is still at or above their minimum variable cost. This caused the extended dispatch of gas plants, pushing the expenses on cost-recovery significantly high. The regulator expected no changes on the SMP through this reform, it was imposed merely to improve the performance of the initial market design.

We have used the Athens Stock Exchange General Index (ase), denominated in Euro. In order to “capture” the independence-interaction of the Greek Stock market with the European financial market, especially during the financial crisis period (focusing on the European sovereign debt crisis in 2010), we have considered also the EURO STOXX 50 price index, in Euro, which covers 50 blue-chip stock from 12 European countries (Austria, Belgium, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, the Netherlands, Portugal and Spain). We choose this particular index, following Koch (2014) [

EURO STOXX 50 options, for the next 30 days. Measuring the so-call investor’s fear in case that it is larger than 30 indicates a large amount of volatility, reflecting the investor’s uncertainty or fear.

For bond, we use the 10-year Greek Government bond index (gbonds) (a long-term index), instead of a short-term index, because monetary policy (especially during the Greek debt Crisis) is more likely to have a confounding impact on the later index.

We include also in the financial data set the stock price of the dominant player in GEM, the incubator Public Power Corporation (PPC). We consider that by analyzing the dynamic evolution of this stock we “capture” the various effects of regulatory policy and fundamental changes, exerted by monetary (macroeconomic) policies to fix the Greek Public Debt problem as well as European Energy Policies.

We have to mention here that for the purposes of this paper, we have included EUA into the group of Energy commodity assets, although there are arguments about this like the work of Kanamura (2010) [

The equation or model of the Conditional mean or first moment is to detect and eliminate any serial correlation in the returns of price data. For a sequence

Name | Description | |
---|---|---|

Financial Data Set | ||

1 | ase: | Athens Stock Exchange General Index |

2 | stoxx: | European Stock 50 Index (Euro stoxx 50) |

3 | vstoxx: | European Stock 50 Volatility Index (vstoxx) |

4 | ppc: | Public Power Corporation (PPC) Stock price |

5 | gbonds: | Greek Government 10 year Bond yield |

Energy Commodities Data Set | ||

1 | eua: | European Union Allowance (EU Emissions Trading Scheme): ?tCO_{2} (Phase II) |

2 | ngas: | Natural gas price, NBP, UK ?MWh |

3 | brent: | Brent Oil price, ?bbl |

4 | Lignite price: | Lignite Fuel Cost of a “typical” Lignite-fired Power plant (?MWh) |

Power (Electricity) Data Set | ||

1 | smp: | Greek Electricity Market wholesale or System Marginal Price (ex-ante) (?MWh) |

2 | load: | Electricity load (Mw) (ex-post) |

of random variables { X t } the conditional mean (or conditional expectation), given its past values is defined as: E [ X | X t − 1 , X t − 2 , ⋯ , X t − j ] . As we will see in Section 5.1, by applying the Ljung-Box test statistics, there is strong evidence of significant serial correlation in the returns. Vector Autoregression (VAR) of lag order p is used in this paper to estimate the first moment.

Let r t symbolizes a k × 1 vector of returns at time t, r t = { r i , t } , where r i , t is the daily log returns, for i = 1 , ⋯ , k . The VAR(p) model is written as

r t = Φ 0 + ∑ j = 1 p Φ j r t − j + ε t or r t = Φ 0 + Φ 1 r t − 1 + ⋯ + Φ p r t − p + ε t (5)

where Φ 0 is a k × 1 vector of constants, Φ j k × k matrix of coefficients and ε t a k × 1 vector of residuals. The “optimum” lag length p of the VAR(p) can be found by minimizing the Akaike Information Criterion (AIC). The specification then of the “best” model, based on AIC, is accepted if the residual “pass” successfully a number of diagnostic tests (e.g. checking for remaining serial correlation).

As an example, let k = 3 , a trivariate model r = ( a s e , s t o x x , v s t o x x ) ′ and let p = 2 , lags, then (A) becomes

[ a s e , t s t o x x , t v s t o x x , t ] = [ Φ 1 , 0 Φ 2 , 0 Φ 3 , 0 ] + [ Φ 11 , 1 Φ 12 , 1 Φ 13 , 1 Φ 21 , 1 Φ 22 , 1 Φ 23 , 1 Φ 31 , 1 Φ 32 , 1 Φ 33 , 1 ] ⋅ [ a s e , t − 1 s t o x x , t − 1 v s t o x x , t − 1 ] + [ Φ 11 , 2 Φ 12 , 2 Φ 13 , 2 Φ 21 , 2 Φ 22 , 2 Φ 23 , 2 Φ 31 , 2 Φ 32 , 2 Φ 33 , 2 ] ⋅ [ a s e , t − 2 s t o x x , t − 2 v s t o x x , t − 2 ] + [ ε a s e , t ε s t o x x , t ε v s t o x x , t ]

Serially uncorrelated residuals are generated by a well-specified model for the first moment of the returns. However, heteroskedasticity (the time-varying variance of the residuals) will remain in the returns, as it is frequently the case in Energy and financial markets. This feature and the excess kurtosis in the returns call for the GARCH-type estimation approach (Engle, 1982 [

Let that the mean of a return time series follows an autoregressive of order p, AR(p), specification

r i , t = a o + ∑ j = 1 p a j r i , t − j + ε i , t (6)

where r i , t is the daily log returns of K time series for i = 1 , ⋯ , K , ε i , t is the residual of series i and a o the drift term.

