Andreas Wagner Energy Finance Conference Essen 2013

Integrated Electricity Spot and Forward ModelAndreas WagnerEnergy Finance ConferenceEssen 2013research supported byOctober 10, 2013

Motivation Framework Model and Results ConclusionsContent1Motivation2Framework3Model and Results4ConclusionsAndreas Wagner – Integrated Electricity Spot and Forward Model2 / 25

Motivation Framework Model and Results ConclusionsMotivationAim of this talkAn electricity price framework and model for the joint modeling ofelectricity spot and forward prices.Information from the futures market is transferred to the spotmarketCombination of the structural and financial modeling approachFundamental market information as well as informationprovided by the electricity futures and options market is usedSome ideas similar to Burger et al. [2004] (SMaPS-Model)Model is a forward-dynamic extension to W. [2014] (ResidualDemand Modeling, see EnergyFinance 2012) and Barlow[2002]Andreas Wagner – Integrated Electricity Spot and Forward Model3 / 25

Motivation Framework Model and Results ConclusionsRemainder: Structural ModelsStructural models follow a basiceconomic concept: market price isthe intersection of supply anddemandStructural models are well suited tomodel electricity prices and havebecome increasingly popularSimple stochastic processes areenough to model the complicatedelectricity spot dynamicsPriceDemand curveMarket priceSupply curve(bid curve)VolumeFundamental market informationcan be includedAndreas Wagner – Integrated Electricity Spot and Forward Model4 / 25

Motivation Framework Model and Results ConclusionsLiteratureStructural (fundamental, hybrid, supply/demand) models findstrong attention in recent literatureGood summary and general structural framework Carmona andCoulon [2012]Barlow Model Barlow [2002]Stochastic Bid Stack Model Coulon and Howison [2009],Fundamental Multi-Fuel Model Carmona et al. [2011]Structural Risk-Neutral Model Aı̈d et al. [2009], Aı̈d et al. [2012]and more Burger et al. [2004], Cartea and Villaplana [2008], Pirrongand Jermakyan [2008], Lyle and Elliott [2009], de MaireD’Aertrycke and Smeers [2010], .Andreas Wagner – Integrated Electricity Spot and Forward Model5 / 25

Motivation Framework Model and Results ConclusionsSimple exampleA simple structural model is (similar to Barlow [2002])St f (Dt )with spot price St , supply function f , and some stochasticprocess Dt .The framework we propose is basically as simple as above, but weallow for a forward dynamic of fAndreas Wagner – Integrated Electricity Spot and Forward Model6 / 25

Motivation Framework Model and Results ConclusionsBasic ideaEPEX Hourly Spot Prices for Germany10080Price [Euro]6040200 20Jan 11Feb 11Mrz 11Apr 11Mai 11Jun 11Jul 11Aug 11Sep 11Okt 11Nov 11Dez 11Jan 12TimeThe electricity spot ( day ahead) price is often seen as asimple time seriesHowever, the spot price moves along two time dimensionsElectricity for delivery at different times is not the samefinancial product (their may be some correlation though)This is due to the non-storeability of electricityAndreas Wagner – Integrated Electricity Spot and Forward Model7 / 25

Motivation Framework Model and Results ConclusionsThe abstract priceDistinguish delivery time t and observation time τThe abstract (electricity) price is the core of the frameworkSτ (t) F(τ )(t, D(t)), τ tF(τ )(t, ·) is a stochastic supply-function for delivery at time tD(t) is the driving factors process (e.g. residual demand)The spot price is St St (t, D(t)), i.e. the abstract price withτ tThe abstract price is a non-traded product depending on twodifferent risk factors, namely the forward dynamic and the drivingfactors.Andreas Wagner – Integrated Electricity Spot and Forward Model8 / 25

