Stochastic modelling of electricity and related markets:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
2008
|
| Series: | Advanced series on statistical science and applied probability
11 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XIV, 337 S. graph. Darst. |
| ISBN: | 9789812812308 981281230X |
Staff View
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| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 2008 | |
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| 490 | 1 | |a Advanced series on statistical science and applied probability |v 11 | |
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| 650 | 4 | |a Energy industries |x Mathematical models | |
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Record in the Search Index
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ADVANCED SERIES ON STATISTICAL SCIENCE & APPLIED PROBABILITY VOL. I I
STOCHASTIC MODELLING OF ELECTRICITY AND RELATED MARKETS FRED ESPEN BENTH
JGRATE SALTYTE BENTH UNIVERSITY OF OSLO, NORWAY STEEN KOEKEBAKKER
UNIVERSITY OFAGDER, NORWAY WORLD SCIENTIFIC NEW JERSEY * LONDON *
SINGAPORE * BEIJING * SHANGHAI * HONG KONG * TAIPEI * CHENNAI CONTENTS
PREFACE VII 1. A SURVEY OF ELECTRICITY AND RELATED MARKETS 1 1.1 THE
ELECTRICITY MARKETS ' 3 1.1.1 ELECTRICITY CONTRACTS WITH PHYSICAL
DELIVERY 3 1.1.2 FINANCIAL ELECTRICITY CONTRACTS 5 1.2 THE GAS MARKET 8
1.2.1 FUTURES AND OPTIONS ON GAS 10 1.3 THE TEMPERATURE MARKET 11 1.4
OTHER RELATED ENERGY MARKETS 14 1.5 STOCHASTIC MODELLING OF ENERGY
MARKETS 18 1.5.1 SPOT PRICE MODELLING 19 1.5.2 FORWARD AND SWAP PRICING
IN ELECTRICITY AND RELATED MARKETS 24 1.6 OUTLINE OF THE BOOK 32 2.
STOCHASTIC ANALYSIS FOR INDEPENDENT INCREMENT PROCESSES 37 2.1
DEFINITIONS 37 2.2 STOCHASTIC INTEGRATION WITH RESPECT TO MARTINGALES 41
2.3 RANDOM JUMP MEASURES AND STOCHASTIC INTEGRATION 43 2.4 THE
LEVY-KINTCHINE DECOMPOSITION AND SEMIMARTINGALES . . 45 2.5 THE ITO
FORMULA FOR SEMIMARTINGALES 48 2.6 EXAMPLES OF INDEPENDENT INCREMENT
PROCESSES 49 2.6.1 TIME-INHOMOGENEOUS COMPOUND POISSON PROCESS . 49
2.6.2 MODELS BASED ON THE GENERALIZED HYPERBOLIC DISTRIBU- TIONS 51 XII
STOCHASTIC MODELLING OF ELECTRICITY AND RELATED MARKETS 2.6.3 MODELS
BASED ON THE VARIANCE-GAMMA AND CGMY DISTRIBUTIONS 55 3. STOCHASTIC
MODELS FOR THE ENERGY SPOT PRICE DYNAMICS 59 3.1 INTRODUCTION 59 3.2
SPOT PRICE MODELLING WITH ORNSTEIN-UHLENBECK PROCESSES . . 60 3.2.1
GEOMETRIC MODELS 66 3.2.2 ARITHMETIC MODELS 74 3.3 THE AUTOCORRELATION
FUNCTION OF MULTI-FACTOR ORNSTEIN- UHLENBECK PROCESSES 78 3.4 SIMULATION
OF STATIONARY ORNSTEIN-UHLENBECK PROCESSES: A CASE STUDY WITH THE
ARITHMETIC SPOT MODEL 82 4. PRICING OF FORWARDS AND SWAPS BASED ON THE