Suppose that F t − 1 is the set of all available information about the process, up to the time t − 1 , then the conditional variance of the residual ε i , t is σ i , t 2 , so ε i , t | F t − 1 ~ N ( 0 , σ i , t 2 ) or ε i , t = σ i , t n t where n t ~ N I D ( 0 , 1 ) .

This ε i , t residual is fitted in the GARCH-type models, described below, to capture the dynamics of the conditional variance.

Let the evolution of the conditional variance in the generic univariate process for each asset, is written as

σ δ 2 = ω + ∑ p = 1 P α p | ε t − p | δ + ∑ o = 1 O γ o | ε t − o | δ I [ ε t − o < o ] + ∑ q = 1 Q β q σ t − q δ (7)

where δ is either 1 for threshold ARCH also known as AVGARCH, ZARCH (Taylor, 1986 [

σ t 2 = ω + α 1 ε t − 1 2 + γ 1 ε t − 1 2 I [ ε t − 1 < 0 ] + β 1 σ t − 1 2 (8)

where I [ ε t − 1 < 0 ] is an indicator function that takes the value 1 if ε t − 1 < 0 and 0 otherwise. This function takes care of the asymmetries of the impact on volatility the returns may have due to “good” or “bad” news. The parameters must be such that ω > 0 , α 1 ≥ 0 , α 1 + γ ≥ 0 and β 1 ≥ 0 , and for the covariance to be

stationary, α 1 + 1 2 γ 1 + β 1 < 1 (mean reverting model). In case α 1 + β 1 = 1 we

have an integrated model.

In estimating h i t from univariate volatility models, the BIC Schwartz Information Criterion is use to select suitable candidate models that capture the stylized facts of the asset return.

A multivariate GARCH(P,O,Q) is a natural extension of the univariate model, and allows for the time-varying correlations between two series, in addition to their conditional variances. To generate a vector of residuals (hopefully serially uncorrelated) we could use a Vector Autoregression model, VAR(p), to model the mean of a 11 ´ 1 vector consisting of the members of the financial, energy and power group of data set, given in

ε t = ( ε a s e , t , ε s t o x x , t , ε v s t o x x , t , ε p p c , t , ε g b o n d s , t , ε e u a , t , ε n g a s , t , ε b r e n t , t , ε s m p , t , , ε l i g n i t e , t , ε l o a d , , t ) ′

We also suppose that the underlying distribution of returns follows a conditional multivariate normal process, therefore we can write ε t | F t − 1 ~ N ( 0 , H t ) , where F t − 1 is a filtration i.e. an information set about the time series up to the time step t − 1 . Thus, the ε t is conditionally heteroskedastic, which means that ε t = H t ⋅ n t , where n t ~ N ( 0 , I ) an iid error process.

For modelling H t a number of specifications has been suggested, the most commonly mentioned is the generic VECH-model, developed by Bollerslev et al. (1986) [

In this paper will apply the parsimonious Dynamic Conditional Correlation (DCC) approach, developed by Engle (2002) [

According to the work of Engle and Sheppard (2001) [

H t = D t R t D t (9)

where D t a k × k diagonal matrix with elements σ i , t 2 on the ith diagonal representing the time-varying standard deviations which are generated by the GARCH models fitted on each residual series, as the ones given in Equation (7). R t is the time-varying conditional correlation matrix. In the case of CCC-model we have:

Model 1: H t = D t R D t (10)

R = ( ρ i j )

where R = Constant Conditional Correlation. The assumption that conditional correlations are constant is unrealistic in particular applications, although the estimation of CCC parameters is simpler. We use CCC hare as a benchmark for testing the consistency of correlations (see

The log-likelihood is our case, for the vector θ of parameters is given by

L ( θ ) = − 1 2 ∑ t = 1 T ( m log ( 2 π ) + 2 log ( | D t | ) + log ( | R t | ) + ξ ′ t R t − 1 ξ t ) (11)

where ξ t ~ N ( 0 , R t ) the standardized residuals, ξ t = ε t D t .

In case that the conditional distribution of ε t is not normal, Equation (9) is the Quasi-likelihood function. The dynamic correlation specification suggested by Engle and Sheppard (2001) [

Q t = ( 1 − ∑ j = 1 P α j − ∑ j = 1 Q β j ) Q ¯ + ∑ j = 1 P α j ( ξ t − j ξ ′ t − j ) + ∑ j = 1 Q β j Q t − j (12)

where Q ¯ is the k × k unconditional covariance matrix of the standardized residuals, generated from the first stage of the process. The extent to which ξ t affect the dynamics of the correlation is captured by the α j , while β j is a parameter measuring the decay in dynamics. If we plug α j = β j = 0 into (11), the CCC model of Bollerslev (1990) [

