Modelling the Volatility of Spot Electricity Prices


 Joseph Rose
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1 Modelling he Volailiy of Spo Elecriciy Price Abrac Nekaria V. Karakaani and Derek W. Bunn 1 Deparmen of Deciion Science London Buine School March 004 Thi paper preen a rucural approach o model ochaic volailiy in po elecriciy price. The peculiariie of elecriciy imply a complex rucure, preen boh in price level and volailiy, which alhough criical for marke and rik aemen, i negleced in ylied model and remain non rivial o model. In hi mehodology, price are fir deached from yemaic componen, uch a economic fundamenal, rik meaure, raegic and marke deign effec. Then, four alernaive approache are preened, where reidual volailiy i aribued o: i) he nonlinear impac of fundamenal, i.e. GLS heerocedaiciy, ii) he aymmeric volailiy repone o lagged price hock, i.e. a regreion + TGARCH rucure, iii) he evoluion of he underlying price model due o marke adapaion, i.e. imevarying regreion effec and iv) he aleraion of price rucure during emporal marke irregulariie, i.e. regimewiching regreion dynamic. Each alernaive i moivaed by differen apec of agen behaviour, bu all derive ochaic volailiy auming a nonlinear, rucural pecificaion for eiher he price formulaion proce (iii, iv) or he random hock (i,ii). Implemenaion of hi modelling o he UK marke reveal raegic behaviour in agen reacion o hock, wih ignifican inraday variaion, and ugge ha volailiy inference are eniive o he aumed price model. For inance, GARCH effec diminih afer adjuing for he imevarying price rucure. JEL: G14, L94 Keyword: Elecriciy, Spo Price Volailiy, Heerocedaiciy, Timevarying parameer regreion, Regimewiching, Marke power 1. Inroducion Following he worldwide rend of rerucuring public uiliie during he 1990, elecriciy ha emerged a an acively raded commodiy in po, forward and derivaive marke. The mo maure marke are hoe of he UK and Scandinavia, which ared heir operaion a he beginning of he 1990, followed horly by Auralaia and everal S. American counrie, and oward he end of he decade, by 1 London Buine School, Suex Place, Regen Park, London, NW1 4SA, UK. The auhor graefully acknowledge financial uppor from ESRC and he Naional Grid Company.
2 Spain, Germany, he Neherland and ome US Sae. Elecriciy price have developed alien and general characeriic 3, mo noably ha of po volailiy, order of magniude higher han in financial ae and oher commodiie. Induced 4 by phyical conrain and perhap by generaor raegic behaviour, erraic volailiy dynamic are preen no only a he highfrequency level of rading period bu alo he aggregaed daily level, a illuraed for he UK in Figure 1. Thi volailiy poe complicaion for hedging and ecuriy of upply, bu may ugge profiable raegie for hoe agen who underand and can anicipae 5 i complexiy. Alhough he proper pecificaion remain challenging, ochaic volailiy model are fundamenal for rading, producion cheduling, derivaive pricing, capaciy invemen and generaion ae evaluaion. Furhermore, volailiy model, if linked o economic fundamenal or raegic effec, can elucidae agen reacion o hock, and hu, reveal apec of marke performance of inere o regulaor. In he reearch lieraure, ylied ochaic model, inpired from financial marke and adaped o elecriciy, replicae ome of he aiical price peculiariie bu ill, diregard he ochaic naure of volailiy or do no clarify i caualiie and rucural properie. Thu, price model end o inroduce a jump componen for pike bu, in order o faciliae analyical derivaive formulae, adop he unrealiic aumpion of conan volailiy for he regular price proce (Johnon and Barz, 1999; Lucia and Schwarz, 00). Alhough hi implificaion i correced in Deng (000), where volailiy i pecified a a ochaic, meanrevering proce, jumpdiffuion model do no dienangle he effec of meanreverion and jump reveral (Huiman and Mahieu, 001) implying a mipecificaion of volailiy. An alernaive cla of model o jumpdiffuion, regimewiching model (Ehier and Moun, 1998; Huiman and Mahieu, 001), poulae ha volailiy alernae ochaically, according o a Markovian proce, beween diinc value, eimaed wih probabiliic inference. In hi ylied framework, volailiy end o be mipecified due o implici rericion on he price proce, uch a aionariy under boh regime, inan reverion o normal level afer an epiode or conan raniion probabiliie. In addiion, he Markovian aumpion could be rericive given he naure of he occurrence of pike, which could more explicily be ignified by a marke variable, uch a expeced capaciy urplu over prediced demand. Convenional form of imevarying volailiy, uch a condiional heerocedaiciy model (GARCH), alhough inuiively appealing, derive erroneou 3 Thee include meanreverion o a longrun level, mulicale eaonaliy (inraday, weekly, eaonal), calendar effec, erraic exreme behaviour wih farevering pike a oppoed o mooh regimewiching,, nonnormaliy manifeed a poiive kewne and lepokuroi, unable correlaion wih fuel price due o he alernaion of marginal plan echnologie. 4 Due o he inananeou naure of he commodiy, po volailiy canno be moohed wih economic invenory bu remain expoed o realime uncerainie, echnical or raegic, uch a plan ouage, inerconnecor failure or demand hock. The effec of nonorabiliy i amplified by he limied demand elaiciy o price in he horerm and oligopoliic marke rucure. In hi eing, porfolio generaor have he abiliy o behave raegically and induce volailiy in he po marke in order o creae incenive for forward conracing and increae rik premia. Anoher poenial ource of volailiy i he preence of muliple, parallel marke for elecriciy rading, wih limied volume and inadequae hedging inrumen o link elecriciy wih fuel price. 5 Thi propecive become more appealing given he currenly inroduced volailiy wap, which poe he challenge of correc pricing.