SPOT PRICE 89 4.1 RISK-NEUTRAL FORWARD AND SWAP PRICE MODELLING 89 4.1.1
RISK-NEUTRAL PROBABILITIES AND THE ESSCHER TRANSFORM 95 4.1.2 THE
ESSCHER TRANSFORM FOR SOME SPECIFIC MODELS . 99 4.2 CURRENCY
CONVERSION FOR FORWARD AND SWAP PRICES 100 4.3 PRICING OF FORWARDS 104
4.3.1 THE GEOMETRIC CASE 104 4.3.2 THE ARITHMETIC CASE 114 4.4 PRICING
OF SWAPS 118 4.4.1 THE GEOMETRIC CASE 119 4.4.2 THE ARITHMETIC CASE 122
5. APPLICATIONS TO THE GAS MARKETS , 129 5.1 MODELLING THE GAS SPOT
PRICE 129 5.1.1 EMPIRICAL ANALYSIS OF UK GAS SPOT PRICES 130 5.1.2
RESIDUALS MODELLED AS A MIXED JUMP-DIFFUSION PROCESS 136 5.1.3 NIG
DISTRIBUTED RESIDUALS 139 5.2 PRICING OF GAS FUTURES 142 5.3 INFERENCE
FOR MULTI-FACTOR PROCESSES 146 5.3.1 KALMAN FILTERING 147 5.3.2
INFERENCE USING FORWARD AND SWAP DATA 150 6. MODELLING FORWARDS AND
SWAPS USING THE HEATH-JARROW- MORTON APPROACH 155 6.1 THE HJM MODELLING
IDEA FOR FORWARD CONTRACTS 156 CONTENTS XIII 6.2 HJM MODELLING OF
FORWARDS 160 6.3 HJM MODELLING OF SWAPS 164 6.3.1 SWAP MODELS BASED ON
FORWARDS 168 6.4 THE MARKET MODELS 172 6.4.1 MODELLING WITH JUMP
PROCESSES 176 7. CONSTRUCTING SMOOTH FORWARD CURVES IN ELECTRICITY
MARKETS 181 7.1 SWAP AND FORWARD PRICES 183 7.1.1 BASIC RELATIONSHIPS -
183 7.1.2 A CONTINUOUS SEASONAL FORWARD CURVE 184 7.2 MAXIMUM SMOOTH
FORWARD CURVE 187 7.2.1 A SMOOTH FORWARD CURVE CONSTRAINED BY CLOSING
PRICES 187 7.2.2 A SMOOTH FORWARD CURVE CONSTRAINED BY BID AND ASK
SPREADS 190 7.3 PUTTING THE ALGORITHM TO WORK 191 7.3.1 NORD POOL
EXAMPLE I: A SMOOTH CURVE 191 7.3.2 NORD POOL EXAMPLE II: PREPARING A
DATA SET AND ANALYSING VOLATILITY - 195 8. MODELLING OF THE ELECTRICITY
FUTURES MARKET 203 8.1 THE NORD POOL MARKET AND FINANCIAL CONTRACTS 205
8.2 PREPARING DATA SETS 206 8.3 DESCRIPTIVE STATISTICS 208 8.4 A MARKET
MODEL FOR ELECTRICITY FUTURES 214 8.5 PRINCIPAL COMPONENT ANALYSIS 215
8.5.1 PRINCIPAL COMPONENT ANALYSIS OF THE TOTAL DATA SET . . 217 8.5.2
PRINCIPAL COMPONENT ANALYSIS FOR INDIVIDUAL MARKET SEGMENTS 220 8.6
ESTIMATING A PARAMETRIC MULTI-FACTOR MARKET MODEL 224 8.6.1 SEASONAL
VOLATILITY 226 8.6.2 MATURITY VOLATILITIES 227 8.7 NORMALISED LOGRETURNS
AND HEAVY TAILS 231 8.8 FINAL REMARKS 235 9. PRICING AND HEDGING OF
ENERGY OPTIONS 237 9.1 PRICING AND HEDGING OPTIONS ON FORWARDS AND SWAPS
238 9.1.1 THE CASE OF NO JUMPS - THE BLACK-76 FORMULA . . . . 238 9.1.2
THE CASE OF JUMPS 247 XIV STOCHASTIC MODELLING OF ELECTRICITY AND
RELATED MARKETS 9.2 EXOTIC OPTIONS 254 9.2.1 SPREAD OPTIONS 254 9.2.2
ASIAN OPTIONS 260 9.3 CASE STUDY: VALUATION OF SPARK SPREAD OPTIONS - A
DIRECT APPROACH 262 9.3.1 MODELLING AND ANALYSIS OF SPARK SPREAD OPTIONS
. . . 264 9.3.2 EMPIRICAL ANALYSIS OF UK GAS AND ELECTRICITY SPREAD .