R t = Q t * − 1 Q t Q t * − 1 (13)

where Q t * is a diagonal matrix ( k × k ) consisting of the square root of the diagonal elements of Q t . Furthermore, the conditional covariance matrix R t of the residuals generated by VAR(p), is obtained by standardizing these residuals by the conditional variances, so a typical element of R t is

ρ i , j , t = q i , j , t q i , i , t q j , j , t (14)

In the framework of this paper estimation, the indices range as

i , j = a s e , s t o x x , v s t o x x , p p c , e u a , n g a s , b r e n t , s m p , l o a d , l i g n i t e

By letting P = Q = 1 in Equation (11) we obtained our DCC model 2 specification:

Model 2: Q t = ( 1 − α − β ) Q ¯ + α ( ξ t − 1 ξ ′ t − 1 ) + β Q t − 1 (15)

The matrix Q t is a symmetric positive matrix, α + β < 1 , and α is the news coefficient and β is the decay coefficient. According to Aielli (2011) [

ρ a s e , p p c , t = q a s e , p p c , t q a s e , p p c , t q a s e , p p c , t (16)

Therefore, by using model 2 above, we have

q a s e , p p c , t = ( 1 − α − β ) q ¯ a s e , p p c + α ( ξ a s e , t − 1 ξ ′ p p c , t − 1 ) + β q a s e , p p c , t − 1 (17)

q a s e , t = ( 1 − α − β ) q ¯ a s e + α ( ξ a s e , t − 1 2 ) + β q a s e , t − 1 (18)

q p p c , t = ( 1 − α − β ) q ¯ p p c + α ( ξ p p c , t − 1 2 ) + β q p p c , t − 1 (19)

Model 1 will be our basic reference model. This scalar DCC specification is the most parsimonious one because of the assumption that all commodities correlations “obey” the same ARMA(P,Q) type specification, which means that they are all governed by the same coefficients α and β . The above assumption might be a valid one, in the case of similar commodities (or “assets” in general), belonging in same asset category or class. However, in our case, our “assets” belong to different categories, namely financial, energy and power; therefore it is a reasonable assumption that these markets exhibit “asset” specific correlation sensitivities. To face this dissimilarity in asset’s class, a generalization of the DCC model has been suggested, incorporating also the impact of any asymmetries on the correlation dynamics. It is known that in a Markov Switching Model (MSM) or in a Threshold Autoregressive Model (TARM), the conditional correlations are allowed to have different evolutionary dynamics. Instead this is not the case for DCC model in which the correlations follow the same dynamics. This is a limitation of the DCC. For example, if the data exhibit structural breaks, DCC model can give misleading conclusions. Another limitation of DCC is that it does not work reliably for large number of assets. Cappielo et al. (2006) [

Engle (2002) [

Model 3: Q t = ( Q ¯ − A ′ Q ¯ A − B ′ Q ¯ B ) + A ′ ξ t − 1 ξ ′ t − 1 A + B ′ Q t − 1 B (20)

where A and B are k × k diagonal matrices of the parameters, A = { α i i } , B = { β i i } .

The positive definiteness requirement is satisfied by α i i + β i i < 1 and α i i , β i i ≥ 0 , ∀ i , j . The above specification tackles the dissimilarity of asset problem by allowing for a high degree of dissimilarity in correlations.

The advantage of G-DCC over the simple scalar DCC is that it can generate a variety of correlation patterns. The coefficients α i i can be considered for measuring the sensitivity of the correlation of asset i with other assets to correlation residuals (Hafner and Frances, 2003) [

Cappielo et al. (2006) [

Model 4: Q t = ( Q ¯ − A ′ Q ¯ A − B ′ Q ¯ B − G ′ N ¯ G ) + A ′ ξ t − 1 ξ ′ t − 1 A + B ′ Q t − 1 B + G ′ n t − 1 n ′ t − 1 G

(21)"

where G is a k × k diagonal matrix of parameters, G = { g i i } , n t = { n i , t } a k × 1 vector with n i , t = min ( ξ t , 0 ) , N ¯ is a k × k matrix of constants, N ¯ = T − 1 ∑ t = 1 T n t n ′ t .

Similarly as in model 3, the positive definiteness requirement is satisfied by α i i + β i i + n i k < 1 and α i i , β i i , n i ≥ 0 , for i = 1 , ⋯ , k where k is the maximum eigenvalue of Q ¯ N ¯ Q ¯ (Cappielo et al., 2006) [

Model 4 is further extended to include control (“exogenous”) variables Vargas (2008) [

By using that A ′ ∗ A = A 2 , B ′ ∗ B = B 2 etc., little algebra transforms model 3 into the following form

Q t = ( 1 − A 2 − B 2 ) Q ¯ + A 2 ξ t − 1 ξ ′ t − 1 + B 2 Q t − 1 + G 2 ( n t − 1 n ′ t − 1 − N ¯ ) (22)

In this subsection we present the empirical findings, while in Section 5.2 we comment on these findings in details.

The correlation matrix between levels of variables yields mostly “rational” results as expected. Financial assets in particular have moderately strong positive (between indexes and stocks) and negative (between bonds and stocks) correlations, and mostly low degree of correlations with energy commodities and electricity.