3 reul for elecriciy price (Duffie e. al., 1998), which i aribued o he preence of exreme value. Thee complicaion however, could be he reul of a mipecified price proce and are indeed reduced in he preence of a richer price pecificaion, a in Ecribano e al. (001), where he price model pecifie meanreverion, jumpdiffuion and eaonaliy in he deerminiic componen and jump ineniy. Applying GARCH modelling, Kniel and Rober (001) documen aymmeric repone of volailiy o poiive and negaive hock and an invere o financial ae leverage effec, bu no explanaion i uggeed for hi inereing idioyncray. Albei inighful for mediumerm price imulaion and derivaive pricing, ylied ochaic model, preen limiaion when adoped for marke aemen or horerm rading. Reaining oo high a level of analyi, he fundamenal ource of po volailiy are no addreed and hence, our underanding of agen reacion o hock and of he way informaion i proceed remain limied. A he link of volailiy o marke fundamenal are ignored, a ignifican componen of uncerainy i reained, which, if furher modelled, could dramaically reduce horerm rik expoure. Sylied model diregard he age of model validaion and do no allow for marke or agen pecificiie, uch a he inegraion of privae expecaion ino he economeric pecificaion. Thi ynhei i however criical for horerm predicion and, given he informaion aymmerie prevailing in elecriciy marke, ranlae o an obviou raegic advanage. Alhough an empirical approach ha model volailiy repone o fundamenal ha no emerged ye, empirical evidence allude o he preence of a complex underlying rucure. Duffie e al. (1998) ugge ha ochaic volailiy model hould accoun for 6 price level, rading volume and pread beween po and forward price, wherea Kniel and Rober (001) generally emphaie he need for rucural price modelling. In hi paper, we have adoped an economeric analyi of UK halfhourly po price, from June 001 o April 00, along wih everal fundamenal and raegic variable, in order o model ource of ochaic volailiy and clarify agen reacion o hock. The exen o which marke price, afer he inroducion of he New Elecriciy Trading Arrangemen (NETA) in 001, were co reflecive, reponded o rik meaure, or manifeed ome form of raegic pricing wa dicued in Karakaani and Bunn (004). Depie he low price era, and i fundamenal explanaion, he daily price dynamic revealed ha price were paricularly eniive o margin variaion and capaciy wihdrawal eemed plauible, hroughou he day and mo inenely around he evening demand peak. Sill, marke power wa no exercied o i full poenial. Exending hi reearch on marke efficiency, hi paper pecifie regreion model for price evoluion, of aic, imevarying or regimewiching pecificaion, and focue on he ochaic and rucural properie of he reidual volailiy ha relae o hem. Thi approach perceive volailiy a an inrinic, unobervable meaure of price movemen ineniy, linked o he flow of financial aciviy and informaion, and imulaneouly a reflecion of incomplee modelling. 6 The fir elemen can be repreened wih GARCH modelling, he econd eem plauible and conien wih evidence in oher energy marke, wherea he la require ome clarificaion, a forward bia i more an implicaion raher han a caual effec of volailiy.
4 Afer dienangling po price from yemaic componen, uch a economic fundamenal, raegic, rikreflecing and marke deign effec, four alernaive ource of uncerainy are uggeed o explain volailiy behaviour; i) he impac of marke fundamenal on uncondiional reidual variance, ii) he aymmeric influence of lagged hock on condiional reidual variance, iii) he adapaion of price rucure due o learning and iv) he occurrence of abnormal marke ae becaue of marke power abue. Each modelling approach provide an alernaive inerpreaion for he nonlinear naure of volailiy and focue on diinc aiical properie of he underlying proce. The fir wo formulaion impoe complexiy on he volailiy pecificaion, wherea he la wo on he price formulaion proce. All reveal apec of marke performance and agen behaviour and have he poenial o reduce horerm rik compared o ylied model, a hey allow agen o include heir predicion for marke fundamenal. All approache are plauible depending on marke condiion, wherea hybrid, albei heoreically appealing, enail convergence complicaion. A halfhourly rading period are differeniaed w.r.. echnical, economic and raegic characeriic, hey are modelled wih eparae price pecificaion. Thi allow appealing inraday properie of volailiy rucure o emerge, which are obcured in aggregaed analye. In erm of mehodology, he paper raie he iue of how eniive o price pecificaion volailiy modelling i. The reul ugge ha, in he preence of muliple complexiie in he price proce, an adequae repreenaion of price rucure i crucial for he correc pecificaion of volailiy. Specifically, he apparen GARCH effec are concealed or exaggeraed depending on he price model and eem o diminih, when he adapive price rucure or uncondiional heerocedaiciy are accouned for. In a ylied framework, hi indicae ha modelling he dynamic rucure of he price proce (e.g. an auoregreive model wih imevarying parameer) may decribe volailiy dynamic beer han a price model wih complex variance rucure (e.g. AR + aymmeric GARCH). The paper i rucured a follow. Secion inroduce a rich regreion model for po elecriciy price, baed on which parimoniou pecificaion are derived, diinc for each load period. In ecion 3, he nonlinear repone of uncondiional reidual variance o economic and raegic impac are modelled followed by he auoregreive rucure of condiional reidual variance. In ecion 4, imevarying volailiy i linked wih he evolving rucural impac on price, a marke adap o endogenou or exogenou change. Secion 5, inveigae he reacion of volailiy o emporal marke abnormaliie. Secion 6 conclude he paper.. Srucural Price Specificaion Volailiy analyi i epecially perinen o he reformed UK po marke under he 001 New Elecriciy Trading Arrangemen (NETA), which induced new rik for marke paricipan, ome of which are unhedgeable. Among he regulaor deliberae inen wa o increae he volailiy in horerm marke, in order o reward flexible capaciy and encourage forward conrac. Thu, we would expec a raher complex volailiy proce in he po marke, where agen behaviour would reflec boh he en year maure experience of wholeale power rading, and he new learning aociaed wih he marke mechanim change.
5 .1 Daa Se The marke regime preceding NETA, he Pool, wa a compulory po marke wih uniform pricing, where dipach wa derived dayahead wih a cominimiaion algorihm on offer ubmied by generaor. A price were pecified on a dayahead bai, hey were ineniive o realime uncerainie and hence, no paricularly volaile. Forward conrac allowed he diverificaion and hedging of po price rik. NETA inroduced a marke iniuion wih bilaeral rading and dicriminaory price in a equence of volunary, unadminiered marke wih conrac horizon up o everal year ahead. More han 95% of elecriciy i currenly raded forward in overhecouner marke. For adjumen of conracual poiion cloe o real ime, Power Exchange (PX) have emerged. Thee operae on a dayahead bai up o Gae Cloure, which wa iniially defined a 3½ hour before real ime and reduced o one hour in July 00. A Gae Cloure, paricipan noify heir final phyical poiion (FPN) o he Syem Operaor. Afer hi poin and in order o reain yem abiliy, he Syem Operaor adminier a balancing mechanim (BM), where generaor and upplier ubmi bid and offer o deviae from heir declared poiion a Gae Cloure. Imbalance, i.e. deviaion beween noified and expo meered poiion of firm are penalied wih dual dicriminaory pricing. Thi render unhedgable rik wih energy deficiency in he BM much more coly han energy urplu. In hi bilaeral environmen, he rucural properie of horerm marke were expeced o influence price in he preceding bilaeral marke and eem he appropriae iniial poin for marke analye (Sweeing, 000). The UKPX, analyed here, i he dayahead po marke ha provide halfhourly po indicaor, perceived a a replacemen of he Pool Purchae Price. The funcion of UKPX include phyical delivery, adjumen of conracual poiion, forward conrac and derivaive linked wih he po index. The daa coni of halfhourly value for he UKPX po price and he explanaory variable of heir variaion. For a given day, load Period 1 i defined a (prior o he day), period a , period 3 a and o on up o period 48 ( ). The ampling period wa pecified a 6 h June, April, 00 including 300 day. Conidering 10 monh of daa for each load period wa ufficien o derive reliable eimae and induced ufficien aionariy in he demand and margin erie. Alhough he reform were implemened in 7 h March, 001, he fir monh of NETA were diregarded due o he pronounced marke inabiliy and he daa qualiy iue ha emerged. Thee mainly involved he occurrence of arificial price pike due o miake and numerical deficiencie of he price algorihm. June 001 wa uggeed by indurial analy a an appropriae iniial poin for repreenaive analye. The halfhourly price erie 7 diplayed he ypical empirical feaure of po elecriciy marke, i.e. large volailiy, poiive kewne and exce kuroi. The daily average price, average daily price profile, iner and inraday volailiie, diplayed in Figure 1, reveal he complexiy of po price dynamic, depie he 7 Pilipovic (1998) howed ha he logarihm of daily average elecriciy price are normally diribued. In hi highfrequency udy, he emphai wa inead on halfhourly price and hu he log ranformaion wa no adoped. Depie i variance abilizing properie, wherever applied, i did no aler he inference and complicaed he inerpreaion of he regreion coefficien.
