The Valuation of Greenhouse Gas (GHG) Emissions Allowances

Transcription

1 he Valuaion of Geenhouse Gas (GHG Emissions Allowances Benhad iee Depamen of Business Adminisaion and Economics hai of Finance a s s a u U n i v e siy Innsaße assau Gemany Absac his pape idenifies fis he impoan pice dives of maginal allowance pices in a pue allowance ading envionmen (wihou he use of abaemen echnologies: companies pofiabiliy emissions inensiies and he coelaion beween eleciciy and allowance pices. Second i shows ha he use of alenaive geenhouse gas (GHG abaemen echnologies changes maginal allowance pices significanly. he fac ha maginal al - lowance pices ae diffeen fo insallaions wih divegen emissions inensiies and ale - naive GHG abaemen echnologies ceaes an ideal envionmen fo allowance ading. In ohe wods his heoeically deived pice behavio is in absolue accodance wih he goals of he Kyoo o ocol. Keywods: GHG abaemen echnology; emissions allowances; geenhouse gases (GHG; isk; valuaion JEL lassificaion: G Q4 el.: ; fax: E-m a i l a d d e s s : n i e u n i -passau.de

2 he Valuaion of Geenhouse Gas (GHG Emissions Allowances. Inoducion. eliminaies Geenhouse gases (GHG in geneal and O in paicula ae said o be he majo cause of global waming. heefoe by way of he Kyoo oocol seveal counies have ageed o educe geenhouse gas emissions via an innovaive mechanism: ading of socalled emissions allowances. he idea behind his paicula design of GHG educion is convincing: i is believed ha makes know bes a wha pice and wih which aba e- men echnology o educe GHG emissions. A peequisie of successful emissions ading is howeve ha decision makes ae able o deemine hei maginal pices fo emissions allowances unde diffeen poducion and abaemen echnologies. Ohewise he make mechanism will be inefficien and allowance ading will neihe be able o povide infomaion on penalies/ewads fo failing o mee/meeing emissions goals (pice of GHG emissions no be able o dise he bes GHG abaemen echnology. Fo ha eason i is he objecive of his pape o deemine maginal allowance pices unde simulaneous consideaion of alenaive GHG abaemen echnologies. o achieve his goal valuaion know-how fom he field of finance is applied o his poblem of enegy economics. Moe pecisely maginal allowance pices ae calculaed via so-called uiliy- based picing a mehodology ha has been developed o compue ma ginal pices of socks and financial deivaives (see e.g. Beeden (979 o ox/ingesoll/ross (985. Wih he help of his mehodology i mpoan pice dives of and hei influence on maginal allowance pices can be ideni fied. Fis maginal allowance pices depend in a pue allowance ading envionmen (wih-

3 ou he use of abaemen echnologies on companies pofiabiliy (he highe he pofiabiliy he lowe maginal allowance pices i.e. negaive influence on maginal al - lowance pices emissions inensiies (posiive influence and he coelaion beween eleciciy and allowance pices (posiive influence. Second he use of alenaive abaemen echnologies exes visible influence on maginal allowance pices. On he one hand he use of GHG abaemen echnologies in he fom of cabon injecion educes he numbe of pice dives o one: maginal payous fo injecions. On he ohe hand swiching poducion beween wo poducion echnologies imposes wo pice bounds on maginal allowance pices. One pice bound is he maginal allowance pice when oal poducion happens a insallaion ; he ohe pice bound sems fom he siuaion whee only insallaion is used fo poducion. In he even boh insallaions poduce el eciciy maginal allowance pices behave linealy b eween hese wo bounds and ae an inceasing funcion of insallaion s oupu. Finally a spo make fo eleciciy is consideed because he spo make fo eleciciy seves as boh a pocuemen and a sales make and hus exes influence on GHG edu cion goals. Spo make ansacions lead o jus one bound fo maginal allowance pices a bound based on he fac ha eleciciy poducion a any insallaion canno be negaive i.e. hee is a maximum fo he amoun of eleciciy puchased on he spo make. Howeve elec - iciy sales on he spo make can be (nealy abiaily high. Ouside his pice bound maginal allowance pices ae a negaive linea funcion of spo make a n s acions. his pape disinguishes iself fom he lieaue in one significan aspec: o he bes of my knowledge i is he fis aemp o value emissions allowances unde isk and unde simu laneous consideaion of alenaive GHG abaemen echnologies. he oveview of he elevan lieaue fom he field of enegy economics in Spinge/Vailek (4 and in paicula in Spinge (3 p. 53 n. poins owad a wide ange of allowance pices (mean pice ove all simulaion sudies: $9/ O and

4 3 sandad deviaion of $5.4/ O in a global ading envionmen; mean of $6.94/ O and sandad deviaion of $.3/ O in an Annex B couny ading envionmen. Moeove Rebeg (4 p. epos a dop of allowance pices on he hi - ca go limae Exchange X fom $3 a he beginning of 4 o $6 in Decembe 4. Boh obsevaions can be inepeed as an indicaion ha allowance pices will be highly isky if emissions ading sas in he Euopean Union in 5. Despie his evi - dence he enegy economics lieaue has unil now negleced isk. Rubin (996 discusses he ole of banking and boowing emissions allowances in a wold unde ce - ainy. Schleich e al. ( p. 67 n. and Faunhofe (3 p. 8 apply pesen valu e fomulas unde ceainy (o a bes isk neualiy o deemine he pice of emi s- sions allowances elaive o abaemen cos. Unde isk howeve neihe of hese simple pesen value fomulas will wok no will alenaive GHG abaemen echnolo gies be pefec subsiues.. Mehodology.. Maginal pice Emissions educions via allowance ading equie companies o o be moe pecise insallaions (powe plans ec. o paicipae in allowance ading. Howeve hee ae wo peequisies o successful emissions ading: fis insallaions mus have a ge neal inees in emissions ading and second some insallaions mus puchase wheeas ohes mus sell emissions al lowances. Boh peequisies depend on allowance pices and hus can be chaaceized wih he help of wha will be called maginal allowance pice. Define he maginal allowance pice of a paicula insallaion as ha pice a which he owne-opeao of ha insal - laion is indiffeen beween paicipaing in o efaining fom allowance ading. hen wheneve eal make pices of emissions allowances ae above he maginal allo wa n c e

