modelling correlation in carbon and energy markets

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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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Estimation Results

Apr05 Feb06 Nov06 Aug07 Jun08 Mar09 Dec09Aug10−0.5

0

0.5

1

Cor

rela

tion

Cond. Correlation EUA and Gas Returns


0

0.5

1

Cor

rela

tion

Cond. Correlation Gas and Elec. Returns


0

0.5

1

Cor

rela

tion

Cond. Correlation EUA and Elec. Returns

RW

DCC

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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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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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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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Future Research

• Repeat analysis further along the forward curve.

• Allow effect of controls on correlation to differ across assets.

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Thank you!

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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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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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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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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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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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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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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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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)|


H1 : |corrt(fuel ,EUA|ιt = 1)| > |corrt(fuel ,EUA|ιt = 0)|

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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


H1 : ψDM > 0

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Figure: Change in merit order of plant portfolio - Source: Delarue et al.(2008)

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modelling correlation in carbon and energy markets

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