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Motivation Data Methods Results Conclusion Future Research Appendix
Modelling Correlation in Carbon and EnergyMarkets
Philipp KoenigElectricity Policy Research Group
University of Cambridge
Research Workshop on Carbon Pricing - HEC / CDC ClimatJanuary 27th, 2012
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Motivation Data Methods Results Conclusion Future Research Appendix
Under which conditions is the cash-flow from a CCGT power plantself-hedged?
Bottom Line
• Self-hedging is the result of positive correlation betweenpower, natural gas and carbon prices.
• Coal-gas fuel switching is the fundamental driver of thecorrelation between carbon and fuel input prices.
Results:
• Correlations are time-varying.
• Extreme weather conditions, high commodity market volatilityand seasons have no effect on correlations.
• There exists a low correlation regime in which no fuelswitching takes place and prices decouple.
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Motivation Data Methods Results Conclusion Future Research Appendix
MotivationMarginal Power Generation Cost and the Switch PricePrevious ResearchCorrelation Regimes and Working Hypothesis
DataCarbon and Energy Market DataCalibration of the Merit Order Regime
MethodsMultivariate GARCH: Dynamic Conditional Correlation
Results
Conclusion
Future Research
Appendix
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Motivation Data Methods Results Conclusion Future Research Appendix
How does the EU-ETS affect the power generation industry?
Marginal power generation cost (MCi ) in e/GJe , burning fuel i , isapproximated by:
MCi =FCi
ηi+
EFi
ηi· EC
FCi fuel cost in e/GJηi plant net thermal efficiency in GJe/GJEFi Greenhouse Gas (GHG) emission factor in kgCO2/GJ
EC GHG emission cost in e/kgCO2.
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Motivation Data Methods Results Conclusion Future Research Appendix
The Switch Price Set marginal power generation costs of naturalgas and coal generation equal to each other, solve for the emissioncost EC
EC ∗ =ηcoal · FCgas − ηgas · FCcoal
ηgas · EFcoal − ηcoal · EFgas
This is the theoretical carbon switch price in e/kgCO2, e.g.empirical carbon price (PEUA) above EC ∗, natural gas generationmore profitable than coal generation.
if EC ∗ > PEUA −→ MCcoal < MCgas Coal preferredif EC ∗ ≈ PEUA −→ MCcoal ≈ MCgas Indifferenceif EC ∗ < PEUA −→ MCcoal > MCgas Gas preferred
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Motivation Data Methods Results Conclusion Future Research Appendix
Why do we care about correlations between carbon and fuelinput prices?
MCi ,t =FCi ,t
ηi+
EFi
ηi· ECt
Due to daily fuel and carbon price changes, MCi is time varying,its variance is given by
σ2MCi=
1
η2iσ2FCi
+EF 2
i
η2iσ2EC + 2
EFi
η2iρFCi ,ECσFCi
σEC
where ρFCi ,EC is the correlation coefficient between fuel inputs andcarbon allowances and σ2i are variances.
Result: Variability of marginal power generation cost isfunction of fuel/carbon correlation.
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Motivation Data Methods Results Conclusion Future Research Appendix
Previous Research
• Significant effect of extreme weather conditions on carbonprice, Mansanet-Bataller et al. (2007)
• Significant effect of energy prices on carbon price, Bunn andFezzi (2007)
• Three main carbon market fundamentals: regulatory design,energy prices and weather, Alberola et al. (2008)
• Carbon price only remotely influenced by macroeconomicenvironment, Chevallier (2009)
• Carbon return volatility not influenced by introduction ofoptions, Chevallier et. al (2009)
• Carbon volatility autoregressive and influenced by crude oiland natural gas return volatility, Mansanet-Bataller andSoriano (2009)
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Motivation Data Methods Results Conclusion Future Research Appendix
Thinking in Correlation RegimesKey Assumptions:
• Profit maximising producer switches input fuels according tochanges in relative marginal costs, which in turn affectscarbon demand through different emission factors.
• Producers operate in carbon markets according to theirexpectation about future carbon demand.
Result: Correlation between fuel and carbon partly driven byfuel-switching.
But initial relative marginal generation costs matter:
• If MCgas ≈ MCcoal , then fuel price changes can lead to achange in merit order and therefore affect annual carbondemand - Producers revise expectations.
• If MCgas ()MCcoal , then fuel price changes leave meritorder unaffected, no change in annual carbon demand -Expectations unchanged.
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Motivation Data Methods Results Conclusion Future Research Appendix
Problem: significant power plant heterogeneity in terms of thermalefficiencies and emission factors. Therefore, no single switch priceexists.
Approach: define upper and lower theoretical switch price andcalibrate to UK power sector.