6 relaively hor ampling period. In Figure, halfhourly price for eleced period illurae he rich inraday variaion in price evoluion and he addiional modelling complexiy ha hi poe a well a he poenial for mileading inference, when diurnal paern are moohed wih averaging. Saionariy e (Augmened Dickey Fuller and PhillipPerron e) for price in each load period, afer adjuing for erial correlaion, rejeced he preence of a uni roo a he 5% ignificance level. The rejecion of he random walk hypohei moivaed he deailed exploraion of price rucure.. Influenial Variable The modelling approach involve he formulaion of a regreion model for he evoluion of po price, wih aic, imevarying or regimewiching pecificaion, and he udy or explici modelling of he reidual variance ha emerge. A nonrivial iue i o define or quanify he facor refleced upon price, uch a economic fundamenal, plan conrain, raegic effec, rik percepion, rading inefficiencie, learning, forward rading and marke deign implicaion. A proper pecificaion 8 of Demand i crucial, boh in ielf a a fundamenal driver of daily price variaion, and in order o formulae a wellpecified background from which o eimae properly oher, perhap more uble, influence on price. In he conex of elecriciy marke, demand can be perceived a an exogenou variable o price, becaue of he abence of demand elaiciy in he horerm. In our applicaion, he nonlinear demand effec wa idenified a a quadraic polynomial. To reflec he iming of he po marke and in order o avoid endogeneiy, Demand wa defined a an expecaion, he 1 p.m. dayahead foreca conduced by he Naional Grid. Due o heir high correlaion, he coexience of he wo demand erm would lead o an illcondiioned marix. To reolve he collineariy, he demand polynomial wa decompoed ino wo orhonormal funcion. Furhermore, ince he exience of a balancing mechanim in NETA could induce he backward migraion of ome pricing of plan dynamic ino he preceding PX rading, he Slope and Curvaure 9 of demand were alo conidered. More pecifically, Demand Slope, he rae of change in demand, could be paricularly influenial and repreen he period when he more flexible plan i able o achieve higher price. Demand Variaion, due o emporal, weaher and conumpion paern, impoe difficulie in load predicion and plan cheduling and evenually implie balancing co. In addiion, unanicipaed demand pah influence agen rik aiude and, given NETA aymmeric penaly for energy Imbalance, could encourage upplier overconracing. However, he noion of demand uncerainy i no obviou o quanify. Relevan meaure include he unexpeced demand derived from a predicive model or he hioric volailiy of demand. Here, i i aumed ha marke paricipan updae heir percepion abou demand flucuaion conidering he 8 Demand appear a a aevariable in equilibrium ochaic model (e.g. Eydeland and Geman, 1998), a criical variable in hrehold auoregreive model (Sevenon, 001), a caual facor in neural nework and linear regreion (e.g. Vuceic e al., 1999). The la pecificaion involve a hird order demand polynomial. 9 Demand change coninuouly bu for impliciy, Demand Slope (Curvaure) wa approximaed by he rae of change of demand (demand lope) in ucceive halfhour period, i.e. by he fir (econd) difference of halfhourly demand meauremen.
7 equence of he 7 mo recen demand value for each period. Thi imehorizon wa eleced for meeorological reaon and enure alway he preence of all weekday and a weekend in a rader daabae. Demand Volailiy wa hen, defined a he coefficien of variaion, i.e. (andard deviaion/mean) in a weekly moving window. Due o large demand flucuaion acro he year, hi andardiaion wa eenial in order o avoid mileading inference. Demand Foreca Error 10 by NGC i a caue for over or underconracing and hu, imbalance. I wa defined a Acual Demand minu he 1pm dayahead Foreca. Marke informaion and poible raegic effec were refleced in he following variable: i) Margin i a meaure of exce generaion capaciy, defined a he aggregaed maximum poible oupu (he final noificaion a gae cloure ) minu he dayahead demand foreca from he Naional Grid. ii) Expeced Imbalance, i defined a Indicaed Generaion minu Prediced Demand a Gae Cloure. iii) Scarciy i derived from he Raio=Margin/Demand (Viudhiphan and Illic, 000) a: max{ Lower Quarile of Raio Raio,0}, where he lower quarile i calculaed from he hioric diribuion of Raio in each load period. Thi variable i inended o capure he eep impac of capaciy urplu on price afer a hrehold. Hioric marke condiion were capured by po price for he ame load period on he previou day and week a well a daily average price on he previou day. The laer creaed he deired link beween byperiod bidding and ignal from he enire day. Price Volailiy, an index of inabiliy and rik, wa defined imilarly wih demand volailiy, a he coefficien of variaion of price in he preceding week. Finally, Spread wa included, defined a he difference beween he wo balancing price for inufficien and exce capaciy 11, and repreening unhedgable rik in he balancing mechanim. A a meaure of rik expoure, i could impac on forward premia and be manifeed in po price. Alhough he value of pread on he day i derived afer he po price, Spread on he previou day could ill ignal relevan rik and influence bidding, paricularly if here wa a endency in he marke (due o peculaor, regulaor or grid aciviie) oward moohing imbalance rik. Alernaively, one could define he difference PXSSP and SBPPX, wo meaure of arbirage ha reflec he value or co of flexibiliy cloe o realime. Thee indice are eenial for conrac evaluaion and informaive abou he relaive aracivene of po and balancing marke. Each load period diplay a raher diinc price profile reflecing he daily variaion of: demand, operaional conrain and co implied by differen plan echnologie, marke deph and poenial for marke power. In order o conrol for hee diimilariie, he modelling wa implemened eparaely for each load period. Thi wa alo inpired by he exenive reearch on demand forecaing which ha 10 The predicion error could, in principle, be correlaed wih demand and incur mulicollineariy, bu hi did no occur in our applicaion. 11 In he balancing mechanim, Spread i he difference beween he Syem Buy Price (SBP) and he Syem Sell Price (SSP).