5 4 pice of one insallaion his insallaion will sell; in he opposie even i will buy emissions allowances. Fo a moe de ailed analysis he definiion of maginal allowance pices mus be fuhe efined. Being indiffeen beween paicipaing in and efaining fom allowance ading means ha he owne -opeao holds an allowance posiion ha es his obligaion each ime GHG limis mus be me bu a ohe poins in ime he does no ade (opimal ansacion size equals zeo. ha is in he even he insallaion needs addiional emi s- sions allowances o e GHG limis he owne-opeao buys exacly he needed quaniy; in he opposie even any suplus is sold. Howeve he owne- opeao does no speculae o hedge wih emissions allowances a inemediae poins in ime no does he cay fowad any suplus of emissions allowances fom one peiod o he nex. Fomally maginal allowance pices can be calculaed wih he help of so-called uiliybased picing a mehodology developed o compue maginal pices of socks and fi - nancial deivaives (see e.g. Beeden (979 o ox/ingesoll/ross (985. Usin g his mehodology maginal allowance pices ae obained as follows. Fis diffeen iae he objecive funcion of he owne-opeao wih espec o he numbe of emissions allowances. Second se he numbe of emissions allowances equal o zeo (opimal ansacion size equals zeo. hid solve he necessay condiion wih espec o he pice of emissions allowances. wo faces mus be aken ino accoun when judging his mehodology. Fis his pocedue looks complicaed compaed o he Black/Scholes (973 appoach of deivaive picing which deemines he pice of a deivaive as he pice of a pofolio ha dupli - caes he deivaive s payoff by coninuously ading he deivaive s undelying and he iskless asse. Howeve GHG emissions do no have a make pice. heefoe he duplicaion appoach is no applicable o emissions allowances. Second he concep of maginal pices in no panacea i has limiaions. On he one hand his mehod can de -

6 5 emine whehe o no insallaions paicipae in emissions ading bu i canno eveal he exen of paicipaion i.e. how many emissions allowances insallaions should buy and sell. o answe his quesion allowance pices mus be assumed as ex ogenously given; based on ha assumpion he opimum numbe of emissions allowances becomes accessible. On he ohe hand his allowance valuaion appoach equies ha he numbe of emissions allowances mus be specified exogenously because decision makes wihou govenmenal powe canno se boh pice and quaniy of an asse. his pape akes his limiaion ino consideaion by seing ansacion sizes equal o zeo which is no as abiay as i migh seem since a ansacion size of zeo sepaaes successful fom unsuccessful emissions ading... Model seup wo foces dive selecion of he valuaion model s seup in geneal and in paicula he choice beween discee- and coninuous-ime valuaion models. he valuaion model mus be able o cope wih majo insiuional deails of allowance ading a e - quiemen ha would seem o favo discee-ime models because hey ae able o easily deal wih feaues such as fee allocaion of emissions allowances a ceain poins in ime GHG consains a he end of each yea and so foh. On he ohe hand ex plici soluions fo allowance pices ae desiable o enable eseaches o make economic i n- epeaions and fo eal-ime ading via fas compuaions fo companies. Unfounaely discee-ime valuaion models ofen canno be solved in explici fom (see e.g. Beeden (4 so in his espec coninuous-ime models ae pefeable. Finally he valuaion model mus be somewha obus wih espec o he disibuion of fuue al - lowance pices a equiemen ha once again makes he choice of ime-discee models supeio. Fo such models can wok wih moe geneal and less specified disibuional h i s i s d o n e i n a c o m p a n i o n p a p e.

7 6 assumpions a feaue ha assumes addiional impoance because i is no ye clea whehe he make fo emissions allowances will be liquid enough o allow fo coninuous-ime ading (see he elaed example of Joskow/Schmalensee/Bailey (998 who epo liquidiy ficions in he ealy yeas of he U.S. sulfu dioxide ma ke. o deal wih hese conflicing equiem ens I have chosen a compomise famewok ha is oulined by he following assumpions. Assumpion : Objecive funcion of he owne-opeao of an enegy- s u p p l y c o m p a n y he owne-opeao of an enegy- supply company i.e. a poenial candidae fo pa i ci - paion in allowance ading has µ-σ -pefeences ove eminal wealh a ime. d e- noes he end of a ading peiod (e.g. Apil 3 7 fo he fis ading peiod o Apil 3 fo he fis Kyoo commimen (second ading peiod see aional Allocaion lan (3 p. 3. µ-σ -pefeences allow fo explici soluions of valuaion poblems even in discee ime. I do no wan o base mean -vaiance calculus on an ex - peced uiliy famewok bu insead follow ha sand of he lieaue (see e.g. Lö f - fle ( p. 57 ielsen (99 p. 6 ha egads µ-σ-pefeences as a pefeence elaion of is own. In summay he objecive funcion of he owne -opeao of an enegy- supply company eads: a Φ E{ W } va( W ( w h e e W denoes wealh of he owne-opeao a ime E{.} expeced value based on infomaion available a ime (he begin of he ading peiod e.g. Januay 5 o Januay 8 and va(. vaiance (based on infomaion available a ime. a is he pefeence paamee which weighs mean and vaiance.

8 7 Assumpion : oducion envionmen Fo he sake of simpliciy i is assumed ha hee is one homogenous good namely eleciciy. Moeove eleciciy oupu is fixed and can be s old compleely; in ohe wods oupu is no a decision vaiable of he owne-opeao. Such assumpions ae no compleely unealisic fo example conside he siuaion in which a local enegy supplie is obligaed o povide eleciciy fo is homeown. Finally he poducion faci l - iy is aleady exisen i.e. no invesmen in poducion echnologies is equied. Assumpion 3: Allowance ading Each insallaion eceives a fee iniial allocaion of emissions allowances a imes... and o equip he insallaion wih a basis fo ading. his allocaion happens annually in equal popoions ahe han once fo he enie peiod (see aional Allocaion lan (3 p. 8 and migh conain special allocaions fo ealy acion combined hea and powe and so foh (see aional Allocaion lan (3 p. 38. A imes... and each insallaion mus mee is GHG limis (see aional Allocaion lan (3 p. 44. I is impoan o noe howeve ha boh iniial allocaion and GHG limis ae defined on he insallaion no he company level (see Aicle 4 Diec - ive 3/87/E. In addiion he owne-opeao can ade emissions allowances a abiay poins in ime wihin he EU (see Aicle paagaph Diecive 3/87/E and aional Allocaion lan (3 p. 4. Alhough i is possible o ansfe a poenial suplus of allowances fom one yea o anohe wihin one ading peiod (so-called banking see Aicle Diecive 3/87/E and aional Allocaion lan (3 p. 4 in Gemany banking is fobidden beween ading peiods (e.g. fom 5-7 o 8- see aional Allocaion lan (3 p. 44. Finally he make fo emi s- sions allowances is compeiive (no make paicipan has monopoly powes and hee I n e a l i y i n i i a l a l l o c a i o n a nd G H G l i m i s o v e l a p s l i g h l y w i h i n a d i n g p e i o d s s i n c e G H G l i m i s mus be me by Apil 3 and iniial allocaion fo he nex peiod happens on Febuay 8 (see A i cle p a a g a p h 4 i n c o n n e cion wih Aicle paagaph Diecive 3/87/E.

