Hedging Strategy and Electricity Contract Engineering - IFOR

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a4i H a4q H f S dS 6 _ 194 Proofs and hence it is equivalent to prove that (A.2) Applying the two inequalities VZG a4i a4q H G 1 V H G a4j a4q H VG a4q a4i H G 1 V H G a4j a4q H 0 8 SWi SWi G a4q S f S dS S4q f S dS SWq SWq and SWq SWq G a4j S f S dS S4q SWj SWj (A.2) follows from SWi SWq V S4q f S dS G 1 V H S4q f S dS 0 SWq SWj VG S4q b4q H G b4i V H G b4 1 j H b4q bWq4 [ bWi 4¡\ 1 7¥[^] bW j 7 \ 1 7¥[^] bWqF 0 7¥[ 0 by definition of b4q . Corollary 6.2 The solution of (6.23) is given by (i) In the trivial case, where WK b41 , 9 4 1 1 (ii) If WK b4r then the problem is infeasible (iii) Else WK b4i 6 b4i 7 1 for some i 9 4 and i 17 W` bWiS 17 bWi bWiS 9 4 , i 1 1 9 4 i . 7
8 _ 195 Proof The results follow immediately from Theorem 6.1. Case (i) corresponds to abundant water and we optimally produce at as low prices as possible, since a is monotone increasing in b. In case (ii) there is not enough water, even if we chose the most conservative strategy to produce only at S S4r . In the general case (iii) the concavity of a in b implies that a convex combination of two adjacent points is optimal, whereas a being monotone increasing in b gives the actual _ weights. Corollary 6.3 Evidently the optimal policy when maximizing the expected profit given a constraint on the averaged produced water is to choose SK such that f S dS WK Proof Let the distance between the thresholds S4i S4i 1 go to zero and consider (6.23) in continuous time, then the results follow 7 immediately from Theorem 6.1. Sa S` Corollary 6.4 The marginal value of water z \ W` 4¡b ] 7 z \ W` ] b (i) Is in the trivial case, WK Y where b41 zero (ii) Is in the general case, where WK b4i 6 b4i 7 1H for some i, given by 17 aWiS aWi , and is constant in the interval c b4i WK 6 b4i 1 bWi WK . bWiS 17 7 Proof In the special case (i) an additional unit of water will not have any value, since we cannot even utilize the currently available water. The general case is easily proven by observing that the marginal value of water is given by the bH slope _ aG of . Proposition 6.5 The marginal value of water is never exceeding the average price of produced . electricity z \ W` ] z \ W` 4¡b ] 7 z \ W` ] W`
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Diss. ETH No. 14727 Hedging Strateg
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Abstract This thesis studies risk m
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Zusammenfassung Die vorliegende Sch
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Contents Acknowledgements ¡ ¢ ¡
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Contents xi 5.1 Overview . . . . .
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List of Figures 2.1 Illustration of
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List of Figures xv 7.6 Marginal val
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List of Tables 2.1 Spot market bid.
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Chapter 1 Introduction 1.1. Motivat
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1.3 Structure of the thesis 5 hedge
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Chapter 2 The electricity market 2.
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2.1 Overview 9 Generation ¥ Distri
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2.2 Liberalization of the electrici
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duction cost Marginal pro © 2.3 Su
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2.4 Transmission costs 15 10 Peak l
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2.4 Transmission costs 17 destinati
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2.5 Demand 19 2.5. Demand Compared
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2.6 Special characteristics of elec
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2.7 Electricity contracts 23 tions.
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0& K $ 0& K K % + $ 2.7 Electricity
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2.7 Electricity contracts 27 2.7.2.