8 generally favoured hi mulimodel approach for accuraely forecaing daily demand (Bunn, 000). The differen demand profile for weekend would be expeced o induce yemaic elemen in he evoluion of demand, margin and hence price, and alo a hif in he morning and nigh peak, compared o weekday. However, eparae modelling of weekday, Saurday and Sunday uggeed ha he above iue did no aler he inference, poibly due o a wellpecified incluion of demand and margin in our model. Seaonaliy, however, wa imporan a a proxy for he yearly paern of fuel price and approximaed wih a inuoidal funcion peaking in winer. The linear regreion model 1 for po price i pecified a: P = β j + ε j, ε j ~ N(0, σ j ) j X j where, Pj denoe he po price on day and load period j, = 1,,..,T and j=1,,...,48, β j a 16x1 vecor of parameer, X j a 16x1 vecor of exogenou explanaory variable, defined afer preliminary analyi a: X j = (1, P j(1), P j(7), Average P 1, Spread j ( 1), Price Volailiy j(1), Demand j (Linear, Quadraic Term), Demand Slope j, Demand Curvaure j, Demand Volailiy j(1), Margin j, Margin j(1), Scarciy j, Time, Seaonal Componen j ) andε j a random and erially uncorrelaed error erm. Thi rich model revealed ignifican inraday variaion of he rucural effec on price (Karakaani and Bunn, 004). Therefore, in he volailiy modelling ha follow, diinc parimoniou model are eleced for each rading period. Thee are no uniquely defined, a everal pecificaion may be equally plauible for he daa depending on he adoped opimaliy crierion and variable elecion procedure (e.g. forward addiion, backward eliminaion, wodirecion epwie, be ube elecion). In addiion, each volailiy modelling approach poe differen convergence complicaion even for he ame load period. The formulaion preened in he illuraive example are he more robu for he paricular eing. 3. Heerocedaiciy Modelling Afer deaching price from fundamenal rucure wih a parimoniou model, queion are raied abou he rucural properie of reidual variance, Var ( ε ). Thi i an expo meaure of price rik ha reflec he model uncerainy around fied price. Alernaively, i can be inerpreed a he predicive uncerainy of a rader who formulae hi price expecaion wih he regreion model and know 1 In he above model wih ochaic regreor, andard aumpion include: i){ P j, X j } i joinly aionary and ergodic, which preclude rending regreor. ii) The regreor are predeermined, which exclude endogenou regreor bu allow lagged dependen variable. Under hee aumpion, which were deemed o be plauible for he daa, he OLS eimae are conien and aympoically normally diribued even under i.i.d., non normal error.
9 apriori 13 he model pecificaion and he correc value of exogenou variable. In rading pracice, an agen would apply he price model ubiuing he exogenou variable by hi own predicion. If here i, in addiion, an explici relaionhip ha link reidual variance o marke fundamenal and pa hock, he rader could derive alo an eimae for hi implici price rik. Syemaic componen in reidual variance could arie due o inadequacie of he price model or heerocedaiciy, condiional or uncondiional, of he random hock. Alhough i i no feaible o dienangle he effec of price model mipecificaion and heerocedaiciy, i i poible o ae heir compounded implicaion on reidual variance and quanify i repone o marke fundamenal and pa hock. 3.1 Uncondiional Heerocedaiciy To clarify he nonlinear repone of reidual variance o raegic and economic effec, Generalied Lea Square (GLS) modelling i adoped. Thi explici modelling of uncondiional price heerocedaiciy allow a formal exploraion of volailiy hypohee and indicae how agen reac o uncerainy under differen marke condiion. Correcing he rericive aumpion of homogeneiy implici in he OLS price model, GLS eimaion hould induce more reliable inference regarding he ignificance, ign and magniude of rucural effec on price level. The GLS regreion model wih nonpherical uncorrelaed diurbance i pecified a: P = β + ε, j X j ε j ~ N n (0, Σ j ), Var(ε j ) = g( v j ) Σ j = diag{ g( v j )} I n where v denoe he covariae driving he variance, g(v) he variance funcion, Σ = E ( ε ε ) he error covariance marix. A criical iue i he elecion of he funcion g, which hould replicae nonlineariie imilar o hoe emerging due o nonconvex marginal co and raegic behaviour. Two funcion eem appealing: i) The power formulaion, defined a g ( v) = ( α + v ), where a, b denoe unknown parameer. The quadraic form allow for a rich volailiy rucure, no necearily monoonic, which include he linear dependence a a pecial cae. v ii) The exponenial formulaion, defined a g ( v) = e, where i an unknown parameer, replicae monoonic, kinked effec on volailiy. GLS modelling of po price acro everal rading period uggeed ha reidual variance preen an heerogeneou rucure wihin he day. Sill, cluer of period wih imilar repone eemed o emerge according o heir poiion in he demand curve and paricularly he degree of demand abiliy or adjumen. Thi inraday variaion i illuraed wih he peak load period 5 and he morning period 15, which repreen a raniory age for he demand curve when flexible plan ar operaing. The price model were parimoniou pecificaion eleced wih epwie procedure from he rich model in ecion. and he profile of reidual volailiy were explored 13 The former aumpion i plauible if he model equaion i able over ime and derived from pa daa. The laer applie o rader wih accurae informaion abou fuure marke fundamenal, which in our applicaion reduce o he variable Capaciy Margin. j j b
10 wih he power pecificaion, which proved here o be more robu o he elecion of iniial value, le eniive o oulier and eaier o converge han he exponenial model. The eimae of he parameer α were effecively zero in all he preened example, which revealed monoonic impac of he conidered covariae on volailiy. The ignificance and ign of he variable in he price model were quie robu acro variance pecificaion, which uggeed ha an OLS model i a valid approximaion of price dynamic, even if GLS effec are ignored. The reul 14 for period 5 are ummaried in Table 1. Reidual volailiy reponded poiively o price ignal, diplaying a linear dependence on Lagged Price and a parabolic, le eep han quadraic, link o Expeced Price. Thee poiive effec uggeed an invere o he leverage effec documened in financial marke, a peculiariy of elecriciy price o be dicued laer. The increae 15 in volailiy a margin decline indicaed he diveriy of raegie and poibly arbirarine of bidding under relaive carciy. Reidual volailiy and demand were almo inverely proporional and hi hyperbolic link could be aribued o everal mode of agen behaviour. The augmened uncerainy during low load migh ignal he decline of price o unexpeced level, below heir fundamenal value, poibly due o overupply. In conra, high demand could moivae imilar price expecaion and perhap eaier colluion, which ranlaed o more predicable price in he conex of a price model ha addree raegic effec. Alernaively, he demand effec could relae o he conervaive bidding of flexible plan, which achieve exceive profi during he morning and evening peak and imply wih o reain heir operaion in inermediae period. If demand i low on a pecific day, hee aion reward decline even furher, which poibly creae incenive for more aggreive and unpredicable bid beween peak. Anoher conjecure i upplier overconracing under high demand, when expoure o imbalance price i paricularly penal, which induce more aciviy in he po marke and more repreenaive price. A oppoed o he previou remark, empirical evidence ugge he increae of price volailiy wih demand. Thi conradicion i only uperficial, a he volailiy meaure analyed here i no he aiical price variance bu he reidual uncerainy afer fundamenal rucure ha been ubraced. Finally, inead of a rucural volailiy equaion, erial correlaion wa aumed for he innovaion erm ε in he form of an AR(1) proce, where cov( ε, ε 1 ) = ρ, = 1,..., n. Thi pecificaion eemed plauible bu auocorrelaion diminihed when a rucural model wa aumed for variance, which ugge ha AR effec are imply a urrogae for omied facor. The adequacy of a variance 14 The parameer in he variance funcion are eimaed wih an ieraive procedure by maximiing he marginal likelihood of he reidual from he leaquare price model. The regreion coefficien are ubequenly eimaed by maximum likelihood auming ha he variance rucure i known, a propoed in McCullagh and Nelder (1989). The derived βˆ GLS i imply he weighedleaquare eimaor: ˆ X ˆ GLS ( X ) X ˆ β = Σ Σ P 1 1 wih eimaed covariance marix: ˆ ( ˆ ) ( ˆ Var β = X Σ X ). GLS 15 The ame ign of he coefficien aociaed wih demand and margin are conien, a he linear correlaion beween he wo variable i low for hi period (0.9).