9 8 ae no echnological exenaliies in he sense of DeAn gelo (98 p. : eleciciy pices ae exogenous and no a funcion of allowance pices. Assumpion 4: Riskless boowing and lending is possible a inees ae he em sucue is assumed o be fla and inees aes consan hough ime he owne -opeao can use he iskless asse o balance his budge consain i.e. o e poenial finance needs o o inves any suplus. o keep he model simple i is also assumed ha emissions allowances ae he only isky asses available fo inves - men puposes.. Emissions allowances: basic valuaion esuls. Wealh dynamics he owne -opeao has he following budge consain a ime : W ( f whee W denoes he owne-opeao s iniial wealh iniial allocaion of emi s- sions allowances a ime he numbe of emissions allowances bough o sold a ime he al lowance pice a ime and f he numbe bough (invesmen o sold (loan of he iskless asse a ime. he pice of he iskless asse is assumed o be. In wods he owne-opeao uses his iniial wealh and he wealh fom he iniial allocaion o inves in emissions allowances and he iskless asse. A ime τ ( < τ < he owne -opeao can esucue his holdings in emissions al - lowances fo speculaive o hedging easons. 3 his invesmen decision yields he fol - lowing wealh a ime τ: 3 Re s u c u i n g s i n a l l o w a n c e h o l d i n g s a e g e n e a l l y s p e a k i n g n o e s i c e d o j u s o n e e s u c u i n g a i m e τ. H o w e v e a d d i n g s e v e a l a d i n g o p p o u n i i e s d o e s n o c h a n g e h e s u c u e o f h e e s u l b u m e e l y c o m p l i c a e s h e c a l c u l a i o n s. h e e f o e h i s p a p e f o c u s e s o n j u s o n e d a e f o i n e m e d i a e e -

10 9 ( τ Wτ τ f (3 whee denoes he iskless ae. Reinvesing wealh a ime τ i.e. esucuing posiions in allowances and he iskless asse yields: W (4 τ τ τ f τ which anslaes ino he following wealh a ime (befoe einvesmen bu afe balancing he GHG consain: ( τ W (5 x E f τ whee x denoes he spead beween payoffs fom eleciciy sales and payous fo eleciciy poducion he fixed poducion oupu E he andom eleciciy pice a ime and he andom allowance pice a ime. Wealh a ime consiss of hee pas. Fis he excess payoff of eleciciy sales ove payous fo poducion which is a he same ime a measue of he insallaion s pofi - abiliy since he insallaion aleady exiss (see Assumpion no iniial invesmen fo poducion is needed. Second he payoff fom ansacions in emissions allowances o mee GHG limis a ime and hid he payoff fom ansacions in he iskless asse. Budge inemediae and eminal wealh equaions ae faily sandad fo a nomal mulipeiod invesmen poblem alhough he invesmen vehicle emissions al lowances is no. Howeve wha disinguishes he decision poblem of allowance ading fom a nomal invesmen poblem is he following GHG consain a ime : e (6 τ whee e denoes he so-called emissions inensiy of insallaion a ime. Accod - s u c u i n g s.

11 ing o equaion (6 emissions inensiies can be sochasic as well as ime dependen. Sochasic emissions inensiies migh esul fom diec measuemen of GHG emi s- sions as opposed o deeminaions based on fuel inpu which yields ex ane known emissions. Boh appoaches ae admissible (see aional Allocaion lan (3 p. 5. he GHG consain (6 demands ha oal GHG emissions caused by he poducion of eleciciy oupu a insallaion mus be eed wih emissions allowances. Emissions allowances sem fom iniial allocaion a ime modified by he numbe of allowances he owne-opeaos owns afe ansacions a ime τ (banking and ansacions a ime ha balance he GHG consain. hese ansacions involve eihe he puchase of allowances o avoid boowing o he sale of any suplus allowances. a y- ous fo buying emissions allowances o avoid boowing ae peequisie fo elec i c i y poducion such as fo example souces of enegy. ash inflows fom selling emi ss i o n s allowances on he ohe hand ae due o he definiion of maginal allowance pices (he GHG consain is o mee exacly see Secion... Wih espec o he imedependen iniial allocaion he GHG consain (6 is slighly moe geneal han he aional Allocaion lan which assumes annual allocaions in equal popoions (see aional Allocaion lan (3 p. 8. Wih espec o he imefame of he GHG consain equaion (6 is slighly diffeen fom he aional Allocaion lan accoding o which (aional Allocaion lan (3 p. 3 n. iniial allocaions fo he nex yea happen by Febuay 8 wheeas he GHG limi mus be me by Apil 3 (a ime diffeence of wo monhs wih one excepion: in Gemany emissions allowances canno be ansfeed beween 5-7 and he fis commimen peiod (8 -; see a - ional Allocaion lan (3 p. 44. he GHG consain (6 uses a ime diffeence of zeo bu allows fo inemediae ading a ime τ and in ha fashion capues he idea of a ime diffeence; in ealiy ading can ake place beween Febuay 8 and Apil

12 3. ombining equaions ( hough (7 and epeaing his pocedue fo evey ime b e- ween and yields 4 he following e minal wealh a ime : W ( x e ( (8 E ( ( ( τ ( ( ( ( τ τ ( ( ( τ τ ( W Accoding o equaion ( 8 he owne-opeao s eminal wealh consiss of fou componens: fis he compounded cumulaed gains and losses fom poducion (fis em of line and he payous fo emissions allowances ha ae needed o e he GHG emissions of (... unde he assumpion ha all 5 allowances o mee he GHG consain ae bough o sold a ime (second em of line ; second he i n- cease in wealh caused by iniial allocaions a imes o (second em; hid compounded cumulaed gains and losses fom ading in emissions allowances a imes τ... τ (hid and fouh ems; and finally compounded iniial wealh (fifh em. 4 S e e A p p e n d i x A. f o a d e i v a i o n w h e e h e f o l l o w i n g m o d i f i c a i o n s a e n e e d e d o c o p e w i h h i s s ce - n a i o : a n d. 5 h a i s h e e i s n o i niial allocaion of allowances and no inemediae allowance ading.