268 10. ANALYSIS OF TEMPERATURE DERIVATIVES 277 10.1 SOME PRELIMINARIES
ON TEMPERATURE FUTURES 277 10.2 MODELLING THE DYNAMICS OF TEMPERATURE
280 10.2.1 THE CAR(P) MODEL WITH SEASONALITY 281 10.2.2 A LINK TO TIME
SERIES 283 10.3 EMPIRICAL ANALYSIS OF STOCKHOLM TEMPERATURE DYNAMICS . .
. 285 10.3.1 DESCRIPTION OF THE DATA 285 10.3.2 ESTIMATING THE CAR(P)
MODELS 287 10.3.2.1 FITTING AN AR(1) MODEL 289 10.3.2.2 FITTING AN AR(3)
MODEL 296 10.3.2.3 IDENTIFICATION OF THE PARAMETERS IN THE CAR(P) MODEL
300 10.4 TEMPERATURE DERIVATIVES PRICING 301 10.4.1 CAT FUTURES 302
10.4.2 HDD/CDD FUTURES 305 10.4.3 FROST DAY INDEX FUTURES ' 312 10.4.4
APPLICATION TO FUTURES ON TEMPERATURES IN STOCKHOLM 314 APPENDIX A LIST
OF ABBREVIATIONS 319 BIBLIOGRAPHY 321 INDEX 333 |
| adam_txt |
ADVANCED SERIES ON STATISTICAL SCIENCE & APPLIED PROBABILITY VOL. I I
STOCHASTIC MODELLING OF ELECTRICITY AND RELATED MARKETS FRED ESPEN BENTH
JGRATE SALTYTE BENTH UNIVERSITY OF OSLO, NORWAY STEEN KOEKEBAKKER
UNIVERSITY OFAGDER, NORWAY WORLD SCIENTIFIC NEW JERSEY * LONDON *
SINGAPORE * BEIJING * SHANGHAI * HONG KONG * TAIPEI * CHENNAI CONTENTS
PREFACE VII 1. A SURVEY OF ELECTRICITY AND RELATED MARKETS 1 1.1 THE
ELECTRICITY MARKETS ' 3 1.1.1 ELECTRICITY CONTRACTS WITH PHYSICAL
DELIVERY 3 1.1.2 FINANCIAL ELECTRICITY CONTRACTS 5 1.2 THE GAS MARKET 8
1.2.1 FUTURES AND OPTIONS ON GAS 10 1.3 THE TEMPERATURE MARKET 11 1.4
OTHER RELATED ENERGY MARKETS 14 1.5 STOCHASTIC MODELLING OF ENERGY
MARKETS 18 1.5.1 SPOT PRICE MODELLING 19 1.5.2 FORWARD AND SWAP PRICING
IN ELECTRICITY AND RELATED MARKETS 24 1.6 OUTLINE OF THE BOOK 32 2.
STOCHASTIC ANALYSIS FOR INDEPENDENT INCREMENT PROCESSES 37 2.1
DEFINITIONS 37 2.2 STOCHASTIC INTEGRATION WITH RESPECT TO MARTINGALES 41
2.3 RANDOM JUMP MEASURES AND STOCHASTIC INTEGRATION 43 2.4 THE
LEVY-KINTCHINE DECOMPOSITION AND SEMIMARTINGALES . . 45 2.5 THE ITO
FORMULA FOR SEMIMARTINGALES 48 2.6 EXAMPLES OF INDEPENDENT INCREMENT
PROCESSES 49 2.6.1 TIME-INHOMOGENEOUS COMPOUND POISSON PROCESS . 49
2.6.2 MODELS BASED ON THE GENERALIZED HYPERBOLIC DISTRIBU- TIONS 51 XII
STOCHASTIC MODELLING OF ELECTRICITY AND RELATED MARKETS 2.6.3 MODELS
BASED ON THE VARIANCE-GAMMA AND CGMY DISTRIBUTIONS 55 3. STOCHASTIC
MODELS FOR THE ENERGY SPOT PRICE DYNAMICS 59 3.1 INTRODUCTION 59 3.2
SPOT PRICE MODELLING WITH ORNSTEIN-UHLENBECK PROCESSES . . 60 3.2.1
GEOMETRIC MODELS 66 3.2.2 ARITHMETIC MODELS 74 3.3 THE AUTOCORRELATION
FUNCTION OF MULTI-FACTOR ORNSTEIN- UHLENBECK PROCESSES 78 3.4 SIMULATION