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04 04 2.7 Electricity contracts 29
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2.8 Power exchanges and pricing mec
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2.8 Power exchanges and pricing mec
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S 0 eH aIKJ 2.9 Price dynamic 35 To
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2.9 Price dynamic 37 400 2000 350 1
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2.9 Price dynamic 39 simple sinus f
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2.9 Price dynamic 41 1800 1800 1600
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2.10 Summary 43 To deal with the un
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Chapter 3 Risk management 3.1. Over
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3.3 The risks in the electricity ma
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3.3 The risks in the electricity ma
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3.4 Traditional risk management mod
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l H xg yLihkjml f 3.5 The need for
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3.5 The need for a new risk measure
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R S x GaRKV is convex and continuou
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R P 3.6 Multi period risk managemen
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“ “ “ 3.7 Valuation models 67
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3.7 Valuation models 69 storability
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3.7 Valuation models 71 by introduc
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“ 3.7 Valuation models 73 formula
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Chapter 4 Contract engineering 4.1.
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4.2 Gas turbine 77 2000 1800 1600 1
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4.2 Gas turbine 79 220 200 Capped l
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4.3 Hydro storage plant 81 facilita
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¢ 4.3 Hydro storage plant 83 I k L
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x k xœk x «k š xœk 0 š x «k 0
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4.4 Coal plant and oil plant 87 4.4
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4.4 Coal plant and oil plant 89 cor
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4.5 Nuclear plant 91 of 1000 MW. Ov
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4.7 All production plants 93 possib
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4.8 Transmission lines 95 Unit type
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4.9 Real option theory 97 The scien
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4.10 Value of different production
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4.12 Summary 101 like the capped sp
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Chapter 5 Hedging strategies 5.1. O
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È È È È È 5.2 Traditional hedg
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É È É È Ì 5.2 Traditional hedg
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5.3 Relevance for electricity hedgi
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5.4 Best Hedge 111 that the expecte
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5.4 Best Hedge 113 that they alread
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Chapter 6 Power portfolio optimizat
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6.3 Power portfolio optimization in
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6.3 Power portfolio optimization in
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6.4 Modeling of plants and their op
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x k xëk x ìk Ü xë k 0Ü x ìk 0
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gìi Û S í SÜ D í DÜ I a í I
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õ õ 6.5 Analysis of optimal dispa
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õ Ü r á 6.5 Analysis of optimal
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¢ é á 6.5 Analysis of optimal di
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ìj Û 1 bë j Ý?Ü j 1Ü á?á@á
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u ¦ j Ü è è aëj ¦ bë j u j
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õ õ õ á á 6.5 Analysis of opti
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Page 173 and 174: ö 6.6 Power portfolio optimization
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Page 181 and 182: î yú1 î é yú1 á ¢ 6.6 Power
Page 183 and 184: 6.7 Summary 167 opportunity set wou
Page 185 and 186: Chapter 7 Case study In this chapte
Page 187 and 188: 171 3200 140 3000 2800 120 2600 240
Page 189 and 190: S7 D7 min 8 0 if S i or D p otherwi
Page 191 and 192: 175 Production Spot price Demand [C
Page 193 and 194: 7.1 Efficient frontier 177 lG x 6 9
Page 195 and 196: 7.2 Spot position 179 of the old po
Page 197 and 198: 7.3 Hedging value of water 181 The
Page 199 and 200: 7.4 Value decomposition 183 expecte
Page 201 and 202: MWh CHF/ P 7.4 Value decomposition
Page 203 and 204: 7.6 Summary 187 2500 2000 Dispatch
Page 205 and 206: 7.6 Summary 189 We have quantified
Page 207 and 208: Chapter 8 Conclusions The special c
Page 209: a4q V a4q G 1 V H a4q 6 Appendix A
Page 213 and 214: g b4i d G9:7j b4 j G 1 9j7j H b4 j
Page 215 and 216: Ax 3 V AxK1 G 1 V H AxK2 V b 1 G 1
Page 217 and 218: Bibliography [ABA98] [AD80] [ADEH97
Page 219 and 220: Bibliography 203 [BS73] [BS98] [BT0
Page 221 and 222: Bibliography 205 [GR92] H. Gravelle
Page 223 and 224: Bibliography 207 [Mer76] R. C. Mert
Page 225 and 226: Bibliography 209 [SC89] [Sch90] [Sc
Page 227: Curriculum Vitae Personal Data Name
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