13 . Valuaion esuls he decision poblem fom which maginal allowance pices will be deived eads as follows: Max τ... τ Φ E { W } va( W a wih W as defined in equaion (8. he numbes of emissions allowances a each ime ( τ τ... τ ae he only decision vaiables available o maximize he pefeence funcional (9. Moe pecisely a ime he owne-opeao seles on a saegy fo he numbe of emissions allowances needed fom ime o ime τ. A saegy encompasses a complee condiional plan i.e. he opimum numbe of allowances a all imes dependen on he sae ha will occu a evey ime. Fo example he owne-opeao deemines he opimum numbe of allowances (S i in he even of sae i (S i a i m e a n d (S i S j a ime assuming ha S i occued a ime and S j a ime and so foh. alculaing maginal allowance pices fo his scenaio yields: 6 (9 E{ } ( ( a a ( ( OV OV whee denoes ansposiion of a veco o maix (his symbol howeve should no be confused wih discouning ove peiods as in ( and i ( { } i he veco of he amoun of poducion o iniial allocaion of allowances a imes.... OV is he aiance maix beween ( τ as ( ( τ ( ( as well τ τ ( ( and ( x e ( τ fo E 6 See Appendices A.3 and A.4 fo a deivaion whee he same modificaion as in foonoe 4 mus be

14 3... and OV is he aiance maix beween τ as well as and ( ( ( fo.... In he special case of seially uncoelaed cash flows emissions inensiies and speads equaion ( simplifies o: 7 E{ } ( ef unc ( a a ( ( va ( x E e ( his is significanly moe simple han he geneal case ( fo seveal easily unde - sood easons. Fis cash flows emissions inensiies and speads ae seially unco e- laed and second emissions allowances do no offe inemediae cash flows such as dividends meaning ha hee is no i neempoal isk. Add o his he hid fac namely ha allowance ading is possible and hus wealh a ime depends only on allowance posiions ha will be esablished a ime τ. In ohe wods in his special case only he mos ecen holdings and pices of eleciciy oupu and emissions allowances ae elevan o valuaion..3 Inepeaion of maginal allowance pices Accoding o equaions ( and ( he maginal allowance pice is deemined by wo fundamenal componens: he discouned expeced allowance pice a ime and a isk coecion. his isk coecion consiss of isk of eminal wealh weighed wih he isk pefeence paamee a of he owne-opeao. So fa he picing fomula coincides wih he one fo abiay cash flows in a µ-σ-wold (see he analogy o e.g. m a d e. 7 h i s c a n b e s e e n i m m e d i a e l y f o m e q u a i o n ( A. 6.

15 4 ox/ingesoll/ross (985 p. 374 if equaions ( and ( ae efomulaed as isk pemiums E{ } (. Howeve wha paiculaizes his valuaion fomula o emissions allowances is he definiion of isk. hee is isk fom ineacions beween eleciciy poducion and allowance holdings on he one hand and on he ohe hand isk fom ineacions beween iniial allocaion and inemediae allowance posiions. he fis isk is capued by he aiance beween cash flows fom eleciciy poduc - ion and allowance pices (second line of equaions ( and ( he second isk by he aiance beween cash flows of allowance posiions semming fom iniial allocaion and inemediae allowance posiions (hid line of equaions ( and (. Since boh eleciciy poducion and iniial allocaions ae posiive he signs of he ai - ance ems deemine whehe maginal allowance pices lie above o below hei discouned expeced allowance pice a ime ( E{ } (. Obviously isk a evey poin in ime is elevan o picing; howeve only he expec ed value a ime maes. his is because expeced values a ime τ... τ τ ae a esul of picing i.e. hei values ae model endogenous no model exogenous such as vaiances and a i - ance. 8 Alhough equaions ( and ( descibe impoan aspecs of maginal allowance pices hey do no compleely chaaceize maginal allowance pices because addi - ional pice bounds fo emissions allowances need o be aken ino consideaion. he lowes allowance pice duing a ading peiod equals zeo which will occu if GHG consains ae no binding. In addiion emissions allowances do no cause cash ouflows iniial allocaion is fee (see aional Allocaion lan (3 p. 8 and hee ae no ohe coss fo example hee ae no disposal coss. Accoding o abiage heoy (see e.g. Dybvig/Ross (99 a nonnegaive cash flow mus have a nonnega- 8 S e e A p p e n d i x A. 4 f o h e f o m a l i m p l e m e n a i o n o f h i s v e b a l d e s c i p i o n.

16 5 ive pice and a cash flow of zeo mus have a pice of zeo. Hence zeo is a lowe p i c e bound fo emissions allowances. he uppe pice consiss of he penaly fo failing o mee GHG consains which is 4 EUR beween 5-7 (see Aicle 6 paagaph 4 Diecive 3/87/E and EUR beween 8- (see Aicle 6 paagaph 3 Diecive 3/87/E. hus no aional buye of emissions allowances will pay moe han 4 ( EUR fo emissions allowances o mee GHG consains a imes.... In his connecion he pice bound holding a imes... has o be anslaed ino a pice bound a ime. Al - lowance ading duing he fis peiod can deal only wih he GHG consain a ime because iniial allocaion a ime... and ading beween ime and ime can ale allowance posiions and hence he poenial violaion of he GHG consain a ime.... heefoe he elevan penaly fom ime is he one fo violaing he GHG consain a ime. o-abiage consideaions again guaanee ha a maximum allowance pice of 4 ( EUR a ime anslaes ino an uppe bound fo allowance pices of he pesen value of 4 ( EUR i.e. 4 ( EUR. 9 In summay maginal allowance pices have a lowe bound a zeo a highe bound a 4 ( EUR and follow beween hese bounds equaions ( o (. Fo moe insigh ino he behavio of maginal allowance pices ( o ( wihin he pice bounds in geneal and in paicula o obain economic inuiion egading aiances signs a moe deailed inepeaion of maginal allowance pices is needed. Because of he simple sucue of he spec i a l c a s e e q u a i o n ( is a good poin of de- 9 h i s e a s o n i n g e m a i n s v a l i d e v e n i f i n i i a l a l l o c a i o n f o h e n e x y e a o c c u s o n F e b u a y 8 a n d h e GHG limi fo he cuen yea mus be me b y A p i l 3 b e c a u s e i n e m e d i a e a d i n g b e w e e n F e b u - ay 8 and Apil 3 can cause a violaion of he GHG consain a Apil 3. Only if he GHG limi v i o l a i o n i s a s s u m e d n o o o c c u b e f o e i m e ( s e e a i o n a l A l l o c a i o n l a n ( 3 p. 4 4 h e u p p e bound fo maginal al l o w a n c e p i c e s w i l l e a d 4 o. ( (

