PROBLÈMES DE VALORISATION ET D ORGANISATION DANS LES MARCHÉS D ÉNERGIE

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1 UNIVERSITÉ PARIS-DAUPHINE U.M.R. MATHÉMATIQUES DE LA DÉCISION N o aribué par a bibiohèque THÈSE pour obenir e grade de DOCTEUR ÈS-SCIENCES SPÉCIALITÉ MATHÉMATIQUES APPLIQUÉES présenée e souenue pubiquemen par Arnaud PORCHET e 23 Janvier 28 sous e ire PROBLÈMES DE VALORISATION ET D ORGANISATION DANS LES MARCHÉS D ÉNERGIE PROBLEMS OF VALUATION AND ORGANIZATION IN ENERGY MARKETS Direceur de Thèse M. Nizar TOUZI, Professeur à Écoe Poyechnique Jury Rapporeurs: Mme. Monique JeanBanc Professeur à Universié d Evry Va d Essonne M. Seven Kou Professeur à Universié Coumbia, USA Examinaeurs: M. René Aïd Ingénieur Chercheur à EDF R&D M. René Carmona Professeur à Universié de Princeon, USA M. Jean Miche Lasry Professeur à Universié Paris Dauphine

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3 L universié n enend donner aucune approbaion ou improbaion aux opinions émises dans es hèses: ces opinions doiven êre considérées comme propres à eurs aueurs.

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5 Remerciemens Les ravaux présenés dans cee hèse de docora son e frui de rois années de coaboraion enre e Laboraoire de Finance-Assurance du Cenre de Recherche en Économie e Saisiques (CREST LFA, e Cenre de Recherche en Mahémaiques de a Décision de Universié Paris Dauphine (CEREMADE, e déparmen de Operaions Research and Financia Engineering de Universié de Princeon (ORFE e e déparemen Opimisaion-Simuaion-Risque d Éecricié de France, Recherche & Déveoppemen (EDF R&D OSIRIS. Je iens ou d abord à remercier Seven Kou e Monique Jeanbanc d avoir accepé d êre rapporeurs e pour eur ecure aenive e criique de mon manuscri. Je remercie ensuie es membres du Jury: René Aïd, René Carmona, Jean Miche Lasry, Monique Jeanbanc e Nizar Touzi, pour m avoir fai honneur de eur présence. Je iens ou paricuièremen à exprimer mes sincères remerciemens e ma profonde reconnaissance à mon direceur de hèse, Nizar Touzi, pour a confiance qu i m a accordée, e souien, a moivaion e a cairvoyance qu i m a apporés ors de ces années, noammen dans es momens de doues, ainsi que pour sa disponibiié, son amabiié e son sens des reaions humaines qui on paricipé à faire de ces rois années un momen à a fois riche, simuan e agréabe. Mes chaeureux remerciemens von aussi à René Carmona de Universié de Princeon pour son inviaion d un an au sein du déparemen ORFE. Je e remercie de a confiance e du souien qu i m a accordés ors de organisaion de a mission, ainsi que pour sa disponibiié e son impicaion dans nore coaboraion. I m a donné a chance de vivre une expérience unique au sein de son universié. Je veux aussi remercier Chrisian Gourieroux, co-direceur du CREST-LFA pour avoir reenu ma candidaure de docoran, m avoir accueii au sein de son aboraoire e m avoir permis d y mener à bien mes recherches. Je saue aussi ous ceux avec qui j ai eu a chance de coaborer au cours de ces années: Juri Hinz, Max Fehr, Gies Chema, René Aïd, Xavier Warin, Cyrie Srugarek, Fabian Asic, Bruno Bouchard, Romuad Eie, Jerôme Wirh, Imen Ben Tahar, Jean François Chassagneux, Parick Cheridio, Aexandre D Aspremon, Rémi Audoin. J ai une pensée rès paricuière pour Jean Sébasien Roy de EDF. Je iens à remercier a direcion du déparemen OSIRIS de EDF R&D pour organisaion e e financemen de ce proje, ainsi que pour e souien e a confiance qui m on éé accordés pendan ces rois années. La hèse a éé financée par EDF R&D e e Minisère de a Recherche français par e biais d une convenion CIFRE de Agence Naionae de a Recherche Technique (ANRT signée enre EDF R&D e e CEREMADE. Je souhaie aussi remercier e personne de gesion de OSIRIS e du CREST, en paricuier Caherine Nicoas e Fanda Traore, pour eur souien e eur efficacié. Je saue aussi ous ceux qui on conribué à faire de ces rois années un momen agréabe e enrichissan, en paricuier Kengy, Mane, Aexandre, Caude, Jerome, Babakar, Abdu Ka, Gregory, Mahieu à EDF; Fuvio, Marco, Kenza, Imen au CREST; Anoine, Ronny, Serguei, Evan, Rober, Mary Beh, Birgi, Juiana, Niin à ORFE. i