• Upper switch price, SPu: carbon price above which naturalgas is preferred technology, independent of thermalcharacteristics of plant portfolio.
• Lower switch price SPl : carbon price below which coal ispreferred technology, independent of thermal characteristics ofplant portfolio.
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Motivation Data Methods Results Conclusion Future Research Appendix
Formally: The upper switch price is defined as
SPu =ηEcoal · FCgas − ηIgas · FCcoal
ηIgas · EFEcoal − ηEcoal · EF I
gas
(1)
The lower switch price is given by
SPl =ηIcoal · FCgas − ηEgas · FCcoal
ηEgas · EF Icoal − ηIcoal · EFE
gas
(2)
where, for fuel i , ηji and EF ji are the respective thermal efficiency
and emission factor of the most efficient (j = E ) and inefficient(j = I ) power plant in the UK portfolio.
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Motivation Data Methods Results Conclusion Future Research Appendix
Using the two switch prices to define two correlation regimes gives:
• Static Merit Order, periods in which marginal generation costssufficiently apart, such that SPu,t ≤ PEUA,t or PEUA,t ≤ SPl ,t .Here, either natural gas or hard coal is preferred technology.Assumption: no fuel-switching takes place.
• Mixed Merit Order, periods in which marginal generationcosts very close, such that SPl ,t < PEUA,t < SPu,t . Here, fuelpreference (switching) depends on thermal characteristics ofplant portfolio.
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Motivation Data Methods Results Conclusion Future Research Appendix
The Working Hypothesis
H0 : |corrt(fuel ,EUA|Mixed)| = |corrt(fuel ,EUA|Static)|
against the alternative
H1 : |corrt(fuel ,EUA|Mixed)| > |corrt(fuel ,EUA|Static)|
Proposition: correlation between fuel and carbon emissionallowance prices is higher when marginal generation costs are close(equal), i.e. merit order is mixed.
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Motivation Data Methods Results Conclusion Future Research Appendix
Sample period:Daily closing values from April 22, 2005 until August 4, 2010, atotal of 1,360 observations.
Energy Market Data (Bloomberg)
• Natural Gas: Intercontinental Exchange (ICE) Natural Gas1-month forward contract for NBP, in GB pence/therm.
• Hard Coal: 1-month forward price of CIF ARA, in USD/ton.
• Oil: ICE Brent 1-month ahead contract traded in USD/barrel.
• Electricity: 1-month forward baseload forward contract(OTC), in GBP/MWh.
Carbon Market Data (European Climate Exchange)
• Emission allowances prices from ’December 07’ (Phase I), ’09’and’10’(Phase II) futures contracts.
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Motivation Data Methods Results Conclusion Future Research Appendix
Calibration of the Merit Order RegimeFollowing values are used to calibrate the switch bounds to the UKpower market:
coupled, as fuel-switching takes places and links price movements.
Based on these upper and lower switch bounds is the calculation of the merit order regime
dummy, as given in equation (6), which is equal to one in the mixed merit order regime. Given
the data, there are 877 observations in the mixed merit order regime in which prices are taken
to be coupled. 481 observations are in the static merit order regime in which prices are taken to
be decoupled, of which 204 correspond to a static gas and 277 to a static coal regime. Figure 7
plots the temporal distribution of all three merit order regimes. In order to provide a rigorous
framework for testing the effect of static and mixed merit order on correlation, the dummy for
mixed merit order is used in an econometric specification for the conditional correlation matrix
of all energy, carbon and electricity returns. Details about the exact specification will be outlined
in the next section.
Table 3: Thermal Power Plant Characteristics
Efficient Plant Inefficient Plant
Natural Gas
η 0.50 0.40
EF 117 163
Hard Coal
η 0.38 0.34
EF 240 280
EF Emission Factor in kg/GJ, η Net Thermal Efficiency in GJe/GJ
Source: Delarue and D’Haeseleer (2008); DECC (2010)
24
The calibration results in 877 observations in the mixed merit orderregime and 481 observations in the static merit order regime, 204of which are static in natural gas and 277 in hard coal.
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Motivation Data Methods Results Conclusion Future Research Appendix
Apr05 Sep05 Feb06 Jul06 Nov06 Apr07 Aug07 Jan08 Jun08 Oct08 Mar09 Dec09 May10Aug090
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
Eur
o/kg
Co2
Upper Switch PriceLower Switch PriceEmpirical CO
2 Price
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Motivation Data Methods Results Conclusion Future Research Appendix
Multivariate GARCH: Dynamic Conditional Correlation(DCC)
Time-varying volatilities are commonly estimated in a GARCHframework. Correlations are modelled in a multivariate framework,such as DCC by Engle (2000).
• Time-varying correlations.