17 6 paue. A posiive aiance beween allowance pice and cash flow fom poducion x E e means ha allowance posiions incease he isk of eminal wealh and a isk deducion is jusified. his isk deducion will be he highe he highe he spead x and he lowe he emissions inensiy e. his conay effec of boh pice dives on maginal allowance pices can be explained as follows. A highe spead signifies on he one hand highe unceain cash flows of he insallaion. Highe sochasic cash flows auomaically imply highe isk unde posiive aiances and heefoe a highe isk deducion (isk-based explanaion. On he ohe hand he highe he spead he moe pofiable he insallaion. In ohe wods highly pofiable insallaions have enough buffe o pay fo emissions allowances a he ime he GHG consain mus be me. Fo ha eason he owne-opeao of he insallaion will no be willing o pay a high pice fo he oppouniy o puchase o sell emissions allowances in advance (demand-based explanaion. hese ineelaions ae diffeen fo he emissions inensiy. he highe he emissions inensiy he lowe ae he insallaion s cash flows. A lowe oveall cash flow howeve means lowe oal isk and hus smalle isk deducions (isk-based explanaion. he demand -based explanaion develops as follows. Since he insallaion is equied o supply a fixed amoun of eleciciy i canno adjus is poducion o coune he negaive effecs of high emissions inensi ies. onsequenly emissions allowances ae moe valuable o insallaions wih highe emissions inensi - ies han hey ae o hose wih lowe emissions inensi ies. In he even of negaive aiances beween cash flows fom eleciciy poducion and allowance pices emissions allowances ac like a hedge agains eminal wealh flucuaions. heefoe he highe he spead he highe he insallaion s cash flow and he o f u h e i l l u s a e h i s f a c s i m p l y c o n s i d e h e v a i a n c e o f o n e s o c k c o m p a e d o h e v a i a n c e o f u n i s o f h e s a m e s o c k w h i c h e q u a l s i m e s he vaiance of one sock.

18 7 highe he hedge (isk-based explanaion. On he ohe hand a hedge vehicle is of highe value o an insallaion s owne -opeao he geae he cash flow isk is; hence he hedge vehicle becomes moe val uable o he owne-opeao wih inceasi n g s p e a d (demand-based explanaion. An analogue easoning shows ha highe emissions inensiies lead o a decease of hedge poenial and hus o a lowe pice of emissions al - lowances. One final quesion aises in connecion wih he fis aiance: Which is moe ealisic a posiive o a negaive aiance beween cash flows fom poducion and allowance pices? Since allowance ading has no ye saed his quesion canno be an - sweed empiically. Howeve a posiive elaion seems o be pobable following he agumenaion of he aional Allocaion lan (3 p. 44 which foecass no poblems wih GHG consains in 5 and 6 bu ha some effo will be needed o mee he consain in 7 (emembe in Gemany emissions allowances canno be ansfeed beween 5-7 and he fis commimen peiod 8 -; see aional Allocaion lan (3 p. 44. he second aiance aiance beween cash flows fom iniial allocaion and inemediae allowance holdings calls fo a pice deducion (isk-based explanaion in he special case as vaiance of allowance pices is posiive. he demand-based explanaion is even moe inuiive. he highe an insallaion s iniial allocaion he les s e h e GHG consain is binding and emissions allowances become less valuable fo his paicula insallaion. hese esuls concening he special case of equaion ( will need o be modified slighly if he geneal case of equaion ( is consideed since ineempoal isk ineelaions ene he valuaion. his is because no only aiances beween cash flows a ime bu also aiances beween cash flows a evey ime beween ime τ an d

19 8 mus be aken ino accoun; fomally all hese aiance ae added up ( OV and OV. hese ineempoal isk ineelaions influence aiances beween cash flows fom eleciciy poducion and allowance pices in wo ways. On he one hand look a he aiances ( x e ( x e τ ( E τ τ ( ( E and τ. he andom vaiable enes he fis aiance em wih wo negaive signs and he second one wih a negaive and a posiive sign. he economic eason behind his is ha he fis aiance em encompasses he siuaion whee eleciciy is sold combined wih a puchase of allowances ( x E e and allowances ae bough a ime ( ( ; he second aiance deals wih a sale of eleciciy combined wih a puchase of allowances and a sale of allowances a ime (. I is easy o undesand ha he elaion beween wo selling ansacions has a sign opposie o he one of a buying and a selling ansacion. On he ohe hand hee ae aiances beween cash flows fom poducion and al - lowance holdings a imes... (in addiion o he aiance a ime ( x e τ ( E. Ineempoal isk ineelaions ae τ even moe ponounced fo he second isk faco he aiance beween cash flows fom iniial allocaion and i nemediae allowance holdings. Fis enes τ ( ( ( wih a diffeen sign han ( τ ( ( τ ( ; he fis aiance em involves allowance sales fom ini - τ ial allocaion ( ( and allowances sales fom ading ( wheeas he second aiance combines sale of allowances fom iniial allocaion wih puchase of allowances a ime ( (. Second he geneal sign of he ai ance beween allowance pices a diffeen imes e.g. ( o ( τ is as ye unknown because allowance ading hasn saed. A posiive coelaion would mean ha

20 9 high allowance pices a one ime lead o even highe al lowances pices a lae imes a negaive aiance induces he conay behavio. A nega ive coelaion howeve seems o be unlikely in a make ha is no dominaed by speculaion which follows fom he aional Allocaion lan (3 p. 44 which foe cass no poblems wih GHG consains in 5 and 6 bu ha some effo will be needed o mee he consain in 7 (again emembe ha in Gemany emissions allowances canno be ansfeed beween 5-7 and he fis commimen peiod 8 -; see aional Allocaion lan (3 p. 44. Alhough a negaive coelaion seems unlikely i canno be excluded. his means ha aiances beween cash flows fom iniial allocaion and inemediae allowance holdings may lead o an incease in maginal allowance pices; obviously allowance pices a ealie imes mus conain a hedge agains allowance pices a lae imes. heefoe isk-based and demand-based explanaions call fo a highe maginal allowance pice. hee final emaks will conclude his secion on maginal allowance pices in a pue al - lowance ading envion men. Fis i is highly pobable ha E { } will be lage han zeo even hough emissions allowances will expie afe ime and become wohless ( i n G e many hey canno be ansfeed beween 5-7 and he fis commimen peiod 8- ; see a- ional Allocaion lan (3 p. 44. Because E { } measues he expeced allowance pice a he las ime he GHG limi had o be me; expiaions will occu only afe his pice has been deemined. Second consid e egulaed eleciciy makes whee he eleciciy pice is nonsochasic. Unde his scenaio and unde he addiional assumpion of nonsochasic speads and emissions inensiies equaion ( simplifies o: E{ } ( ( a va ( ( ( e