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7 Résumé Pendan es rene dernières années, indusrie éecrique a connu des changemens considérabes dans son organisaion, e ce parou dans e monde. Indusrie radiionneemen cenraisée, organisée en monopoe, au moins ocaemen, souven déenue pubiquemen, a producion e a fourniure d éecricié s es progressivemen ouvere aux règes du marché e de a concurrence. A ce jour, un grand nombre de pays se son doés de marchés de gros où produceurs e fournisseurs s échangen de éecricié afin de saisfaire es besoins des consommaeurs finaux. Ces marchés ne son pus seuemen naionaux e es échanges ransfronaiers son de pus en pus fréquens. La quesion de organisaion de ces marchés es primordiae compe enu de ampeur des conséquences en cas de défaiance (on se souvien de a crise caifornienne ou du scandae Enron en 21. Pus généraemen, ce son es marchés d énergie dans eur ensembe qui se son ransformés dans un conexe de croissance de a demande, de menace d épuisemen des énergies fossies, de prise de conscience environnemenae e de ensions poiiques pour accès aux ressources. Auour d un marché du péroe sous pression, es marchés du gaz e du charbon on vu eurs voumes augmener. La signaure du proocoe de Kyoo e a mise en pace d une poiique voonarise de réducion des émissions de gaz à effe de serre on aboui à a créaion de marchés de permis d émission e simué e recours aux énergies renouveabes, aux biocarburans ainsi qu à énergie nucéaire. L exposiion de pus en pus fore de économie mondiae aux prix de énergie a ammené es marchés financiers a déveopper des produis de gesion de risque adapés au monde des commodiés (énergie, agricuure, méaux. Ce son des produis de gesion de risque de prix, mais aussi de risque de voume, afin de couvrir e risque de fucuaion de a demande. Ce son aussi mainenan des produis dérivés ou d assurance sur e risque cimaique. Cee hèse de docora s inscri dans ce conexe. Ee es composée de quare chapires qui peuven êre us de manière indépendane. Le premier chapire concerne a vaorisaion d acifs de producion du ype cenrae hermique. Cee méhode de vaorisaion Opion Réee se base sur un cacu d indifférence d uiié e perme a prise en compe de conraines de producion e de fricions de marché. La vaeur d acif es caracérisée à aide d équaions différeniees sochasiques rérogrades e donne accès à des méhodes de résouion du ype Mone Caro e EDP. Le second chapire s inéresse à a vaorisaion des acifs de sockage du ype barrage hydrauique. Le rendemen moyen de acif es caracérisé comme unique souion de viscosié d une équaion aux dérivées pariees non inéaire. L impémenaion numérique par un schéma aux différences finies es discuée. Le roisième chapire es dédié à une modéisaion du marché des permis d émissions de CO 2. Un modèe d équiibre concurrenie à deux marchés (spo d éecricié e drois d émission es inrodui en environnemen aéaoire. Les prix d équiibres ainsi que es sraégies des aceurs son caracérisés grâce à une propriéé d agen représenaif. On discue aors impac de a réguaion CO 2 sur es prix de éecricié e inroducion de nouvees règes de marché permean de diminuer augmenaion des prix de éecricié. Le dernier chapire es une éude des reaions enre gesion des risques e srucure indusriee des aceurs. On inrodui e caracérise équiibre compéiif d une économie à rois marchés, reai, forward e spo, en présence d inceriude. Les aceurs peuven avoir des srucures indusriees différenes, fournisseur, produceur, rader ou êre vericaemen inégrés. On dérive a reaion enre es prix sur es différens marchés e on compare impac sur es prix e es uiiés de a présence d un marché à erme ou d aceurs inégrés. iii

