Hedging Strategy and Electricity Contract Engineering - IFOR

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176 Case study mal production portfolio is given by the following optimization problem subject to max x>?.5@A>B? 605 z>B? 2505CD>?.5 L>? 336E 250 I 1 250 1 250 250 jF 1 lG x 6 9 6 y jH (7.3) z j C (7.4) 1 G 0 90H 250 jF 1 8 z j x 6 9 6 y jH I 6 j 1 6 8J88 6 250 (7.5) lG 0 V j6 k5 k 1 88J8 6 6 336 6 j 1 8J88 6 6 250 (7.6) V k5 j 1500000 6 k 1 8J88 6 336 6 j 1 8J88 6 6 250 (7.7) L k5 j 0 6 k 1 88J8 6 336 6 j 1 8J88 6 6 250 (7.8) 250 1450000 1 250 V 3365 j (7.9) 1 jF 30 94 i 1 6 94 i 0 6 i 1 6 88J8 6 30 (7.10) iF 1 30 9:7 i 1 6 9:7 i 0 6 i 1 6 88J8 6 30 (7.11) 1 iF 10000 x 10000 6 (7.12) where the water level in period k and scenario j is given by V k5 j 1450000 30 lF 1 7 l 9 k k k I i5 j L i5 4 j G 9 l g4l S i5 j D i5 jH iF 1 iF 1 iF 1 lF 1 jH l S i5 j D i5 G (7.13) g7 30 and the loss function, where no discounting is performed due to the short horizon, is in scenario j given by
7.1 Efficient frontier 177 lG x 6 9 6 y jH 39 336x 40 336 1 iF l G S i5 j6 D i5 jH x D i5 j 8 g7 D i5 j 336 iF 1 S i5 j 30 lF 1 4 l 9 1 0 8 70 30 lF 1 4 l 9 g4l G S i5 j6 D i5 jH (7.14) The marginal costs for production and pumping are, as seen, not present. They are typically very low and are negligible in this analysis. 7.1. Efficient frontier The tightest risk constraint for which there exists a feasible solution to (7.3)-(7.12) is C min 5 8 657 million CHF. This means that the polyeder of feasible solutions is empty for risk constraints lower than C min , which hence is the minimum achievable risk. A number of optimizations were performed for different constraints on the risk, varying from C min to 2 million CHF, where the latter corresponds to a pure profit maximization without any regards to the riskiness of the portfolio. The maximum expected profit plotted against the risk constraint gives us the utility specific efficient frontier, which is shown in Figure 7.3. Any portfolio under the efficient frontier is inefficient, since there exists a portfolio with a higher expected profit at the same risk. This corresponds to the efficient frontier in the Markowitz portfolio optimization approach, where however risk is measured as variance [Mar52]. The efficient frontier is shown to be piecewise linear and concave, which is consistent with Corollary 6.13. The expected profit as a function of the maximum risk is strictly increasing for risk constraints tighter than 1325000 CHF. For looser risk constraints the expected profit is constant, as seen in Figure 7.3. The reason for this is that the risk constraint is inactive for C 1325000 CHF. The future position is then already at its maximum, x 10000 MW, as can be seen in Figure 7.4, and the production cannot be changed towards a more profit oriented dispatch. This would in the mean-variance case correspond to a full investment in the single stock with the highest expected profit and with short positions prohibited. The marginal value
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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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6.4 Modeling of plants and their op
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Page 143 and 144: 6.4 Modeling of plants and their op
Page 145 and 146: gìi Û S í SÜ D í DÜ I a í I
Page 147 and 148: õ õ 6.5 Analysis of optimal dispa
Page 149 and 150: õ Ü r á 6.5 Analysis of optimal
Page 151 and 152: ¢ é á 6.5 Analysis of optimal di
Page 153 and 154: ìj Û 1 bë j Ý?Ü j 1Ü á?á@á
Page 155 and 156: u ¦ j Ü è è aëj ¦ bë j u j
Page 157 and 158: õ õ õ á á 6.5 Analysis of opti
Page 159 and 160: 6.6 Power portfolio optimization wi
Page 161 and 162: è á 6.6 Power portfolio optimizat
Page 163 and 164: x Û x p Ü x c Ý Û xë1 Ü á@á
Page 167 and 168: ááá ááá ááá ááá ááá
Page 169 and 170: F Û 0Ü 3Ý í è F Û 0Ü 1Ý?Ü
Page 173 and 174: ö 6.6 Power portfolio optimization
Page 175 and 176: ö Ü 6.6 Power portfolio optimizat
Page 177 and 178: ö S kã j á 6.6 Power portfolio o
Page 179 and 180: ¢ ¢ 6.6 Power portfolio optimizat
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: 175 Production Spot price Demand [C
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 and 210: a4q V a4q G 1 V H a4q 6 Appendix A
Page 211 and 212: 8 _ 195 Proof The results follow im
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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