11 pecificaion can be aeed wih he value of he Log Likelihood funcion and he Reidual Sandard Error (RSS). Table 1. PX Price, Period 5. Variance Srucure from GLS Modelling. Price Model P ~ Conan + P 1 + MP 1 + SBP 1 + Price Volailiy + Demand + Demand Curvaure + Margin + ε Volailiy Model Var (ε ) = g (v) = v b Covariae v Coefficien (b) Log Likelihood RSE Expeced Price Demand Margin P Auocorrelaion ( ρ ) Inference abou he variance rucure in period 15 are ummaried in Table. The effec of Margin and Demand remained negaive, a in period 5, bu heir magniude were coniderably differen, wih he former porraying a limied impac of he order of ¼ roo and he laer a more dramaic, almo invere quadraic effec. One inerpreaion i ha flexible plan, which ar heir operaion a hi age and require a premium for he implici rik, behave in a more predicable manner a demand increae, poibly becaue co implicaion are more dramaic or colluion eaier. Finally, Expeced and Lagged Price diplayed negaive effec on reidual volailiy, which implie more uncerainy around low price, he oppoie condiion of he peak period 5. Thi diimilariy in he repone of volailiy o price ignal poibly arie from he differen poiion of he wo period in he demand curve. Firm behaviour eem o be dominaed by profi maximiaion in period 15 v. operaing conrain in period 5. Table. PX Price, Period 15. Variance Srucure from GLS Modelling. Price Model P ~Conan+P 1 + P 7 + Demand + Demand Slope + Margin + Margin 1 + ε Volailiy Model Var (ε ) = g (v) = v b Covariae v Coefficien (b) Log Likelihood RSE Expeced Price Demand Margin P Auocorrelaion ( ρ ) Condiional Heerocedaiciy The previou modelling uggeed ha uncondiional heerocedaiciy i a plauible explanaion for he erraic volailiy dynamic. The volailiy repone o fundamenal ended o be nonlinear and revered ign wihin he day reflecing dynamic operaing conrain and firm raegie or inadequacie of he price model. I hould be emphaied ha, afer accouning for he impac of fundamenal on volailiy, GLS reidual preened no ignifican GARCH rucure. Thi implied ha
12 he auoregreive volailiy rucure, oberved in pracice, i eliminaed, if a fundamenal explanaion for variance i poulaed. Alhough a urrogae for omied facor, condiional heerocedaiciy i ill an appealing price propery for rading and conien wih he realied pah of elecriciy price, ofen characeried by period of high inabiliy followed by period of relaive ranquilliy. Thi volailiy cluering implie ome predicabiliy, which could be enhanced when accouning for aymmerie and nonlineariie in he repone of volailiy o new. The occurrence of jump however, prohibi he applicabiliy of GARCH model. Duffie e al. (1998) conclude ha erroneou reul, uch a inegraed volailiy procee, are uually derived due o he bia inroduced by exreme price. Such undeirable effec are conrained however, if regreiongarch modelling i adoped, a GARCH effec are hen explored in regreion diurbance and no pure price. Deached from yemaic componen, which may preen exreme value for cerain value of he covariae, regreion reidual are mooher, even during pike, and allow convenional volailiy modelling. The regreiongarch approach inroduce implicily a diincion beween unexpeced hock ouide he model boundary, which reflec new and creae volailiy, and exreme value of influenial variable, poibly anicipaed and perien for a ime period, which induce high price. The regreion model wih GARCH (1,1) normal error i defined a: = P X β + ε ε = h u, ~ N(0,1) h = ao + a1 1 + ah 1, ao > 0, a1, a 0. where P i he po price in a pecific load period (he ubcrip j i omied for impliciy), ε an i.i.d. erially uncorrelaed innovaion proce, aionary under he condiion a + a 1, wih condiional variance h Var ε I ) E( ε I ), a 1 < ε u = ( 1 = 1 imevarying, poiive and meaurable funcion of I 1, he informaion e a ime 1. In order o accoun for he lepokuroi of elecriciy price, a andardized Suden' diribuion i aumed for u. Having defined he RegreionGARCH model, he volailiy properie of po elecriciy price are explored wih differen pecificaion for he condiional mean and condiional variance. The equaion, diplayed in Table 3, vary w.r.. adequacy of price decripion and complexiy. The naïve price model I, convenional in financial pracice, implie ha price follow a lepokuric diribuion flucuaing randomly around a longrun mean value. To reflec meanreverion, model II impoe an AuoRegreive (AR) proce wih opimal number of lag w.r.. o he AIC crierion. Equaion III poulae a regreion model inended o capure yemaic price rucure. Among he variance equaion, IV implie a ymmeric GARCH (1,1) rucure for he reidual of he price model, i.e. aume ha poiive and negaive diurbance have he ame impac on h. Model (V) impoe he Threhold GARCH (1,1) rucure, inroduced by Zakoian (1994), which allow for aymmeric effec of poiive and negaive lagged hock on he condiional andard deviaion. Poiive
13 new ( ε > 0 1 ) have an effec of α 1 on h, wherea negaive new have an effec of α 1 + γ. The price and variance equaion are eimaed joinly, a he former involve lagged value of he repone. The likelihood funcion 16 i maximized via dual quainewon. The aring value for he regreion parameer are obained from OLS eimaion or YuleWalker equaion when auoregreive parameer are preen. Table 3. Price and Variance Specificaion in GARCH Modelling. Price Model Variance Model P = c + ε (I) h a + 0 α 1ε + 1 ah 1 (IV) P = c + L( ) + ε (II) P P = β + ε (III) X h = = a0 + 1ε 1 + γ S 1ε 1 + a h 1 α (V) In he above, L denoe a diribued lag polynomial and S 1 he indicaor 1, if ε 1 < 0 funcion: S 1 =. 