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9 Absrac In he pas hiry years, he eecriciy indusry has experienced significan srucura changes in is organizaion a over he word. Tradiionay cenraized and organized in monopoies, a eas ocay, and ofen pubicy owned, he aciviies of eecriciy producion and reai have moved owards a marke-based organizaion. Nowadays, a significan number of counries hos eecriciy whoesae markes where producers and reaiers exchange eecriciy o saisfy he demand of end consumers. These markes are no sricy naiona and he voume of cross-border exchanges is increasing. The quesion of he organizaion of hese markes is crucia wih regards o he dire consequences in cases of faiure ( we refer for exampe o he Caifornia crisis or he Enron scanda in 21. The whoe se of energy markes has been ransformed in a broader conex of demand growh, hrea of exhausion of fossi energies, environmena awareness and poiica ensions for he access o naura resources. Beside an oi marke under pressure, he gas and coa markes have seen heir voumes increasing. The raificaion of he Kyoo prooco and he enforcemen of a greenhouse gases reducion poicy have ead o he creaion of markes for emissions permis and simuaed he use of renewabe and nucear energies and biofues. The increasing exposure of he word economy o energy prices incied he financia markes o deveop new commodiy risk managemen producs (energy, agricuuras, meas. These are price risk and aso voume risk managemen producs, in order o hedge he risk of fucuaing demand. These are aso derivaives or insurance producs agains weaher risk. This PhD disseraion keeps wihin his conex. I is composed of four chapers ha are independen of each oher. The firs chaper concerns he vauaion of physica asses such as herma power pans. This Rea Opion vauaion mehod is based on a uiiy indifference anaysis and accouns for producion consrains and marke fricions. The asse vaue is characerized by means of backward sochasic differenia equaions and aows for Mone Caro- and PDE-based numerica mehods. The second chaper focuses on he vauaion of sorage asses ike hydro power pans. The average revenue of he asse is characerized as he unique viscosiy souion of a noninear paria differenia equaion. The numerica impemenaion by means of a finie difference scheme is discussed. The hird chaper is dedicaed o a mode of CO 2 emission permi marke. A compeiive equiibrium mode wih wo markes (eecriciy spo and CO 2 is inroduced in a sochasic framework. The equiibrium prices and he posiions of he acors are characerized wih he aid of a represenaive agen propery. We discuss he impac of he CO 2 reguaion on eecriciy prices, as we as he inroducion of aernaive rading schemes which ead o ower eecriciy prices. The as chaper is a sudy of he reaions beween hedging and indusria srucure. We inroduce and characerize he compeiive equiibrium of an economy wih hree markes (reai, forward and spo in he presence of uncerainy. The acors can have differen indusria srucures: reaier, producer, rader, or vericay inegraed. We derive he reaion beween he prices and we compare he impac on prices and uiiies of he presence of a forward marke or of inegraed acors. v

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11 Conens Inroducion 1.1 Eecric Power Indusry: Engineering and Economics Eecriciy Markes and Risk Managemen Chaenges Organizaion of he Thesis Vauaion of Therma Power Pans by Uiiy Indifference Inroducion Noaions Probem Formuaion Verificaion Resu Exisence Compee Marke Incompee Marke PDE Numerics I Numerics II Concusion Vauaion of Hydro Power Pans Inroducion Probem Formuaion Properies Main Resu Viscosiy Propery Comparison vii

12 CONTENTS CONTENTS 2.7 Numerics Exampe Marke Design for Emission Trading Schemes Inroducion Seing Equiibrium Goba Opimaiy Exensions Numerics Concusion Hedging and Verica Inegraion in Compeiive Markes Inroducion Formuaion No Forward Marke Forward Marke Numerics Easic Demand Concusion References 115 viii

13 Chaper Inroducion Conens.1 Eecric Power Indusry: Engineering and Economics Engineering of Eecriciy Generaion Liberaizaion of Eecric Power Indusries Economics of Eecriciy Generaion Eecriciy Markes and Risk Managemen Undersanding Eecriciy Spo Prices Risk Managemen Insrumens Chaenges Re-hinking he Fundamenas of Risk Managemen Managing and Vauing Socks Assessing Fricions in he Markes Indusria Organizaion Reguaion Organizaion of he Thesis