21 ha is he vaiance of allowance pices is he only isk dive. Regadless of he size of va ( maginal allowance pices depend on he elaion beween emissions allowances obained via iniial allocaion and emissions allowances acually needed due o cuen emissions e. If exceeds e a pice discoun obains (he GHG consain can be me easily and he insallaion does no have a song demand fo inemediae allowance posiions: demand-based explanaion; he iniial al - locaion inceases he isk of he owne-opeao s wealh: isk-based explanaion in he conay even a pice ise esuls. Ineesingly fo he special case ha iniial allocaion a ime exacly maches emissions a ime he isk em vanishes and al - lowances ae piced as in a isk-neual wold. hid equaions ( a n d ( demonsae ha maginal allowance pices do indeed suppo allowance ading. Maginal allowance pices ae diffeen fo insallaions wih divegen emissions inensiies. Hence ading can ake place because insallaions wih highe emissions inensiies will likely puchase and hose wih lowe emissions inensiies will pobably sell emissions allowances a behavio ha fully maches he spii of he Kyoo oocol. Moeove hee ae ohe souces of ading ha ae no diecly elaed o he Kyoo oocol: heeogenous expecaions and diffeen isk pefeence paamees. Owne-opeaos wih highe isk pefeence paamees will have lowe maginal allowance pices unde posiive aiances (highe maginal allowance pices unde negaive aiances and hus be moe inclined o sell (buy emissions allowances han owne-opeaos wih lowe isk pefeence paamees. Following a sugge s- ion by Löffle ( p. 6 and paiculaizing he isk pefeence pa amee a W i becomes clea ha owne-opeaos of small companies have highe isk pefeence paamees and hence will moe likely sell emissions allowances han will owneopeaos of lage insallaions.

22 3. Emissions allowances and alenaive GHG abaemen echnologies So fa he ole of emissions allowances as make-based penalies/ewads fo exceed - ing/emaining below planned GHG emissions has been discussed. Howeve he Kyoo oocol aims no only o deemine pices of GHG bu also o find he bes aba e m e n echnology via allowance ading. heefoe his secion deals wih he i nfluence of hee alenaive GHG abaemen echnologies on maginal allowance pices: an ex plici abaemen echnology he swiching beween wo insallaions wih diffeen emissions inensiies and he use of he spo make fo eleciciy. 3. Explici abaemen echnologies (abaemen echnology in he naowe sense Explici abaemen echnology in he naowe sense means ha GHG emissions ae educed wih he help of a echnical device whee he oiginal insallaion coninues o be used fo eleciciy poducion. One such abaemen echnology which will be avai l - able in he nea fuue is inegaed gasificaion and combined cycle wih capue an d sequesaion (IG (see e.g. Manne/Richels (4 p. 67 o Kuosawa (4 p. 68. he capued GHG is anspoed and injeced e.g. ino depleed gas wells o he ocean. 3.. Wealh dynamics As in he efeence case of Secion (pue allowance ading envionmen wihou abaemen echnology i is assumed ha he insallaion aleady exiss i.e. no iniial invesmen fo he poducion faciliy is needed. Howeve he injecion of GHG causes known payous ha depend on he amoun of GHG injeced. he owne-opeao mus decide a ime on he amoun A- ha will be injeced a ime. Injecing occus simulaneously wih poducion: GHG have o exis befoe hey can be capued and injeced. he decision on he amoun o be injeced mus be made befoe he injecing i - self occus because he injecion company needs o know in advance he amoun ha

23 will be injeced so ha i can make appopiae pepaaions. Based on hese exposiions he GHG consain eads: e (3 A τ whee A denoes he amoun of GHG ha has been decided upon a ime o be i n- jeced a ime. Assuming payous fo injecions ae due a he ime he injecions occu and ae nonlinea in he amoun of GHG injeced (see Kuosawa (4 p. 68 wealh a ime (befoe einvesmen bu afe balancing he GHG consain holds as follows: W τ ( K( x E f A whee K ( A denoes payous fo injecions. oceeding fom ime o ime one obains: τ (4 W W ( K( ( ef A A (5 whee he las em of equaion (5 descibes he wealh effecs of GHG injecions compaed o he efeence case of pue allowance ading as shown in equaion (8. In ohe wods i consiss of he cash flow consequences of GHG injecion in he fom of fewe allowance puchases (moe allowance sales a ime and addiional payous fo GHG injecions. 3.. Valuaion esuls he decision poblem fom which he valuaion esuls will be deived eads as follows: Max τ... τ A... A Φ E { W } va( W a (6 S e e A p p e n d i x A. f o a d e i v a i o n w h e e h e f o l l o w i n g f o m a l m o d i f i c a i o n s h a v e o b e m a d e : h e s ec - K( A ond insallaion equals he abaemen echnology i.e. x x and e e. A E

24 3 wih W as defined in equaion (5. ha is he owne -opeao can choose he numbe of emissions allowances a each ime ( τ τ... τ as well as he numbe of GHG injecions a imes... so as o maximize he pefeence funcional of equaion (6. o be moe pecise he owne-opeao deemines a saegy fo boh decision vai ables i.e. a complee condiional plan. alculaing maginal allowance pices fo his scenaio yields: ef a OV (7 ( A A whee ef denoes he maginal allowance pice of he efeence case of equaion ( and OV A is he aiance maix beween ( fo.... and τ as well as Fo he special case of seially uncoelaed cash flows emissions inensiies and speads one obains: ef unv a va (8 ( ( A whee denoes he maginal allowance pice of he efeence case of equaion ef unv (. Equaions (7 and (8 define he ange of maginal allowance pices unde GHG i n- jecion. he amoun of GHG injeced mus be nonnegaive (minimal A- fo... because i is impossible o injec a negaive amoun. heefoe one pice bound is he maginal allowance pice wihou GHG injecions i.e. he efeence pice of equaion ( o (. he ohe pice bound sems fom he siuaion whee all GHG emissions S e e A p p e n d i c e s A. 3 a n d A. 4 f o a d e i v a i o n u s i n g h e p o p e v a l u e s f o x a n d e.