Motivation Framework Model and Results ConclusionsDriving factorsAbstract priceSτ (t) F(τ )(t, D(t)), τ tdelivery time t, observation time τThe abstract price evolves as a function of the driving factorsprocess D(t)D(t) is assumed to be a time-τ -stationary stochastic process,i.e. its distribution does not change in observation timeD(t) represents unhedgeable risks like demand, renewableinfeed, interconnectors, etc., i.e. factors where no knowledge isobtained in observation time (at least not until short before)Andreas Wagner – Integrated Electricity Spot and Forward Model9 / 25

Motivation Framework Model and Results ConclusionsForward DynamicAbstract priceSτ (t) F(τ )(t, D(t)), τ tdelivery time t, observation time τStochastic supply-functional F(·) represents hedgeable risks inthe abstract price, e.g. changing fuel pricesMulti-factor standard model (Black-model) is suitabledF(τ )(t, x) F(τ )(t, x) Σ(τ, t) dWτ , F(0)(t, x) f0 (t, x)Wτ : d-dimensional Brownian motion independent ofF DΣ(τ, t): 1 d (deterministic) volatility vectorSupply-functional is assumed independent of D(t), i.e. thestructure of the generation stack is independent of the drivingfactorsAndreas Wagner – Integrated Electricity Spot and Forward Model10 / 25

Motivation Framework Model and Results ConclusionsForwards IIn contrast to storeable commodities, there is no clearrelationship between electricity spot and forward prices in theelectricity marketFτ (t) 6 e r (t τ ) SτFτ (t): Forward-price at time τ for delivery at time tSτ : Spot-price at time τThis is (again) due to the non-storeability of electricityTherefore we define the forward price in a suitable wayTraded forwards give an indication of the spot price level atdelivery (remember also that a forward always covers adelivery period)Andreas Wagner – Integrated Electricity Spot and Forward Model11 / 25

Motivation Framework Model and Results ConclusionsForwards IIDefinition (Forward price)The time-τ -price Fτ (t) of a forward contract with delivery attime t is a random variable defined as the conditional expectationof Sτ (t), i.e.hiFτ (t) : E Sτ (t) FτW ,where FτW is the filtration generated by Wτ .Heuristically, the forward price is the expectation over thepossible realisations of the driving factors process (whichcannot be hedged)For each supply-dynamic (generated by the Wτ ), a differentforward price path is realizedAndreas Wagner – Integrated Electricity Spot and Forward Model12 / 25

Motivation Framework Model and Results ConclusionsPropertiesThe forward price follows a geometric Brownian motion(sensible, as the forward can be bought and stored withoutcosts)The log-normal distribution makes the pricing of Europeanoptions an easy exercise (Black-formula)In the market, only forwards with delivery period andEuropean options on those are tradedUsing the common “the sum of lognormal random variables isitself lognormal“ assumption and a moment matching, we canhandle those productsAndreas Wagner – Integrated Electricity Spot and Forward Model13 / 25

Motivation Framework Model and Results ConclusionsAn explicit modelWe define an explicit model within the framework for theGerman/Austria marketInitial supply functionF(0)(t, x) a(t) g (x)This additive structure of F allows for a quick calibrationFor the driving factors process D(t), we use a stochasticmodel for residual demand ( total demand – wind infeed –solar infeed)For the volatility, we use the two-factor approach fromBoerger et al. [2009] for the modeling of electricity futures(see next slides)Andreas Wagner – Integrated Electricity Spot and Forward Model14 / 25

Motivation Framework Model and Results ConclusionsCalibration of F(0)Initial calibration of F(0) on historical spot prices and residualdemand dataBootstrapped term-structure of EEX futures is then used toshift a(t)OffpeakBootstrapped Term Structure 01/08/2012Peak20065SettlementPriceEPEX Spot Price [Euro]60100055ProfileOffpeak50Peak4540 1002040608020406080Residual Demand Germany [GW]Andreas Wagner

Andreas Wagner { Integrated Electricity Spot and Forward Model 16/25. MotivationFrameworkModel and ResultsConclusions Volatility of supply-functional This observation motivates the following volatility structure (as in Boerger et al. [2009]) Volatility structure ( ;t) e (t ) 1; 2(t) ; where 1 is the (additional) short-term volatility, is a positive constant controlling the in .