14 Chaper. Inroducion The work presened in his disseraion concerns vauaion, organizaion and risk managemen in energy markes, wih a srong emphasis on eecriciy. This manuscrip is composed of four main chapers ha rea disinc research quesions and can be read independeny of each oher. We presen in his inroducion some generaiies abou eecriciy producion and eecriciy markes ha underine how hese quesions nauray arise in dereguaed eecriciy markes..1 Eecric Power Indusry: Engineering and Economics.1.1 Engineering of Eecriciy Generaion We usuay disinguish beween 3 major aciviies in he eecriciy indusry: generaion, ransmission and disribuion. Generaion refers o he producion of eecriciy from differen kinds of primary energy sources: fossi fues (coa, gas, oi, nucear fues, renewabes (hydro, wind, soar, geoherma ec.. Once produced, eecriciy is ransmied from generaion ocaions o areas of consumpion via a nework, he grid, composed of high and ow voage ines. High voage ines aow for onger disance ransmission and ower osses. Transformers reduce he voage cose o consumpion areas where eecriciy is disribued o end consumers. Markeing and disribuion of eecriciy is aso referred o as suppy or reai aciviy. The paricuariy of eecriciy in comparison o oher commodiies is reaed o is physica naure. Eecriciy is a fow of eecrons ha circuaes in he wires of he nework. In order o preserve he quaiy of he eecriciy deivered, and he sabiiy of he grid, is physica properies (especiay is frequency mus remain sabe over ime, meaning ha suppy (quaniy of eecriciy enering he nework mus mee demand (quaniy of eecriciy exiing he nework a a ime. In addiion o he necessiy of a consan baance beween demand and suppy, eecriciy is a highy non-sorabe commodiy. Whereas gas can be sored in gas sorages, or as iquefied gas in anks, or oi in barres, sorage of eecriciy is hard o achieve. Eecriciy can be sored in baeries, bu in sma quaniies and a high cos. Waer reservoirs consiue he unique sorage faciiies for arge quaniies of eecriciy. The energy is sored as poenia energy in he waer and ransformed ino eecriciy via waer urbines. In he absence of sorage echnoogy, he eecriciy generaed a one ime mus be consumed insananeousy, and suppy mus adap o demand a each momen in ime. Knowedge of hese feaures is crucia o undersanding he fundamenas of eecriciy markes. The non-sorabiiy and insananeous suppy-demand equiibrium properies of a good can greay simpify producion managemen sraegies: each day a producer needs o know how much of he good he ciens wan, produce i and se i. Non-sorabiiy aso impies ha producion decisions made oday and omorrow are compeey uncorreaed, avoiding he probem of managing invenories. If eecriciy were compeey non-sorabe and if power pans were perfecy fexibe, managing a porfoio of power pans over ime reduces o a series of idenica managing decisions: he pas managing decisions have no impac on he decisions o be aken in he fuure. However, producion asses are no as fexibe as o be urned on and off a any ime. In addiion, eecriciy demand is no perfecy known in advance since consumers do no order eecriciy bu raher consume i based on heir needs. Finay cever managemen of hydro reservoirs can decrease producion coss by adding cheap addiiona producion capaciy when demand or fue prices are high. We undersand ha managing iner-emporaiy is an imporan ask because generaion decisions are couped in ime. Power pans vary in fexibiiy, depending on heir echnoogy. Each ime a power pan is urned on, some ime is needed o reach fu power. The speed a which a power pan can reach maximum power is caed he ramp rae. There aso exiss a minima ime of usage. Power pans canno be urned on and off oo quicky. The mos fexibe echnoogy is usuay gas- or oi-fired and is used o adjus generaion o demand. The ess fexibe echnoogy is he nucear pan, 2