25 4 ae injeced ( A e fo.... In ohe wods GHG injecions elimi - nae emissions and hus hei diec pice influence compleely. Accoding o equ a i o n s (7 and (8 maginal allowance pices ae a linea funcion of he amoun injeced 3 beween hese wo bounds. o deemine whehe he deived pice bounds ae uppe o lowe bounds and o co m- pae allowance pices unde GHG injecions (equaions (7 a n d (8 wih hose of he efeence case in equaions ( and ( (pue allowance ading envionmen wihou abaemen echnology equaions (7 and (8 mus be analyzed in moe deail. Since A mus be posiive maginal allowance pices in he special case of equaion (8 lie below maginal pices of he efeence case; equaion ( consiues an uppe bound he exeme even of oal injecion a lowe pice bound. he eason fo his pice behavio is inuiive. he abaemen echnology makes he GHG consain easie o mee hence emissions allowances become less valuable o he owne-opeao (d emand-based explanaion. Simulaneously cash flows a ime will be highe because fewe allowances need o be bough hanks o he abaemen echnology. hus oal isk is highe which jusifies a pice discoun (isk-based explanaion. hings ae slighly moe complicaed in he geneal case of equaion (7 because emissions allowances disinguish hemselves by ineempoal isk connecions fom hose of he special case. Fo ha eason maginal allowance pices unde a posiive (negaive aiance beween ( and τ as well as lie below (above he ones of he efe ence case. A posiive aiance adds addiional isk compaed o he special case of se ially uncoelaed cash flows emissions inensiies and speads; a nega ive aiance i n- duces hedge aspecs. eveheless he same fundamenal pice bounds obain as in he special case. 3 I n a s i d e n o e o b s e v e h a e q u a i o n s ( 7 a n d ( 8 hold iespecive of whehe GHG injecions ae i n - finiely divisible.

26 5 Finally o descibe maginal allowance pices fully unde GHG injecions he pice bounds of he efeence case have o be aken ino accoun i.e. he lowe bound a zeo and he uppe bound a 4 ( EUR. his means ha maginal allowance pices unde GHG injecions ae a posiive linea funcion of he amoun injeced and ae l o- 4 caed beween max{ allowance pice wih full injecion } and min{ (} o min{ 4 (}. So fa a posiive linea elaionship beween maginal allowance pices and he amoun injeced has been diseed. his esul should no be confused wih he saemen ha maginal allowance pices will be a linea funcion of he (nonivial pice dives spead and emissions inensiy. o analyze hei elaion o maginal al lowance pices ely on he opimum amoun of injecions. Fo he special case of seially uncoelaed cash flows emissions inensiies and speads equaion (8 simplifies o: 4 K( A ( A (9 O in wods he maginal allowance pice equals he pesen value of maginal payous fo injecions. In paicula he owne-opeao s isk avesion he isk of he emissions allowances and he iniial allocaion of emissions allowances do no seem o influence maginal allowance pices. his is because GHG injecions and emissions allowances ae subsiues wih espec o he GHG consain. heefoe he maginal payou fo K injecinos ( ( A A is he benchmak fo he pice of emissions allowances. his inepeaion of equaion (9 pomps a waning. Since maginal payous fo 4 See Appendix A.6 fo a deivaion. he calculaions fo he geneal case ae omied because hey do no yield such an insucively com - p a c f o m u l a. h i s i s n o e a l l y s u p i s i n g. S i n c e h e g e n e a l c a s e i n v o l v e s i n e e m p o a l i s k c o n n e c - i o n s a b a e m e n echnology and allowance ading ae no longe pefec subs i u e s.

27 6 GHG injecions ae a nonlinea funcion of he amoun injeced he owne-opeao of he insallaion has o know his opimal injecions o deemine maginal allowance pices. Howeve A - accoding o equaion (A.3 is a funcion of he owneopeao s isk avesion he isk of emissions allowances and he iniial allocaion. In ohe wods a naïve inepeaion of equaion ( 9 is deceiving excep fo one payou funcion: K( A- is linea in A Swiching beween wo poducion echnologies Swiching beween wo 5 poducion echnologies me ans ha he owne-opeao of an enegy- supply company has wo insallaions available fo poducing eleciciy. his flexibiliy also allows he owne-opeao wo ways of meeing GHG consains: allowance ading and/o inceasing he oupu of he in sallaion wih he lowe emissions in ensiy. 3.. Wealh dynamics As in he efeence case of Secion (pue allowance ading envionmen wihou abaemen echnology i is assumed ha boh insallaions aleady exis i.e. no ini ial invesmen fo poducion faciliies is needed. Howeve because oal oupu emains fixed a poducion consain has o be added o he decision poblem: oal poducion is spli beween poducion a insallaions and ; fomally: ( whee (i denoes eleciciy poducion a insallaion i. i Equaion ( claifies ha he poducion of only one insallaion is decision vaiable; he ohe is deemined via he poducion consain. o ensue ha swiching be w e e n boh insallaions is due o GHG emissions only i is assumed ha boh insallaions 5 S w i c h i n g b e w e e n m o e h a n w o i n s a l l a i o n s d o e s n o p o d u c e s u b s a n i a l l y d i f f e e n e s u l s b u c o n a i n s b y f a m o e l e n g h y d e i v a i o n s. F o h a e a s o n h i s c a s e i s o m i e d.

28 7 have a capaciy high enough o poduce ; ohewise poducion swiching could be due o he lack of capaciy insead of lowe GHG emissions of one ins allaion. Since hee ae wo insallaions wo GHG consains need o be consideed (see Ai - cle 4 in connecion wih Annex I Diecive 3/87/E as long as combusion insallaions have a aed hemal inpu exceeding MW. he GHG consain fo insallaion is: ( τ e ( and he GHG consain fo insallaion is: e ( τ whee denoes iniial allocaion fo insallaion i (i a ime and is i he numbe of emissions allowances aded fo insallaion i a ime ( τ. Howeve ading in emissions allowances does no disinguish beween allowances fom insallaion and hose fom i nsallaion (see Aicle paagaph Diecive 3/87/E and aional Allocaion lan (3 p. 4. his means ha allowance ad - ing can be cenalized wihin a company as long as he cenal ading depamen has allocaed o each insallaion enough allowances o mee is own GHG cons ain. heefoe i becomes possible o focus on oal ansacions in emissions allowances insead of ansacions fo each insallaion. In paicula hee is only he following GHG consain: 6 ( e τ e (3 he GHG consain of equaion (3 implies howeve ha swiching poducion does no lead o a educion of iniial allocaion fo each insallaion. Accoding o he a- i 6 In o h e w o d s h e e w i l l b e n o d i f f e e n c e b e w e e n G H G c o n s a i n s a h e i n s a l l a i o n o c o m p a n y l e v e l i f h e e i s a m a k e f o e m i s s i o n s a l l o w a n c e s. W i h o u a m a k e f o e m i s s i o n s a l l o w a n c e s h e wo GHG consains ae clealy diffeen. An insallaion ha p o d u c e s a s m a l l a m o u n o f G H G c a n h e d g e a n i n s a l l a i o n h a p o d u c e s a h u g e a m o u n o f G H G u n d e G H G c o n s a i n s a h e c o m p a n y l e v e l b u n o u n d e G H G c o n s a i n s a h e i n s a l l a i o n l e v e l. E m i s s i o n s a l l o w a n c e s e e s a b l i s h h i s