• Very parsimonious compared to other methodologies (BEKK)
• Easily generalized to account for different pairwise correlationdynamics across asset classes.
• Can be extended to account for correlation control variables.
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Motivation Data Methods Results Conclusion Future Research Appendix
Correlation Controls
• The April 2006 compliance event (oversupply) dummy, April25, 2006 until June 23, 2006.
• Seasonal effect - again through effect on heating and lighting.
• Global Volatility Control: Standard & Poor’s Goldman SachsNon-Energy Commodity Index (GSCI).
• UK Population weighted weather controls: extreme airtemperature (heating), wind speed and precipitation(hydro/wind power).
• Static Merit order dummy.
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Motivation Data Methods Results Conclusion Future Research Appendix
Estimation Results
Apr05 Feb06 Nov06 Aug07 Jun08 Mar09 Dec09Aug10−0.5
0
0.5
1
Cor
rela
tion
Cond. Correlation EUA and Gas Returns
Apr05 Feb06 Nov06 Aug07 Jun08 Mar09 Dec09Aug10−0.5
0
0.5
1
Cor
rela
tion
Cond. Correlation Gas and Elec. Returns
Apr05 Feb06 Nov06 Aug07 Jun08 Mar09 Dec09Aug10−0.5
0
0.5
1
Cor
rela
tion
Cond. Correlation EUA and Elec. Returns
RW
DCC
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Motivation Data Methods Results Conclusion Future Research Appendix
Control Variable Estimation Results
• Weather controls and seasonal dummy show no significanteffect on correlation.
• April 06 oversupply reduced correlation of EUAs with energyand electricity returns.
• Key: Working null-hypothesis can be rejected in favour ofexistence of merit order correlation regimes, i.e. pricesdecouple during the static merit order regime.
• Decoupling of fuel and carbon prices reduces variability ofmarginal generation costs.
• Decoupling of power and fuel/carbon prices reducesself-hedging property*.
*Note: Limitation of results in light of model specification.
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Motivation Data Methods Results Conclusion Future Research Appendix
Apr05 Feb06 Nov06 Aug07 Jun08 Mar09 Dec09 Aug10−0.2
0
0.2
0.4
0.6C
orr
AG−DCC−X Cond. Correlation EUA and Gas Returns
Apr05 Feb06 Nov06 Aug07 Jun08 Mar09 Dec09 Aug100
1Static Merit Order
Figure: Cond. Correlation EUA/Natgas - Model with Controls
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Motivation Data Methods Results Conclusion Future Research Appendix
Conclusion• The existence of correlation regimes between carbon emission
allowances, energy and electricity prices was examined basedon empirical price data and theoretical fuel-switch pricescalibrated to the UK power generation industry.
• Correlations were estimated using the (Generalized) DynamicConditional Correlation framework.
• Estimation results show no significant effect of extremeweather conditions, seasonal influences and generalcommodity market volatility.
• The April 2006 oversupply event as well as static merit order,in either natural gas or hard coal, significantly reducecorrelations.
• Key: in a static merit order regime, in which relativemarket prices result in static fuel choices, the correlationbetween energy, carbon and power prices is reduced -they decouple.
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Motivation Data Methods Results Conclusion Future Research Appendix
Future Research
• Repeat analysis further along the forward curve.
• Allow effect of controls on correlation to differ across assets.
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Motivation Data Methods Results Conclusion Future Research Appendix
Thank you!
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Motivation Data Methods Results Conclusion Future Research Appendix
Multivariate GARCH: Dynamic Conditional Correlation
• rt = ri ,t for i = 1...k
• εt|Ωt−1 ∼ N(0,Ht)
• εt is conditionally heteroskedastic, i.e. εt = H1/2t ηt
• ηt ∼ N(0, I )
• Ωt−1 is information set up to and including period t − 1.
• Typical diagonal element of the conditional covariance matrixHt can be modelled in a univariate GARCH(p,q) framework
σ2i ,t = β0 +
p∑j=1
βjσ2i ,t−j +
q∑j=1
γjε2i ,t−j
• Need multivariate structure to model correlation processes.
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Motivation Data Methods Results Conclusion Future Research Appendix
Dynamic Conditional Correlations (DCC)Engle and Sheppard (2001) propose parsimonious two-stageestimator.
Stage One:
• Estimate univariate GARCH(p,q) for each series.
• Obtain Dt the diagonal matrix of time-varying standarddeviations.
• Standardize residuals as ξt = D−1t εt.
• Rewrite: Ht = DtRtDt where Rt is the time-varyingconditional correlation matrix, such that ξt ∼ N(0,Rt)
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Motivation Data Methods Results Conclusion Future Research Appendix
Stage Two: Estimate correlation of standardized residualsconditional on ξt = D−1t εt.