0, oherwie Implemenaion of he modelling o UK po price howed ha he pecificaion poulaed for price do affec he idenificaion of volailiy dynamic and may even ugge conflicing concluion. A an illuraion, Table 45 preen GARCH reul for wo peak period wih paricularly volaile dynamic. For period 5, he opimal AR(6) model did no converge and wa replaced by an AR(4). GARCH effec, revealed under oher price pecificaion, proved inignifican afer removing he rucural componen of price. For period 35, he regreion price model implied ignifican volailiy aymmery, which wa however inignifican under AR model. To faciliae convergence, he opimal AR (4) wa ubiued by he robu AR(1) pecificaion. The reul could be ummaried a follow: i) Wihin he Regreion + GARCH model, he complicaion documened by Duffie e al. (1998) diminih. Thi could be aribued o he fac ha high price frequenly emerge from he ame rucural model a regular price bu for exreme value of he covariae. Wherea he regreion model could anicipae o ome exen he abnormal price level, a nonrucural model could erroneouly perceive high price a large hock and hu, bia he eimaion. More pecifically, wo ype of reul emerged. For ome load period, when a regreion price pecificaion wa 16 The Log likelihood funcion under he error diribuion i: T v + 1 v 1 log L = log( Γ( )) log( Γ( )) log(( v ) h ) = 1 where Γ i he gamma funcion and v denoe he degree of freedom in he condiional diribuion, an addiional parameer o be eimaed.
14 aumed, a rong auoregreive rucure wa deeced in he variance. However, GARCH effec eemed inignifican or he model failed o converge, when price were inead decribed wih an AR proce. In oher cae, he oppoie reul wa oberved. The perience of exreme bu anicipaed marke condiion (e.g. high demand), which induced a erie of high price, wa inerpreed a perience of random hock by impliic GARCH model. The above obervaion ugge he eniiviy of volailiy inference o he price model. ii) Model I wa enirely inadequae and led o erroneou reul, uch a exploive variance. Impoing an opimal AR model (II) wa ofen ufficien o avoid unreaonable eimae, poibly becaue auocorrelaion had a rong preence in he new marke due o learning and rading inefficiencie. A i wa expeced, reidual uncerainy wa reduced ignificanly 17 when price level were modelled wih a rucural formulaion. Thi wa refleced boh in longerm (aympoic variance) and horerm (impac of lagged hock on condiional variance) meaure of uncerainy. Thi could be parially aribued o he fac ha realied value of exogenou variable, uch a Margin, were ued in he price model. Sill, imulaion of expeced Margin uggeed ha hi propery of regreiongarch modelling i reained in forecaing eing. Thi finding i crucial for dayahead rading, a forward price convey lile informaion abou inraday po price flucuaion, epecially when repored only a aggregaed indice (peak/baeload). iii) In everal rading period, condiional variance eemed o repond aymmerically o poiive and negaive pa hock. The negaiviy of he parameer γ uggeed ha he invere of he leverage effec idenified in financial ae applie o elecriciy price. Thi mean ha poiive diurbance have a ronger impac on volailiy han negaive one, a documened in Kniel and Rober (000) for California price. One poible explanaion i ha in he cae of ock, low price increae he leverage expoiion of he firm and have a direc impac on he percepion of ockholder; in conra, in he cae of elecriciy, price higher han expeced may arac regulaory inervenion or new enry, boh undeirable oucome for generaor and ufficien o creae emporal uncerainy. An alernaive inerpreaion ugge ha a price exceed heir anicipaed level, ofen due o marke power abue, here i a lack of conenu abou he rue value of he commodiy and a endency oward more aggreive bidding. Speculaor araced by poenial profi add o hi diperion of expecaion, which caue more inene price flucuaion han during lower price. iv) When a covariae wa inroduced ino he GARCH equaion, uch a Demand or Margin, he coefficien were inignifican or convergence wa infeaible. 17 Even when hey involved more variable, AR+GARCH model indicaed more volaile innovaion procee han Regreion +GARCH model. The more he exreme price prediced by he regreion model, he more dramaic he deviaion in he reul were.
15 Table 4. GARCH Modelling for PX Price, Period 5. Price Equaion Model (I) Model (II) Model (III) Variance Equaion + h a α ε a h (IV) o = α 3.01 (0.03).46 (0.01) 3.87 (0.00) α 0.39 (0.003) 0.9 (0.007) 0.8 (0.015) 1 α 0.46 (0.006) 0.46 (0.00) 0.17 (0.) diribuion (df) Aympoic S.Deviaion Table 5. GARCH Modelling for PX Price, Period 35. Price Equaion Model (I) Model (II) Model (III) Variance Equaion h = a0 + α 1ε 1 + γ S 1ε 1 + a h 1 (V) α o 6.76 (0) 0.51 (0.06) 1. (0.01) α (0) 0.6 (0.0) 0.17 (0.0) α 0.17 (0) 0.8 (0) 0.9 (0) γ (0.03) (0.10) (0.007) diribuion (df) Aympoic S. Deviaion Evoluion of Price Srucure 4. 1 Moivaion Thi ecion inend o ae wheher he eviden imevarying po volailiy reflec an evolving price rucure, reul of a highly repeaed aucion and coninuou agen adjumen o change in marke rucure and rule. A dynamic fundamenal price analyi i hu propoed o reveal he direcion oward which price evolve, uch a more coreflecing, rikrelaed or raegically abued level. In order o follow he complex proce of marke adapaion, he rucural price model aumed in previou ecion are repecified here wih imevarying parameer. An apriori aemen of he marke orienaion i no obviou. The halfhourly ineracion among marke paricipan and beween hem and he yem operaor induce learning, which reveal profiable raegie bu imulaneouly moivae more efficien reacion by he yem operaor. Under he new uncerainie, induced by NETA, individual acor or group (generaor v. upplier, peculaor, generaion echnologie, NGC) updae heir uiliy funcion, rik averion parameer and raegie. I i however queionable wheher he adjumen of everal parie wih conflicing inere are couneraced or move oward a imilar direcion, which aiude dominae and how he orienaion of he enire marke evolve a a reul of hee dynamic ineracion. Aeing price convergence wihou a fundamenal analyi migh be mileading in he preence of eaonaliy, conradicory or unable marke ignal, and muliple exogenou or endogenou hock affecing rading.