15 Chaper. Inroducion which mus run for onger periods of ime and is used o produce a raher consan quaniy of eecriciy. Renewabe energies have a specia feaure whereby hey can be very fexibe (e.g. soar or wind bu heir producion capaciy depends on he weaher and is hus uncerain. In addiion o fexibiiy, panned ouages aso creae empora dependencies in he generaion managemen. Power pans mus be shu down reguary for mainenance and he decision o shu down a pan for mainenance oday has a direc impac on he generaion decisions of he weeks o come. Owning arge hydroeecric capaciies is a rea advanage, since producion coss are very ow and iner-empora arbirages are possibe. For exampe, i is possibe o produce fossi-fueed eecriciy o pump waer ino he reservoir when prices and/or demand are ow (e.g. a nigh, and o uiize he waer aer o produce eecriciy when prices and/or demand are high. In some counries, he proporion of eecriciy generaed by hydro pans is very high: 99% for Norway and Paraguay, 84% for Brazi, 55% for New Zeaand and Swizerand (daa EIA 25. For hese counries, managing heir waer resources, i.e. managing iner-emporaiy, is crucia. Anoher imporan source of iner-emporaiy arises wih he creaion of forward/fuures markes for eecriciy. Managing a porfoio of forward conrac dynamicay over ime is simiar o managing a sock of energy. Simiary, he inroducion of a cap-and-rade scheme o reduce emissions of greenhouse gases induces he managemen of socks of emissions over ime. We wi furher discuss hese aspecs in he seques..1.2 Liberaizaion of Eecric Power Indusries Uni he ae 197s, he eecriciy indusries a over he word were organized as inegraed oca monopoies, ofen pubicy owned. There are severa reasons ha expain he choice of such an organizaion. Firs, he ransmission of eecriciy is a naura monopoy, as i is he case for raiway, waer or gas neworks. I woud be very cosy and inefficien o superpose severa eecriciy grids in he same area. Second, his indusry is very capia inensive and some invesmens coud ony be borne by saes (e.g. nucear and hydro pans in he absence of sufficien financing capaciies in financia markes. Invesmen horizons, of up o severa decades, can aso be oo ong o arac privae invesors. Finay, safey issues, especiay in he case of nucear echnoogy, encouraged saes o keep a direc conro over he producion means. In he search for a beer usage of producion capaciies and cheaper eecriciy prices, severa counries sared o iberaize heir eecriciy indusry. In Lain America, Chie and hen Argenina, Peru, Brazi and Coombia, were among he pioneers. The iberaizaion of UK power sysems in 199 served as a caays for oher Commonweah counries ike Ausraia and New Zeaand. Liberaizaion aso occurred in he USA and receny in he EU. A counries did no foow he same iberaizaion process, nor did hey reach he same end-sage, bu he basic process was simiar: creaion of whoesae eecriciy markes opened o free compeiion and he privaizaion, and ofen unbunding, of he former monopoies; creaion of a reai marke and suppression, or imiaion, of reguaed ariffs; separaion of he ransmission sysem, which is generay kep as an independen reguaed monopoy, from he generaion and reai aciviies. There is ofen confusion beween he erms iberaizaion, dereguaion and privaizaion. Liberaizaion refers o ess governmen inervenion, inroducion of compeiion and opening of markes o foreign paricipans; dereguaion refers o ess reguaion. Whie ofen concomian, hese wo conceps can be divergen. The Enron and Caifornia crisis have shown ha reguaion is necessary o ensure fair compeiion and efficiency of eecriciy markes. Meanwhie, privaizaion refers o he eiminaion of pubic owned companies. Privaizaion is ofen a means o achieve iberaizaion, bu i is no a necessary condiion, and pariay pubicay-owned uiiies can and do compee wih privae ones in cerain iberaized markes. The experience of iberaizaion in he eecric power indusry is highy varied. Major faiures such as he Caifornia crisis of 21 poined ou he imporance of marke design, i.e. defining marke rues, and he difficuy of carrying i ou. In paricuar, i si remains uncear wheher oday s markes provide he righ price signas o incie invesmen in fuure producion capaciies. 3