Proposed correlation structure:
Rt = Q∗−1t QtQ∗−1t =
1 ρeua,gas,t ρeua,coal ,t ρeua,oil ,t ρeua,elec,t
ρgas,eua,t 1 ρgas,coal ,t ρgas,oil ,t ρgas,elec,tρcoal ,eua,t ρcoal ,gas,t 1 ρcoal ,oil ,t ρcoal ,elec,tρoil ,eua,t ρoil ,gas,t ρoil ,coal ,t 1 ρoil ,elec,tρelec,eua,t ρelec,gas,t ρelec,coal ,t ρelec,oil ,t 1
• Qt = (1− α− β)Q + α(ξt−1ξ′t−1) + β Qt−1
• Q∗t is a diagonal matrix of the square root of the diagonalelements of Qt .
• Q is the unconditional covariance matrix.
• α (β) measures the sensitivity of the correlations to residualinnovation (decay).
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Motivation Data Methods Results Conclusion Future Research Appendix
A typical element of Rt is given by
ρi ,j ,t =qij ,t√
qii ,tqjj ,t
where qij ,t is a typical element of Qt and given by
qij ,t = (1− α− β)qij + α(ξi ,t−1ξj ,t−1) + β qij ,t−1
DCC Limitation: same α and β for all series.
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Motivation Data Methods Results Conclusion Future Research Appendix
DCC Generalizations to account for asymmetries andheterogeneity in correlation processes
DCC Qt = (1− α− β)Q + α(ξt−1ξ′t−1) + β Qt−1
AG-DCC Qt = (Q − A′QA− B ′QB − G ′NG )
+ A′ξt−1ξ′t−1A + B ′ Qt−1 B + G ′ηt−1η
′t−1G
• A = αii, B = βii and G = gii are k × k diagonalparameter matrices.
• ηt = ηi ,t is a k × 1 vector with ηi ,t = min(ξi ,t , 0).
• N is a k × k matrix of constants, N = T−1∑T
t=1 ηtη′t .
• To maintain positive definiteness of Qt , αii + βii + ηiκ < 1and αii , βii , ηi ≥ 0 for i = 1...k, where κ is the maximum
eigenvalue of Q12 NQ
12 .
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Motivation Data Methods Results Conclusion Future Research Appendix
The AG-DCC-X Model
Qt = (Q − A′QA− B ′QB − G ′NG − K (ψ′x))
+ A′ξt−1ξ′t−1A + B ′ Qt−1 B + G ′ηt−1η
′t−1G
+ K (ψ′xt−1)
• K is a k-dimensional identity matrix.
• xt is a p × 1 vector of control variables.
• ψ = ψp is a p × 1 parameter vector.
• x is a p × 1 vector of constants, such that x = T−1∑T
t=1 xt .
• Qt remains pos. definite for ψj ∈ (0, 1), j = 1...p.
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Motivation Data Methods Results Conclusion Future Research Appendix
Correlation Controls
xt = (Apr06,t DSt DCvolt DTt DWt DPt DMt)′
• The April 2006 compliance event (oversupply) dummy, April25, 2006 until June 23, 2006.
• Seasonal effect - again through effect on heating and lighting.
• Global Volatility Control: Standard & Poor’s Goldman SachsNon-Energy Commodity Index (GSCI).
• UK Population weighted weather controls: extreme airtemperature (heating), wind speed and precipitation(hydro/wind power).
• Static Merit order dummy.
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Motivation Data Methods Results Conclusion Future Research Appendix
Testing for the Existence of Correlation Regimes
Formally, the merit order dummy is defined as
ιt (PEUA,t , SPl ,t ,SPu,t) = 1t (SPl ,t < PEUA,t < SPu,t) (3)
where PEUA,t is the price of a carbon allowance at time t and 1t isthe indicator function. The Working Hypothesis then becomes:
H0 : |corrt(fuel ,EUA|ιt = 1)| = |corrt(fuel ,EUA|ιt = 0)|
against the alternative
H1 : |corrt(fuel ,EUA|ιt = 1)| > |corrt(fuel ,EUA|ιt = 0)|
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Motivation Data Methods Results Conclusion Future Research Appendix
A typical element of resulting conditional correlation matrix Rt inStep 3 is given by
ρij ,t =qij ,t√
(qii ,t +ψ′(xt−1 − x))(qjj ,t +ψ′(xt−1 − x))
The key hypothesis is then re-written as follows
H0 : ψDM = 0
against the alternative
H1 : ψDM > 0
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Motivation Data Methods Results Conclusion Future Research Appendix
Figure: Change in merit order of plant portfolio - Source: Delarue et al.(2008)
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