16 4. TimeVarying Parameer Regreion Model In order o follow he evoluion of rucural effec on price and hence, clarify he imeheerogeneiy of volailiy, a TimeVarying Parameer (TVP) regreion model i pecified: P = β + ε Meauremen equaion j X j j j β j = β j( 1) + v j Traniion equaion where, ε j ~ i. i. d. N(0, σ ε ), v (,,..., ) j j = v j1 v j v jk, v j ~ N k (0, Σ j ), E( ε jv j ) = 0 and Σ j = diag σ v }. { jk In he above aepace formulaion, he regreion coefficien are no unknown conan bu laen, ochaic variable ha follow random walk. Thi pecificaion wa plauible for everal load period, a indicaed by abiliy 18 e (ypically a ignificance level of 510%). Thi reul i inuiive a many hock during he ampling period had a permanen or cumulaive raher han diminihing effec in marke adapaion. Such hock include rule modificaion, regulaor announcemen abou he lengh of he Balancing Marke and a new rule for price calculaion, policie regarding renewable, merger and acquiiion in he elecriciy indury in addiion o he Enron collape. The aepace model wa eimaed wih dicree Kalman Filer. The filer recurion indicae how a raional economic agen would revie hi eimae of he model parameer in a Bayeian fahion wihin an environmen of uncerainy, a new informaion become available. In our conex, he recurion indicae how he marke a a whole evolve aaching varying imporance o fundamenal. The Kalman Filer Algorihm for he TVP model i decribed in Appendix I. I hould be emphaied ha TVP model are differeniaed from he ARCH cla of model implemened in 3. wih repec o he feaure of uncerainy hey inend o capure (Kim and Nelon, 001). In he laer ype of model, changing uncerainy abou he fuure i focued on he condiional heerocedaiciy in regreion diurbance. In imevarying regreion however, an agen uncerainy abou he fuure arie parially from fuure random erm. I alo reflec uncerainy abou curren parameer value and he model abiliy o link he preen o he fuure. The uncerainy abou curren regreion coefficien reul in he changing condiional variance of price. Thi decompoiion of uncerainy i capured in he equaion for he variance of he condiional foreca error: H = X P X j 1 j 1 j 1 j 1 + σ ε j, where P repreen he degree of uncerainy aociaed wih an inference on β j 1 j condiional on informaion up o ime Two ype of abiliy e were performed; he homogeneiy e (Brown, Durbin, Evan, 1995) again he alernaive hypohei of unable regreion coefficien and he Engle and Waon (1985) again he alernaive hypohei of random walk coefficien
17 4.3 Dynamic of Price Srucure Implemenaion of he TVP modelling o NETA elucidaed everal apec of he marke evoluion proce. Alhough cluer of period wih imilar paern of rucural evoluion emerged, inraday variaion wa ill coniderable. Thi indicaed ha he fragmenaion of rading acro period allowed he perience of differen rucural rend wihin he day and delayed marke convergence. Even when he variance of he effec were no aiically ignifican, he dynamic eimaion procedure uncovered uble deail of he adapaion proce, which were negleced when a aic regreion model wa aumed. In general, adjumen effec remained rong up o December 001 and were ill preen one year afer he inroducion of NETA. The analyi indicaed a gradual hif of marke orienaion oward more ophiicaed rading and poibly more cobaed price wih greaer reponivene o perceived rik. In conra o he erraic dynamic of demand effec, he decreaing impac of margin wa eviden and ignified a rend oward le raegic bidding, a lea in he convenional ene. Some evidence of capaciy wihholding, implied by he negaive effec of Lagged Margin, alo diminihed in January 00. The decline of raegic impac and auocorrelaion indicaed ha he iniially prevailing inefficiencie in he reformed marke were progreively being eliminaed o a large exen. Typical ochaic paern of he evolving price rucure are illuraed wih period 5 and 35. The price model eleced were again he more robu for he pecific eing. Table 6 repor model formulae and parameer eimae for he illuraive model. Figure 34 depic Kalman Filer he dynamic regreion coefficien condiional on informaion up o ime 1. The recurion illurae how price eniiviie o variou facor were revied during he ampling period. I i apparen ha a ignifican proporion of price variaion i due o he evoluion of regreion coefficien in he price equaion. In pecific, he impac on po price of price ignal from he previou day and week decreaed over ime for variou load period. Thi apec of bidding behaviour, diplayed in Figure 3ab and 4ac, indicaed increaing limiaion in price forecaing wih auoregreive model. One plauible inerpreaion i ha bidding became progreively more ophiicaed or more baed on privae daa raher han hiorical price. Thi wa conien wih he marke endency oward verical inegraion and wihinfirm rading for rik managemen. The alernaive conjecure ha he marke became more efficien and gradually cancelled price auocorrelaion eem quie unrealiic given he perience of relaive illiquidiy. In conra wih pa price, he role of hioric PX volailiy increaed dramaically for ome peak period. A Figure 3g illurae, in period 5 he volailiy impac on price, reflecing forward premia, ripled in March 00 compared o July 001. Even if he iniial eimae were eniive o he eleced prior, he increaing rend wa ill obviou. Thi implied ha he hedging of rik via he dayahead marke became more expenive over ime in repone o he unpredicable SBP and primarily, credi rik. The Enron collape and he fir ign of generaor bankrupcie creaed an inecure rading environmen, where rik were convered o more expenive pricing. An alernaive plauible view i ha generaor ended o exploi progreively upplier expoure o penal imbalance price, a lea occaionally. A final componen manifeed in hi dynamic behaviour i he regulaory rik induced wih NETA and
18 demyified over ime wih he dicuion abou a new pricing cheme and he reducion of Gae Cloure o one hour. The repone of price o Margin evolved in a fairly uniform fahion acro period. A Figure 3g and 4g illurae, he parially raegic effec of Margin declined yemaically, depie he poibly favourable winer condiion and reached in March 00 approximaely 60% and 18% of heir iniial value in period 5 and 35 repecively. Thi decline of raegic elemen in dayahead pricing could imply ha he marke i converging gradually o a compeiive ae given overcapaciy and fragmened upplier more acive role, generaor marke rucure or heir inenion o eliminae inefficiencie in he fear of eminen reform. Sandardiaion of coefficien furher revealed ha for everal period margin ceaed o be he mo influenial facor of po price afer December 00. In hi repec, he marke gradually reached more cobaed oucome. The paern diplayed in Figure 4h aroe in everal period and clarified he enigmaic effec of Lagged Margin on price. Alhough negaive in he beginning, a expeced, he coefficien revered ign during he winer, poibly manifeing capaciy wihholding. Thi noncompeiive elemen of pricing wa invered in January 00. The evoluion of he demand effec