Price (level) Series | ase | stoxx | vstoxx | ppc | gbonds | eua | ngas | brent | lignite | smp | load | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Observations | 2160 | 2160 | 2160 | 2160 | 2160 | 2160 | 2160 | 2160 | 2160 | 2160 | 2160 | |

Mean | 1561.76 | 2703.01 | 27.40 | 8.81 | 12.19 | 12.16 | 21.71 | 95.24 | 33.69 | 56.05 | 5998.79 | |

Median | 1437.66 | 2710.37 | 24.40 | 9.55 | 10.15 | 12.90 | 23.50 | 105.78 | 35.10 | 52.49 | 5907.71 | |

Maximum | 4303.77 | 3882.28 | 85.44 | 21.92 | 37.10 | 31.71 | 36.91 | 143.95 | 48.53 | 123.77 | 8555.83 | |

Minimum | 476.36 | 1809.98 | 13.82 | 1.15 | 4.42 | 2.70 | 7.08 | 34.45 | 21.98 | 10.24 | 3684.54 | |

Std. Dev. | 837.03 | 359.95 | 10.42 | 3.81 | 8.09 | 6.24 | 6.26 | 23.59 | 5.77 | 19.27 | 801.24 | |

Skewness | 1.35 | 0.60 | 1.86 | 0.44 | 1.33 | 0.79 | −0.61 | −0.68 | −0.20 | 0.74 | 0.63 | |

Kurtosis | 3.98 | 3.89 | 7.50 | 4.01 | 3.95 | 3.40 | 2.36 | 2.54 | 2.76 | 3.04 | 3.48 | |

JB | h | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

p-value | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | |

Stat. | 669.95 | 198.92 | 3069.40 | 163.04 | 714.96 | 240.4 | 170.20 | 183.73 | 19.27 | 198.71 | 162.19 | |

ADF | h | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 |

p-value | 0.00 | 0.34 | 0.14 | 0.05 | 0.38 | 0.03 | 0.46 | 0.55 | 0.84 | 0.00 | 0.34 | |

Stat. | −3.30 | −1.45 | −1.97 | −0.74 | −2.10 | −0.53 | −0.28 | 0.59 | −3.31 | −0.86 | 0.59 | |

PP | h | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0.00 |

p-value | 0.00 | 0.34 | 0.14 | 0.05 | 0.38 | 0.03 | 0.46 | 0.55 | 0.84 | 0.00 | 0.34 | |

Stat. | −3.30 | −0.85 | −1.45 | −1.97 | −0.74 | −2.10 | −0.53 | −0.28 | 0.59 | −3.31 | −0.86 |

Interpretation of the Boolean variable h: h = 1 the null hypothesis of the test is rejected, h = 0 fail to reject the null hypothesis of the test. JB test the null hypothesis of normality, ADF and PP test the null hypothesis of unit root.

“ase” | “stoxx” | “vstoxx” | “ppc” | “gbonds” | “eua” | “ngUK” | “brent” | “lignite” | “smp” | “load” | |
---|---|---|---|---|---|---|---|---|---|---|---|

“ase” | 1 | 0.6504 | 0.0851 | 0.8790 | −0.6797 | 0.8527 | −0.2440 | −0.2276 | −0.7683 | 0.2562 | 0.3134 |

“stoxx” | - | 1 | −0.5302 | 0.7323 | −0.4838 | 0.4718 | 0.2077 | 0.3467 | −0.1803 | 0.1619 | 0.0633 |

“vstoxx” | - | - | 1 | −0.0913 | −0.0307 | 0.2897 | −0.1447 | −0.5587 | −0.4267 | 0.3028 | 0.1319 |

“ppc” | - | - | - | 1 | −0.7478 | 0.7086 | −0.2340 | −0.1821 | −0.4764 | 0.1143 | 0.2468 |

“gbonds” | - | - | - | - | 1 | −0.4271 | 0.2796 | 0.4740 | 0.3777 | 0.1455 | −0.0716 |

“eua” | - | - | - | - | - | 1 | −0.1364 | −0.1550 | −0.8159 | 0.4379 | 0.4122 |

“ngUK” | - | - | - | - | - | - | 1 | 0.6567 | 0.2481 | 0.3734 | −0.1327 |

“brent” | - | - | - | - | - | - | - | 1 | 0.3749 | 0.1706 | −0.0773 |

“lignite” | - | - | - | - | - | - | - | - | 1 | −0.3414 | −0.3944 |

“smp” | - | - | - | - | - | - | - | - | - | 1 | 0.4675 |

“loadep” | - | - | - | - | - | - | - | - | - | - | 1 |

Log Return Series | ase | stoxx | vstoxx | ppc | gbonds | eua | ngas | brent | lignite | smp | load | ||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Panel A: Descriptive statistics | |||||||||||||||

Observations | 2159 | 2159 | 2159 | 2159 | 2159 | 2159 | 2159 | 2159 | 2159 | 2159 | 2159 | ||||

Mean | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | ||||

Median | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||||

Maximum | 0.13 | 0.10 | 0.33 | 0.22 | 0.14 | 0.24 | 0.36 | 0.18 | 0.29 | 1.02 | 0.20 | ||||