29 8 ional Allocaion lan (3 p. 3 an insallaion s iniial allocaion will be educed popoional o he capaciy uilizaion of he insallaion if is annual emissions ae lowe han 6% of is aveage annual emissions duing he efeence p eiod -. ombining ansacions in emissions allowances and iniial allocaions fo insallaions a n d a s i n h e G H G c o n s a i n (3 i.e. using oal ansacions and oal iniial allocaion budge equaion a ime wealh fom inemediae allowance ading and wealh a ime (befoe einvesmen bu afe balancing he GHG consains ae no diffeen compaed o he efeence case. hus hese inemediae seps ae omied and one immediaely obains: 7 W W (( x x ( e e ( e f (4 E he las em of equaion (4 descibes he wealh effecs of swiching beween wo insallaions elaive o he efeence case of pue a llowance ading (see equaion (8 (if is assumed. I sems fom he fac ha swiching poducion o insallaion ceaes cash flows ha ae based on speads and emissions inensiies of insalla - ion insead of hose of insallaion. 3.. Valuaion esuls he decision poblem fom which he valuaion esuls will be deived is fomulaed as follows: Max τ... τ... Φ E { W } va( W a wih W as defined in equaion (5. ha is he owne -opeao can choose he numbe of emissions allowances a each ime ( τ τ... τ as well as he oupu poduced a insallaion a imes (5 h e d g i n g o ppouniy. 7 See Appendix A. fo a deivaion.

30 9... so as o maximize he pefeence funcional (6. o be moe pecise he owne-opeao deemines a saegy fo boh decision vaiables i.e. a complee condi - ional plan. Appendices A.3 and A.4 show ha maginal allowance pices fo his scenaio ead: whee ef 7 a OV (6 ( OV denoes he aiance maix beween τ as well as and (( x x ( e e ( fo.... E Fo he special case of seially uncoelaed cash flows emissions inensiies and speads one obains: ef unc a (7 ( (( x x E ( e e Fom equaions (6 and (7 i is obvious ha hee ae pice bounds fo allowance pices unde swiching poducion. he amoun poduced a eihe insallaion mus be nonnegaive because i is impossible o poduce a negaive amoun. heefoe one pice bound is he maginal allowance pice when oal poducion happens a insallaion ( fo... he ohe pice bound sems fom he siuaion whee all poducion is poduced a insallaion ( fo.... Boh pice bounds can be calculaed wih equaions ( o ( because hese equaions descibe he behavio of maginal allowance pices in an envionmen wih jus one insallaion. Moeove accoding o equaions (6 a n d (7 beween hese wo bounds maginal allowance pices ae a posiive linea funcion of he oupu of insallaion. o deemine whehe he idenified pice bounds ae uppe o lowe bounds and o compae allowance pices unde swiching poducion (equaions (6 and (7 wih hose of he efeence case (equaions ( and ( (pue allowance ading envion-

31 3 men wihou abaemen echnology equaions (6 and (7 need o be analyzed in moe deail. Since mus be posiive maginal allowance pices i n he special case of equaion ( 7 depend on he sign of he diffeence be w e e n ( x e i.e. aiance beween cash flows fom eleciciy po - E ducion a insallaion and allowance pices and ( x e E i.e. aiance beween cash flows fom eleciciy poducion a insallaion and allowance pices. If his diffeence is posiive ef unc will be an uppe bound fo maginal allowance pices unde swiching poducion. his inepeaion is easy o undesand. A posiive diffeence means ha isk has inceased by poducing oupu a insallaion. Highe isk howeve calls fo a pice discoun. A negaive diffeence signifies educed isk by swiching poducion (paial ly o insallaion ; a lowe pice discoun fol lows. In ha even ef unc will be a lowe bound fo maginal allowance pices unde swiching poducion. In addiion he isk-based explanaion claifies ha a dominan poducion insallaion i.e. an insallaion wih boh a highe spead and a lowe emissions inensiy canno guaanee an unambiguous influence on maginal allowance pices. o see his conside a highe isk due o poducion a insallaion i.e. a posiive sign o f (( x x E ( e e. Assuming a posiive sign of ( E and nonsochasic speads and emissions inensiies he posiive sign of he above aiance will be ue if x wih ( ( va > x ( e e (8 ( ( va E E /egession coefficien of he egession of E on. Obviously hee ae paamee consellaions possible whee e is smalle han e a n d x lage han x bu equaion (8 i s neveheless violaed. hus he ambiguous

32 3 effec of a dominan poducion insallaion on maginal allowance pices is poven. he demand-based explanaion of maginal allowance pices adds fuhe illusaive insighs. Assume ha he owne-opeao poduces some eleciciy a insallaion. A smalle maginal allowance pice wih inceasing oupu of insallaion signifies ha he owne-opeao feels less pessue o puchase allowances which could be due o he fac ha insallaion has a lowe emissions inensiy. Maginal allowance pices ha ise wih an inceasing oupu a insallaion make emissions allowances moe val u- able o he owne-opeao he highe insallaion s oupu is. One possible explanaion is ha emissions allowan ces allow fo swiching o a moe pofiable i nsallaion albei one wih a highe emissions inensiy ha makes GHG consains moe difficul o mee. Since he geneal case of equaion (6 meely conains ineempoal a iance ems he esuls of he special case can be ansfeed seamlessly. Finally o descibe maginal allowance pices fully unde swiching poducion he pice bounds of he efeence case have o be aken ino accoun i.e. he lowe bound a zeo and he uppe bound a 4 ( EUR. his means ha maginal allowance pices unde swiching poducion ae a posiive linea funcion of insallaion s oupu and ae locaed beween max{ ( o ( calculaed based on oal oupu pod u c e d a insallaion } o max{ ( o ( calculaed based on oal oupu poduced a insallaion } and min{ 4 ( o ( calculaed based on oal oupu poduced a insallaion } o min{ 4 ( o ( calcula ed based on oal oupu p o- duced a insal laion }. So fa a posiive linea elaionship beween maginal allowance pices and he amoun poduced a insallaion has been diseed. his esul should no be confused wih