16 Chaper. Inroducion In addiion, iberaizaion has no been accompanied everywhere by he expeced reducion in whoesae and reai prices. A he EU-eve, here is si open debae beween he Commission, he member saes and he uiiies regarding which reguaion shoud be appied for he goba European energy marke. On he one hand Bruxees cas for more separaion beween reai and generaion aciviies as we as for a higher number of acors in he marke. On he oher hand, he succession of mergers and ake-over bids in Europe shows ha uiiies seek a arge inegraed srucure ha woud aow for beer ong erm sraegies, invesmens, compeiion wih foreign rivas, securiy of fue suppy (by he associaion of gas and power aciviies, and for more price conro and marke power. Finay saes have a sraegic ineres in keeping naiona champions o ensure fue suppy a a naiona eve, and hey may be wiing o imi he opening of heir naiona markes o foreign uiiies..1.3 Economics of Eecriciy Generaion As menioned above, eecriciy is a produc wih disinc properies ha make i subsaniay differen from oher goods. I is highy non sorabe, ike airpane ickes or hoe reservaions; for a cerain cass of cusomers, i is a service, more han a good; and a reai conrac for eecriciy gives unimied access o consumpion. This is aso he case for gas, waer, he Inerne and cerain eephone services. Unike wih hese producs, however, cusomers canno wai for eecriciy, and eecriciy canno be overbooked eiher. Residenia consumers end o have ie responsiveness o prices in he very shor run, which as a resu end o be ineasic. In he onger run, ciens can inves in subsiue echnoogies (e.g. gas for heaing which creaes more easiciy for ong run demand. As a consequence of he physica properies of eecriciy, eecriciy generaed and consumed a wo differen imes mus be viewed as differen producs. Eecriciy consumed now and eecriciy consumed omorrow are wo differen producs if he eecriciy generaed oday canno be sored and deivered omorrow. When eecriciy was produced by sae-owned monopoies, ariffs were usuay se based on average cos anaysis. Eecriciy was sod o end-cusomers a average cos so ha oa producion cos was recovered. Toa cos incuded producion coss as we as he coss of abor, mainenance, invesmens ec. In a marke-based economy, eecriciy is priced by a margina cos anaysis. Each producer bids a suppy funcion ha indicaes he minima price per Mega Wa-hour (MWh a which he producer is ready o se for every producion eve (in MWh. Each buyer simiary provides a demand funcion indicaing he maxima price per Mega Wa-hour (MWh a which he buyer is ready o buy for every quaniy. The aucioneer of he marke aggregaes and compares hese suppy and demand funcions o deermine he producion eve and price of eecriciy. In a perfecy compeiive marke, each producer bids his margina cos funcion, and he aggregae suppy funcion is he aggregae margina cos funcion (in bue in Figure 1. This curve is obained by ranking a producion unis by meri order, i.e. from owes o highes margina cos. The aggregae margina cos funcion is usuay caed he sack. The compeiive price (cmarg is se by he inersecion of he margina cos funcion and he demand funcion: i is he margina cos of he mos expansive producion uni used o mee demand. We can prove ha his compeiive equiibrium yieds he same producion as a goba panner seeking demand saisfacion a minima cos. This mechanism describes he price fixaion of spo markes, such as Powernex in France or PJM in he USA. Spo conracs are conracs for deivery of a fixed eecric power during a hiry-minue o one-hour window ha wi open a a specified hour on he foowing day (e.g. deivery of 1 MW omorrow beween 8am and 9am. In order o adap producion o demand, inra-day markes, or adjusmen markes have been creaed. They are usuay managed by he grid manager (or ISO - Independen Sysem Operaor o adjus in rea ime o demand fucuaions. Each producer is asked by he ISO o repor his remaining avaiabe capaciy and he price a which he producer is wiing o saisfy he remaining demand. Finay, ong erm conracs are usuay avaiabe over-he-couner or a Fuures exchanges. They aow for purchase of eecriciy from one 4

17 Chaper. Inroducion Figure 1: Suppy-Demand Equiibrium. week o severa years before deivery. The sequence of decisions for an eecriciy producer is hen he foowing: Long Term Conracs Spo Marke Adjusmen Marke Generaion Long erm conracs, spo marke and adjusmen mechanisms aow producers o se heir producion o reaiers or direcy o cusomers. Reaiers hen marke eecriciy o residenia or indusria end-cusomers. We refer o he reai marke for eecriciy when speaking of he compeiion of reaiers o suppy end-cusomers..2 Eecriciy Markes and Risk Managemen In he previous secion we gave an overview of eecriciy producion and commerciaizaion. In addiion o physica whoesae and reai markes, markes for financiay-seed risk hedging insrumens have emerged. We provide an overview of he risks inheren o eecriciy producion and rading, which drive he need for risk managemen insrumens. We hen enumerae he mos popuar risk hedging conracs..2.1 Undersanding Eecriciy Spo Prices The primary whoesae markes for exchange of eecriciy are he spo and adjusmen markes, whose prices depend on severa drivers. In his subsecion, we wi define he spo price as he idea insananeous price ha encompasses boh he day-ahead and rea-ime prices. We can schemaicay decompose his spo price ino 5 componens: he compeiive margina cos, he conribuion of fixed coss, ransmission coss, he impac of reguaion and he marke power deviaion. 5