Minimum | −0.10 | −0.08 | −0.27 | −0.25 | −0.68 | −0.43 | −0.11 | −0.17 | −0.25 | −0.87 | −0.25 | ||||

Std. Dev. | 0.02 | 0.01 | 0.05 | 0.03 | 0.02 | 0.03 | 0.02 | 0.02 | 0.02 | 0.16 | 0.04 | ||||

Skewness | 0.06 | 0.12 | 0.86 | −0.18 | −12.55 | −1.21 | 3.29 | 0.02 | 4.21 | 0.03 | −0.63 | ||||

Kurtosis | 7.31 | 11.32 | 8.09 | 10.70 | 327.73 | 34.44 | 46.55 | 16.49 | 103.69 | 8.82 | 10.22 | ||||

JB (p-value) | h | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1.00 | |||

p-value | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | ||||

Stat. | 1670 | 6231.9 | 2591.4 | 5342.8 | 9543009.1 | 89462.8 | 174476.26 | 16361.3 | 918408.54 | 3051.87 | 4831.9 | ||||

Panel B: Stationarity | |||||||||||||||

ADF | h1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |||

p-value | 0.000 | 0.000 | 0.000 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | ||||

Stat. | −43.78 | −45.64 | −46.43 | −42.92 | −42.06 | −44.7 | −47.17 | −58.80 | −62.95 | −52.21 | −58.80 | ||||

PP | h | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0.00 | |||

p-value | 0.000 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | ||||

Stat. | −43.78 | −45.64 | −46.43 | −42.92 | −42.06 | −44.7 | −46.43 | −47.17 | −58.80 | −62.95 | −52.21 | ||||

Panel C: Serial Correlation. ARCH tests | |||||||||||||||

Q (20) | h | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |||

p-value | 0.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | ||||

Stat. | 30.7 | 56.53 | 52.55 | 52.41 | 58.22 | 67.50 | 53.44 | 41.76 | 187.97 | 243.84 | 162.24 | ||||

Q^{2} (20) | h | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | |||

p-value | 0. | 0.00 | 0.00 | 0.00 | 0.99 | 0.00 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | ||||

Stat. | 250.8 | 888.27 | 166.38 | 280.2 | 1.18 | 154.9 | 11.06 | 386.1 | 286.8 | 376.23 | 125.35 | ||||

ARCH-LM (20) | h | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | |||

p-value | 0.000 | 0.00 | 0.00 | 0.00 | 0.99 | 0.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | ||||

Stat. | 155.45 | 408.07 | 119.35 | 182.30 | 1.13 | 120 | 9.42 | 206.8 | 247.3 | 240.01 | 120.82 | ||||

Q (20) and Q^{2} (20) are Ljung-Box or Q statistics for testing the null hypothesis of no autocorrelation in the residuals. The 5% critical values of X^{2} (20) distributions is 31.41. For ADF and PP test, the 1% critical value is −3.44.

An interesting result is the correlation between smp and lignite. While a significant positive correlation has been found between electricity prices and coal prices in European Union (ECOFYS, 2016) [_{2} quotas and SMP. However the DCC between them is much smaller, as it will be described later on.

By observing

We have also applied the Augmented-Dickey-Fuller (ADF) and Phillips-Perron (PP) unit root tests. As we observe, both tests give values larger than the critical value for the 1% level of significance. Therefore, we can reject the null-hypothesis of a unit root for all returns, so they are taken to be stationary.

To detect autocorrelations in the returns we have used the Ljung-Box or Q statistic. From

All log returns have a mean zero. GEM wholesale price (smp) returns are most volatile (std. Dev ≃ 0.16) followed by vstoxx and load returns, while stoxx returns are the less volatile.

All returns show evidence of volatility clustering (ARCH effects) as the visual inspection of the log return (see Figures 9-11) and the ARCH-Lagrangean Multiplier (ARCH-LM) test in

Figures 9-11 depict the dynamic evolution of the returns of the time series used. All returns are characterized by the well-known phenomena of volatility clusters. Furthermore, as the figures show, during the aftermath of the Lehman Brothers bankruptcy, September 2008, and during the European Sovereign Debt Crisis, mid 2010, all returns exhibit high level of volatility and the associated clustering. The sample autocorrelation function of the squared returns (not shown here due to space limitation) is slowly decaying, a typical feature for daily

returns exhibiting volatility clustering. The ARCH-LM test results, mentioned before, confirm the existence of this stylized fact.