wa paricularly volaile wihou a conien paern acro period. The eviden inraday and annual inabiliy refleced he abence of cenral cominimiing dipach and he implied mixure of differen echnologie, he alernaion of marginal capaciy acro he year, he pah of fuel co and he variabiliy in operaional co uch a arup, which under NETA would be inernalied in bid condiional on daily cheduling. In period of peak demand, uch a 35, he impac of he quadraic demand erm increaed dramaically in repone o weaher condiion and declined abruply afer January 00 (Figure 0, 1). In houlder period however, uch a 5, paern were differen. (Figure 3e, 3f). Boh he linear and quadraic componen of demand were moly negaive and exremely volaile bu diminihed or converged o zero. Alhough periodic cycle could be diinguihed, a eaonal inerpreaion wa no apparen. The mo plauible peculaion i ha a po price were collaping, flexible generaor were becoming more relucan o compromie wih low price for houlder period in order o reain heir preence in he evening peak. A a reul, demand wa becoming le influenial on bidding. A dicued in ecion 3., rong ARCH effec were deeced when price model wih fixed coefficien were aumed. Serial correlaion wa no deeced however in he quared foreca error of he TVP pecificaion afer adjuing hem for he condiional TVP heerocedaiciy ( Η 1/ / 1n / 1 ). Thi implie ha he exience of GARCH effec could be due o he varying rucural componen of price level. Figure 56 illurae condiional andard deviaion for period 5 and 35, eimaed from he previou TVP regreion model and he correponding RegreionGARCH model. Regarding he laer, aymmeric effec of poiive and negaive hock, in he form of TGARCH (1,1), were ignifican for period 35 bu no 5, where GARCH (1,1) wa ufficien. I hould be noed ha he TVP eimae are apriori volailiy expecaion, baed on informaion up o 1, wherea he GARCH eimae are derived expo. Sill, wihin he TVP framework, uncerainy i ignificanly reduced. TVP model eem o uncover much more ubleie of he volailiy proce,
19 paricularly in unable ime period. Day 1 i lighly differen in he wo clae of model, a TVP required more obervaion for filer iniialiaion. Table 6. PX Price, Period 5 and 35. Parameer Eimae for he TimeVarying Regreion Model. Period 5 Period 35 σ 0.75 ε σ ε.4 Variable σ Variable v k σ v k Inercep 0.0 Inercep 0.03 P * P * P P * Spo Volailiy * MP Demand Linear 0.7* Demand Linear 0.54* DemandQuadraic DemandQuadraic 0.63* Margin * Margin * Demand Volailiy Margin * Demand Curvaure Demand Curvaure The aerik denoe a variance ignificanly differen han zero a he 95% level. 5. Diconinuiie in Price Srucure 5.1 Moivaion The previou analyi uggeed raegic manipulaion of capaciy o a cerain exen hroughou he day, bu mo inenely around he evening demand peak. Thi reveal ome kind of elecive agen behaviour, which induce diconinuou volailiy, and may alo appear wihin a ingle rading period. To uncover he ochaic dynamic of uch elecive behaviour, he magniude of any raegic effec and heir implicaion on volailiy, regreion regimewiching i adoped a he high frequency level. The more heuriic approach of imply analying exreme price would be inufficien, a price effec hould be aeed afer conrolling for variou fundamenal, i.e. in he conex of a rucural model, raher han purely from heir level. One of he peculiariie of po elecriciy price i ha hey exhibi regular paern diruped by recurren bu aperiodic, farevering pike, which induce evere financial rik. Thee exreme price ignify emporal marke irregulariie, uch a unexpeced weaher/demand, echnical hock (e.g. plan/inerconnecor failure, coningencie in ranmiion nework), raegic behaviour, rading inefficiencie (e.g. illiquidiy), crocommodiy leakage (e.g. fuel price exploion) or accumulaion of credi rik. Each of he above caualiie i linked wih differen aribue of he commodiy (e.g. nonorabiliy, demand inelaiciy o price) or he marke deign and rucure Specifying he ource of irregulariy in each cae would require an analyi of he value of he covariae in every abnormal cae. Such a deailed evaluaion exceed he purpoe of hi udy.
20 The modelling queion explored in hi ecion i wheher he diconinuou price rucure, ariing from he emporal irregulariie dicued above, could be ufficienly capured wih a few rucural regime wih diinc volailiie. In he conex of elecriciy price, regimewiching ha been adoped o replicae he erraic marke alernaion beween normal and abnormal equilibrium ae of upply and demand. Exiing model refer o daily average price and ofen aume an auoregreive proce under boh regime (Ehier and Moun, 1998; Deng, 000), which inroduce eimaion bia, a i doe no dienangle meanreverion from pike reveral and incorrecly impoe aionariy on he irregular price proce. A coninuouime proce ha correc hi mipecificaion i derived by Kholodnyi (000), where elfrevering nonmarkovian pike are added o a Markovian regular price proce. The mipecificaion i alo eliminaed in dicree ime by (Huiman and Mahieu, 001) wih he aumpion of hree regime, a regular ae of meanrevering price, a jump regime ha creae he pike and a jump reveral regime ha enure wih cerainy price reverion o heir previou normal level. Thi regimeraniion rucure i however rericive, a i doe no allow for conecuive pike. Thi conrain i relaxed by de Jong and Huiman (00), where a able meanrevering regime i propoed and an independen pike regime of lognormal price, which implie cloedform oluion for opion pricing. In conra o hee ylied mulipleregime model, regimewiching i adoped here wihin a regreion model and a a highfrequency level, eparaely for each rading period. Thi rucural pecificaion allow he replicaion of more realiic price pah for inraday rading and primarily, addree iue of marke performance and agen conduc. In principle, he propoed modelling preen he following properie: i) I provide a more adequae decripion and poenially horerm predicion of price dynamic. In paricular, i reolve he limiaion of a aic model by deriving properie uch a: kewne and lepokuroi (due o he mixure of price diribuion) and diconinuou hif in price level and volailiy. ii) I clarifie he rucural profile of diimilar and recurren pricing regime. If yemaic rucure i idenified in exreme price, hi mean ha heir magniude i no arbirary bu reflec a recurren generaor reacion o marke abnormaliie, whenever hee arie and irrepecively of heir exac caualiy. Depending on he plauible inerpreaion of he laen marke ae (which relae o marke pecificiie and model formulaion), he modelling could indicae how ofen and for how long on average: a) Shorerm raegic effec peri given he fear for regulaory inervenion and new enry, b) A emporary hock in demand or upply inflae price, c) The marke remain illiquid before agen ge araced by price level and induce aciviy. iii) I reveal he ochaic dynamic of regimewiching baed on fundamenal raher han olely price level and hu, allow a more accurae evaluaion of he rik induced by price pike.
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