18 Chaper. Inroducion Spo Price = Margina Cos + Fixed Coss + Transmission Coss + Reguaory Impac + Marke Power As we saw in he previous secion, in an idea word where eecriciy is produced and consumed a he same ocaion, and where a producers charge a margina cos, he equiibrium spo price is equa o he margina producion cos a he curren demand eve. The shape of he sack depends on he capaciies and margina coss of each producion uni, and hus varies over ime. Each margina cos depends on many facors. In he case of a herma power pan, i depends on he price of he fue burn, he efficiency of he pan (caed hea rae, isef depending on parameers such as he generaion eve, he emperaure, ec., emissions of greenhouse gases when pouion reducion schemes exis, price of emission credis, mainenance coss ec. Hydro-pans and renewabe sources have very ow margina cos oher han mainenance cos. The avaiabe generaion capaciy of each pan depends on he presence of ouages, rain precipiaions for hydropans, sun and wind for soar panes and wind urbines. On he oher hand, oad depends srongy on he weaher (emperaure and nebuosiy. Because of he non-sorabiiy of he produc, he srong ineasiciy of he oad, he non-ineariy of he sack and he number of sochasic drivers infuencing he price, i is no surprise ha spo prices vary srongy and quicky over ime, showing excepionay high voaiiy ( someimes higher han 1%, spikes, mean reversion and seasonaiy. In addiion o his compex suppy-demand equiibrium, eecriciy spo prices mus refec some ransporaion coss hrough he grid. In paricuar, he presence of congesion in he nework is a source of price spikes. If cheap generaion means canno be used o mee demand in a paricuar region because ransmission beween hese wo poins is difficu, more expensive unis mus be run esewhere. Thus, he sack aso varies wih he opoogy of he grid. Reguaion can induce a significan deviaion beween spo prices and coss. For exampe, he presence of price caps on he spo marke can preven acors from recovering heir coss. The iberaizaion of energy markes is accompanied by he creaion of new reguaions ha can be modified in he fuure. This reguaory risk can have an infuence on he prices. For exampe, he uncerainy surrounding he appicaion of Kyoo s prooco and he inroducion of emission reducion poicies creaes uncerainy wih regards o he cos of emissions and hus on he spo prices. Reguaion rues can aso be used or circumvened by some acors who exercise marke power o drive prices up and make exra profis. One simpe exampe of marke power is he emporary monopoy. If for some reasons (e.g. congesions, high demand an acor becomes he ony producer abe o suppy par of he oad, he has enire conro on he price. The Enron case is perhaps he mos embemaic case of (iega marke power in eecriciy markes..2.2 Risk Managemen Insrumens We previousy menioned ha he exisence of efficien financia markes is necessary o susain he deveopmen of iberaized eecriciy marke, because eecric power sysems are highy capiainensive. Beside financing, risk managemen is a fundamena aspec of dereguaed eecriciy markes due o he high uncerainy of spo prices highighed above. Therefore, financia markes for risk managemen insrumens are a key feaure in he success of compeiive energy markes. As described in he previous secion, many sources of uncerainies impac spo prices, and more generay he revenue of uiiies. Beside price risk, i.e. risk in fue and eecriciy prices, he oher imporan sources of risk are voume risk, i.e. risk in demand, weaher risk and ouages. The second whoesae marke for exchanging eecriciy is he forward/fuures marke. Forward/Fuures conracs are conracs for deivery of a fixed eecric power during a fixed period saring a a fixed dae in he fuure (e.g. deivery of 1 MW for one monh beginning on he 6

19 Chaper. Inroducion firs day of January nex year. Forward conracs are usuay exchanged over he couner whie fuures are raded in an exchange and are free of counerpary risk. They can be boh physicay or financiay seed. Fuures conracs are usuay sandardized and deivery akes pace a specific periods, e.g. nex monh, nex hree monhs, nex year... Oher insrumens for hedging price risk have been deveoped, some inspired by he producs avaiabe in oher financia markes, ohers designed especiay for he needs of he indusry. Some exampes incude pus, cas, swaps and swapions, wrien on eecriciy or fue prices. Opions on spreads are very popuar in energy markes: caendar spreads are differences in he prices of a commodiy on wo differen daes whie fue spreads are differences in he prices of wo differen fues. To dea wih voumeric risk in energy markes, swing opions have been inroduced. They give he buyer he opion o buy a fexibe quaniy of eecriciy a a specific price and specific daes. I is a hedge agains voumeric risk because he oa quaniy of eecriciy ha can be chosen wihin he imis of specified bounds. The buyer hus has he fexibiiy of adjusing his consumpion o his needs. Temperaure derivaives, such as Heaing Degree Days or Cooing Degree Days, offer proecion agains emperaure risk and can be of ineres for energy risk managers since oad is srongy correaed o emperaure. New derivaive- or insurance-based producs have receny been creaed o dea wih oher weaher risks such as precipiaion and wind, or power pan ouages. Finay, more compicaed srucures such as oing agreemens are exchanged. Toing agreemens invove easing conracs for power pans and hey aow for he compee hedge of a producion asse..3 Chaenges.3.1 Re-hinking he Fundamenas of Risk Managemen The chaenge in deveoping risk managemen oos for energy markes is o cope wih he physica naure of he underyings, he presence of unhedgeabe risks and he unique feaures of he conracs. If one wans o draw a parae beween fixed-income or equiy derivaives and eecriciy risk managemen insrumens, one woud ry o mode eecriciy spo prices and appy he echniques of pricing and hedging, boh of which are we known in hese markes. However, a spo conrac canno be hed over ime and hedging wih spo conracs is impossibe in eecriciy markes. Oher echniques mus be used o price, hedge and manage eecriciy risk managemen insrumens. Even he reaionship beween spo price and forward price becomes more compicaed for eecriciy. For a sock paying no dividends, absence of arbirage opporuniies impies ha he forward price F T a ime for mauriy T is inked o he spo price S by he reaion: F T = e r(t S = E Q [S T ] where r is a consan risk-free rae and Q is he risk neura probabiiy. The firs equaiy is proved by a buy-and-hod argumen: a ime one can buy he sock a price S and se he forward conrac, his sraegy yieds a weah F T e r(t S a ime T ha mus be. The second inequaiy is proved by consrucing he repicaing porfoio composed of one sock. In he case of eecriciy, hese argumens are invaid because i is impossibe o hod a spo conrac. A spo conrac bough oday does no exis anymore omorrow. In fac we use he same name spo price or spo conrac for eecriciy deivered oday or omorrow bu hey are differen conracs on a differen commodiy. In addiion, as menioned earier, a forward conrac on eecriciy is no a conrac ha deivers one uni of eecriciy a ime T, or pays S T if i is financiay seed. I is raher a conrac ha deivers a quaniy of eecriciy over a period of ime. So a financiay 7