Since all the return series are stationary we proceed by fitting a VAR(1) model for the mean equation (results in

the fitted GARCH(1,1) model on each individual asset are given in

We estimated the dynamic conditional correlations between all of the assets and

GARCH (1.1) Parameters | |||||
---|---|---|---|---|---|

Residuals | ω | α_{1} | β_{1} | α_{1} + β_{1} | LL |

ase_res | 0.0000 | 0.0421 | 0.9264 | 0.9685 | 5621 |

stoxx_res | 0.0000 | 0.0540 | 0.9351 | 0.9891 | 6480 |

ppc_res | 0.0001 | 0.0438 | 0.9099 | 0.9536 | 3431 |

vstoxx_res | 0.0000 | 0.0463 | 0.9436 | 0.9899 | 4684 |

gbonds_res | 0.0000 | 0.0688 | 0.8964 | 0.9652 | 5074 |

eua_res | 0.0000 | 0.0900 | 0.9098 | 0.9998 | 5085 |

ngasUK_res | 0.0000 | 0.0691 | 0.9307 | 0.9998 | 5403 |

brent_res | 0.0000 | 0.0331 | 0.9652 | 0.9983 | 5989 |

smp_res | 0.0000 | 0.0305 | 0.8475 | 0.8780 | 5838 |

loadep_res | 0.0000 | 0.0260 | 0.9729 | 0.9989 | 1209 |

lignitep_res | 0.0011 | 0.1326 | 0.0000 | 0.1326 | 4131 |

the most interesting results are presented in

Specifically the correlation dynamics between indexes (stoxx and ase) and gbonds firmly confirm the classical macroeconomic approach that in times of rising (falling) stock markets bonds are decreasing (increasing) (Durre A. et al. 2005) [

Regarding the linkages between the energy commodities (brent, eua and ngasUK) strong positive correlations were found throughout the sample, with higher volatility and peak values in the period of Financial Crisis. Specifically Brent-Eua are highly correlated in periods of financial stress (Koch (2014) [

Pair of “Assets” residuals | Estimated Parameters | |||||
---|---|---|---|---|---|---|

CCC | DCC(1,1) | |||||

Model 1 | Model 2 equation (10) | |||||

ρ | α | β | α + β | LL | ||

ase_res | stoxx_res | 0.4565 | 0.0041 | 0.9954 | 0.9996 | 12394 |

ase_res | vstoxx_res | −0.3124 | 0.0000 | 0.9998 | 0.9998 | 9180 |

ase_res | ppc_res | 0.6276 | 0.0066 | 0.9927 | 0.9993 | 10894 |

ase_res | gbonds_res | −0.2025 | 0.0388 | 0.9552 | 0.9940 | 10806 |

ase_res | ngasUK_res | 0.0316 | 0.0171 | 0.9179 | 0.9351 | 11031 |

ase_res | brent_res | 0.1822 | 0.0129 | 0.9797 | 0.9926 | 11667 |

ase_res | eua_res | 0.0924 | 0.0077 | 0.9815 | 0.9892 | 10726 |

ase_res | lignite_res | 0.0357 | 0.0068 | 0.9505 | 0.9572 | 11462 |

gbonds_res | vstoxx_res | 0.1189 | 0.0156 | 0.9813 | 0.9968 | 8543 |

eua_res | ngasUK_res | 0.1306 | 0.0085 | 0.9664 | 0.9748 | 10511 |

eua_res | brent_res | 0.2222 | 0.0135 | 0.9759 | 0.9893 | 11147 |

eua_res | ppc_res | 0.0355 | 0.0118 | 0.9326 | 0.9444 | 9774 |

eua_res | vstoxx_res | −0.1499 | 0.0159 | 0.9580 | 0.9739 | 8550 |

eua_res | smp_res | 0.0076 | 0.0387 | 0.3117 | 0.3504 | 6298 |

eua_res | loadep_res | 0.0340 | 0.0074 | 0.0003 | 0.0076 | 9217 |

smp_res | ngasUK_res | −0.0029 | 0.0070 | 0.9629 | 0.9699 | 6616 |

smp_res | loadep_res | 0.2783 | 0.0132 | 0.9344 | 0.9476 | 5434 |

loadep_res | ase_res | −0.0706 | 0.0297 | 0.2594 | 0.2892 | 9759 |

smp_res | ase_res | −0.0204 | 0.0070 | 0.9230 | 0.9301 | 6832 |

lignitep_res | smp_res | −0.0567 | 0.0194 | 0.9286 | 0.9480 | 7055 |

lignitep_res | eua_res | −0.0119 | 0.0025 | 0.9922 | 0.9947 | 10924 |

lignitep_res | ngasUK_res | −0.0109 | 0.0000 | 0.9874 | 0.9874 | 11242 |

lignitep_res | ppc_res | 0.0195 | 0.0000 | 0.0033 | 0.0033 | 10524 |

gbonds_res | brent_res | −0.0416 | 0.0086 | 0.9880 | 0.9966 | 11074 |

gbonds_res | ngasUK_res | 0.0433 | 0.0069 | 0.9728 | 0.9797 | 10481 |

gbonds_res | eua_res | 0.0258 | 0.0428 | 0.0016 | 0.0444 | 10161 |

stoxx_res | brent_res | 0.3607 | 0.0186 | 0.9728 | 0.9914 | 12691 |

stoxx_res | eua_res | 0.1723 | 0.0133 | 0.9783 | 0.9916 | 11624 |

stoxx_res | ngasUK_res | 0.0060 | 0.0194 | 0.9354 | 0.9547 | 11891 |

smp_res | brent_res | −0.0207 | 0.0033 | 0.3918 | 0.3951 | 7199 |

ppc_res | brent_res | 0.0791 | 0.0002 | 0.9861 | 0.9862 | 10685 |

ppc_res | ngasUK_res | 0.0216 | 0.0000 | 0.9017 | 0.9017 | 10089 |

loadep_res | lignitep_res | −0.0708 | 0.0109 | 0.9637 | 0.9746 | 9977 |

ppc_res | gbonds_res | −0.1325 | 0.0376 | 0.9553 | 0.9929 | 9798 |

latter part of our sample converge to their pre-crisis dynamics. In the case of lignite (coal), our findings suggest the uncoupling with the other energy commodities, which was expected since lignite is produced locally and it is not internationally traded.