20 Chaper. Inroducion seed forward conracs wih mauriy T 1 and deivery period [T 1, T 2 ] pays T 2 T 1 e r( T1 S d a ime T 2. As a consequence, even if he above formua hod, he imiing price of a fuure conrac wih mauriy T woud no be he spo price a ime T. The fundamena properies of forward prices ha are we know for equiy of fixed income underyings, no onger hod when deaing wih eecriciy. Forward conracs can be greaer or smaer han he expeced spo price, he deviaion being inerpreed as a risk premium. Bessembinder and Lemmon (Bessembinder & Lemmon, 22 inroduced a mode o assess his risk premium. We obain an exension of his formuaion in Chaper 4. Forward price modes radiionay used for pricing and hedging derivaives are direcy wrien under risk neura probabiiy. The canonic mode is he mui-facor mode: df T n F T = σ i,t dw i i=1 where he W i are Brownian facors. As forward or fuures conracs are more iquid han he spo conracs and are rea financia conracs ha can be hod, hey are he cornersone of hedging sraegies. Compex derivaives are aways hedged using forward/fuures conracs and oher simper derivaives. The spo marke is ony used by producers and spo conracs are aways physicay seed. However, he pricing of some derivaives requires he modeing of spo prices. Sophisicaed sochasic modes have been deveoped o capure he specia feaures of spo prices such as sochasic voaiiy, jump diffusions, non-gaussian processes, hidden Markov chains, regime swiching..3.2 Managing and Vauing Socks As underined in he previous secion, managing socks dynamicay in ime is of grea imporance. The hree main socks are waer, greenhouse gas emissions and forward conracs. Hydro pans have ow margina cos, hus consiuing a cheap source of eecriciy, and aow for iner-empora arbirages beween eecriciy prices. Swing opions ha offer proecion agains voume risk aso consiue socks ha are simiar o hydro pans. A arge body of ieraure has been devoed o he opic of hydro pan managemen (cf. Chaper 2. In chaper 2 we propose a coninuous ime mode for he managemen a singe hydro sock in he presence of a wo-dimensiona uncerainy, ypicay price and infows. We characerize he vaue funcion of he sochasic opima probem as he souion of a non-inear paria differenia equaion (PDE. In he presence of emission reducion poicies such as he European Union Emission Trading Scheme, acors pay a penay a he end of he compiance period ha is proporiona o he emissions hey coud no offse by emission permis. The conro of cumuaed emissions corresponds o managing a sock. In chaper 3 we presen a join equiibrium mode of carbon rading and eecriciy producion and show how o characerize he opima emission poicy. Finay, he chaenge of dynamicay managing a porfoio of forward/fuures conracs and producion raises more quesions si. When i comes o financiay hedging producion, a cassica anaysis can be performed wihin a mui-facor mode. However, ong erm conracs may be beer exchanged wih physica deivery. In his case, ong erm conrac porfoio managemen as we as producion are more deepy conneced and he quesion of assessing he righ mix of producion and conracs becomes edious. Managing a porfoio of conracs is equivaen o managing a sock of energy..3.3 Assessing Fricions in he Markes The imperfecions of markes are anoher issue of imporance. By imperfecions, we firs refer o physica consrains in he managemen of physica asses. Fixed swiching coss, minima 8

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