As our main target is to provide empirical evidence of the coupling or decoupling between the assets of three different markets: the Greek Electricity market, Financial markets, the three most influential commodities markets, Brent Oil, Natural Gas and Carbon allowances (via their corresponding Futures Contracts prices) and for lignite (coal) fuel price, our comments will focus on these pairs and most correlations between assets of the same class will not be further analyzed. Additionally as our sample begins on March 2008 the well documented effect of the 2007 subprime financial crisis in the USA, will be omitted by our analysis, and our work will be focused on the 2010 Greek debt crisis and thereafter. We wish to analyze the coupling and decoupling periods between the markets under consideration, as well as demonstrate the Greek debt crisis effects in the Greek electricity market versus the other two markets, as well as the convergence of the markets’ dynamics to pre-crisis levels, thereafter. In general we expect correlations between assets from different sectors to be lower than the ones of assets from the same sector, as can be shown in the work of Ensor, et al. (2014) [

The financial crisis, which begun in 2007, had a significant effect on the correlations between financial markets and energy commodities. The stock market collapse significantly decreased the correlations between stock markets and energy markets returns, as documented Creti (2013) [

Our sample begins in April of 2008, in the midst of the Financial crisis period and all correlations between ase and energy commodities present a peak negative value. Specifically correlation between Brent oil, which is the energy commodity most related with the stock market due to the “speculation effect” (increasing crude prices in times of rising stock markets) and the Greek stock market has a significant evolution in the period of our study, with a positive peak 0.45 in the mid of the Greek debt crisis. Comparing the correlations between ase and stoxx with brent oil, as seen in

Similarly correlations between EUA returns and the indexes both peaked around the Lehman Brothers collapse, when it became apparent that the financial crisis, which up until then was contained within the financial sector, would affect the real economy and slow down economic growth, thus confirming the “contagion” effect. In the following years correlations, especially with stoxx remained mostly positive and highly volatile. EUA as a commodity reflects the economic growth as expressed by industrial production, and the decreased production in Greece, with consideration of the structure of the Greek electricity market (lignite, a CO_{2}-intense fuel, is a “cheap” domestically produced resource in the GEM), results in the decoupling of the two markets.

Finally correlation between Natural gas and the Greek stock market increased in the beginning of our sample and remain fairly stable in the whole period, with a slightly increased volatility during the period of Greek Debt Crisis. This behavior is consistent with the evolution of the stoxx-gas conditional correlation, suggesting that natural gas has the weakest link to equity markets. Regarding the Greek market, a more concrete and robust analysis should be undertaken, using Natural Gas prices provided from the Greek Natural Gas System Operator (DESFA), in order to check any dependencies with not publicly traded (exchange) markets, but on a bilateral trading rationale between Greece and other countries, e.g. Russia, Algeria.

Turning to the relations between 10-year Greek bonds and energy commodities, our results in

co-movements correspond to times with weaker (stronger) bonds-commodities co-movements. Finally eua-gbonds present a highly anti-persistent conditional volatility which oscillates close to zero, which suggests no significant link between the assets.

Examining the linkages between PPC, the main player of GEM, and energy commodities, the conditional correlations are presented in

Overall our results depict a strong linkage between financial and energy commodity markets in periods of financial turmoil, with Brent and EUA being the most “finacialized commodities”, with correlations that remained highly volatile throughout the Greek debt crisis and move towards decoupling in the years after.

Our findings suggest that GEM’s spot electricity price (SMP) presents significant correlation with the load forecast, which was expected since supply and demand must be in a constant equilibrium in order for the network to operate properly.

The Greek electricity market operates under the merit order principle, meaning that the order of the existing power plants to be dispatched follows the ascending order of the respective fuel variable costs, with renewable energy sources being dispatched first, followed by lignite power plants. Natural gas has the higher variable cost and oil is used only for extreme peaks in demand. The last power plant to enter production in order to cover the demand, also sets the uniform market price (IEA, 2014) [

Correlations between smp and brent oil are insignificant since it’s rarely used, thus almost never sets the price. Regarding natural gas, correlations are mostly positive with smp and tend to increase in the latter years. Again, a more concrete and robust analysis should be undertaken, using Natural Gas prices DESFA, in order to truly capture the dynamics with the electricity prices. Correlations with EUA are highly anti-persistent, as suggested by the results in

Finally turning to the pair smp-lignite, the conditional correlation is volatile and mostly negative. Lignite is in abundance in Greece and while its price increases over time, it remains lower most of the time than the fuel variable cost of a gas power plant, meaning that when the price is set by lignite fired plants it’s decreasing (IEA, 2014) [

Turning to the correlations between electricity and financial markets, we present in

In this paper we have investigated the pairwise dynamics of return conditional correlation between assets “belonging” to three markets, namely electricity, energy commodity and financial. By using Dynamic Condition Correlation model, a model with proven computational advantages, also chosen due to the data stylized facts (e.g. fat tails, volatility clustering etc. of the assets in each market, suggesting a GARCH-type estimation framework), we have examined the co-movement of co-volatility between pairs of assets of these 3 markets.

Emphasis was given in the effects of the 2008 financial as well as the 2010 Greek Sovereign debt crisis on the pairwise DCC of the markets.

We present evidence of significant co-movements between financial market and energy commodities, namely Brent oil and carbon allowances, in periods of financial turmoil, with strong positive and highly volatile correlations. These findings confirm the volatility spillover between these two markets and prove the “financialization” of these energy commodities. Overall the correlations between financial and energy commodities were the most significant between the

different classes of assets.

Regarding the linkages of the Greek Electricity Market, lower conditional correlations were found with the financial and energy market respectively and the periods of financial crisis of 2008 and the Greek Sovereign Debt crisis do not seem to have had a significant effect in the evolution of the dynamic linkages between GEM and other two markets. Finally mostly negative correlations were found between the indigenous lignite price and the System Marginal Price, suggesting that while lignite’s price rises over the years, coal-fired plants are decreasing the price when they set the price via the merit order principle.

We conclude that there is limited liquidity in the GEM which causes spot market’s dynamics to be dependent not only on load forecast but also on the strategic position of the dominant player of this market. Since the Greek Electricity Market is in a transitional phase with the upcoming market coupling with Italy as well as with the upcoming introduction of new markets (intra-day market, balancing market) we expect higher linkage with the other two markets in the next years.

Papaioannou, P.G., Papaioannou, G.P., Stratigakos, A. and Dikaiakos, C. (2017) Dynamic Conditional Correlation between Electricity, Energy (Commodity) and Financial Markets during the Financial Crisis in Greece. Journal of Mathematical Finance, 7, 990-1033. https://doi.org/10.4236/jmf.2017.74055

constant | |
---|---|

ase | −0.0005 |

stoxx | −0.0001 |

ppc | −0.0002 |

vstoxx | −0.0002 |

gbonds | 0.0001 |

eua | −0.0005 |

ngasUK | 0.0000 |

brent | 0.0000 |

smp | 0.0004 |

loadep | 0.0000 |

lignitep | 0.0001 |

Coefficients | “ase” | “stoxx” | “vstoxx” | “ppc” | “gbonds” | “eua” | “ngUK” | “brent” | “smp” | “load” | “lignite” |
---|---|---|---|---|---|---|---|---|---|---|---|

“ase(−1)” | −0.0295 | 0.1717 | 0.0101 | 0.0301 | −0.0145 | −0.0107 | −0.0283 | 0.0042 | 0.0101 | −0.0041 | 0.0049 |

“stoxx(−1)” | 0.0208 | 0.0222 | 0.0089 | 0.0077 | −0.0038 | 0.0010 | −0.0273 | −0.0009 | −0.0022 | −0.0007 | −0.0112 |

“vstoxx(−1)” | −0.2317 | −0.2081 | −0.0738 | 0.0066 | 0.0336 | −0.0103 | 0.1524 | −0.0568 | 0.0392 | −0.0038 | 0.0383 |

“ppc(−1)” | 0.0005 | 0.1182 | −0.0049 | 0.0651 | 0.0085 | −0.0079 | −0.0320 | −0.0485 | −0.0127 | −0.0109 | 0.0202 |

“gbonds(−1)” | −0.0511 | −0.1269 | −0.0146 | −0.0193 | 0.0763 | −0.0111 | 0.0319 | 0.0468 | −0.0178 | 0.0050 | 0.0075 |

“eua(−1)” | 0.0602 | −0.0016 | 0.0248 | −0.0106 | 0.0091 | 0.0552 | −0.0178 | −0.0769 | −0.0256 | 0.0057 | −0.0317 |

“ngUK(−1)” | −0.0447 | 0.0016 | −0.0140 | −0.0042 | −0.0186 | 0.0174 | 0.0023 | −0.0497 | 0.0246 | 0.0013 | −0.0014 |

“brent(−1)” | −0.0127 | 0.0411 | 0.0151 | 0.0270 | −0.0154 | 0.0207 | 0.0412 | −0.0300 | −0.0071 | −0.0023 | −0.0008 |

“smp(−1)” | −0.0021 | 0.0286 | −0.0120 | 0.0046 | 0.0030 | −0.0044 | 0.0244 | −0.0357 | −0.2271 | 0.0020 | 0.0429 |

“load(−1)” | 0.3564 | −0.4768 | −0.0046 | 0.0863 | 0.1917 | −0.0644 | 0.1848 | 0.1352 | −0.1476 | −0.3191 | 0.4495 |

“lignite(−1)” | −0.0492 | 0.0956 | 0.0600 | 0.0427 | −0.0283 | −0.0276 | −0.0196 | 0.0236 | −0.2920 | 0.0042 | −0.1234 |