OF STATIONARY ORNSTEIN-UHLENBECK PROCESSES: A CASE STUDY WITH THE
ARITHMETIC SPOT MODEL 82 4. PRICING OF FORWARDS AND SWAPS BASED ON THE
SPOT PRICE 89 4.1 RISK-NEUTRAL FORWARD AND SWAP PRICE MODELLING 89 4.1.1
RISK-NEUTRAL PROBABILITIES AND THE ESSCHER TRANSFORM 95 4.1.2 THE
ESSCHER TRANSFORM FOR SOME SPECIFIC MODELS . 99 4.2 CURRENCY
CONVERSION FOR FORWARD AND SWAP PRICES 100 4.3 PRICING OF FORWARDS 104
4.3.1 THE GEOMETRIC CASE 104 4.3.2 THE ARITHMETIC CASE 114 4.4 PRICING
OF SWAPS 118 4.4.1 THE GEOMETRIC CASE 119 4.4.2 THE ARITHMETIC CASE 122
5. APPLICATIONS TO THE GAS MARKETS , 129 5.1 MODELLING THE GAS SPOT
PRICE 129 5.1.1 EMPIRICAL ANALYSIS OF UK GAS SPOT PRICES 130 5.1.2
RESIDUALS MODELLED AS A MIXED JUMP-DIFFUSION PROCESS 136 5.1.3 NIG
DISTRIBUTED RESIDUALS 139 5.2 PRICING OF GAS FUTURES 142 5.3 INFERENCE
FOR MULTI-FACTOR PROCESSES 146 5.3.1 KALMAN FILTERING 147 5.3.2
INFERENCE USING FORWARD AND SWAP DATA 150 6. MODELLING FORWARDS AND
SWAPS USING THE HEATH-JARROW- MORTON APPROACH 155 6.1 THE HJM MODELLING
IDEA FOR FORWARD CONTRACTS 156 CONTENTS XIII 6.2 HJM MODELLING OF
FORWARDS 160 6.3 HJM MODELLING OF SWAPS 164 6.3.1 SWAP MODELS BASED ON
FORWARDS 168 6.4 THE MARKET MODELS 172 6.4.1 MODELLING WITH JUMP
PROCESSES 176 7. CONSTRUCTING SMOOTH FORWARD CURVES IN ELECTRICITY
MARKETS 181 7.1 SWAP AND FORWARD PRICES 183 7.1.1 BASIC RELATIONSHIPS -
183 7.1.2 A CONTINUOUS SEASONAL FORWARD CURVE 184 7.2 MAXIMUM SMOOTH
FORWARD CURVE 187 7.2.1 A SMOOTH FORWARD CURVE CONSTRAINED BY CLOSING
PRICES 187 7.2.2 A SMOOTH FORWARD CURVE CONSTRAINED BY BID AND ASK
SPREADS 190 7.3 PUTTING THE ALGORITHM TO WORK 191 7.3.1 NORD POOL
EXAMPLE I: A SMOOTH CURVE 191 7.3.2 NORD POOL EXAMPLE II: PREPARING A
DATA SET AND ANALYSING VOLATILITY - 195 8. MODELLING OF THE ELECTRICITY
FUTURES MARKET 203 8.1 THE NORD POOL MARKET AND FINANCIAL CONTRACTS 205
8.2 PREPARING DATA SETS 206 8.3 DESCRIPTIVE STATISTICS 208 8.4 A MARKET
MODEL FOR ELECTRICITY FUTURES 214 8.5 PRINCIPAL COMPONENT ANALYSIS 215
8.5.1 PRINCIPAL COMPONENT ANALYSIS OF THE TOTAL DATA SET . . 217 8.5.2
PRINCIPAL COMPONENT ANALYSIS FOR INDIVIDUAL MARKET SEGMENTS 220 8.6
ESTIMATING A PARAMETRIC MULTI-FACTOR MARKET MODEL 224 8.6.1 SEASONAL
VOLATILITY 226 8.6.2 MATURITY VOLATILITIES 227 8.7 NORMALISED LOGRETURNS
AND HEAVY TAILS 231 8.8 FINAL REMARKS 235 9. PRICING AND HEDGING OF
ENERGY OPTIONS 237 9.1 PRICING AND HEDGING OPTIONS ON FORWARDS AND SWAPS
238 9.1.1 THE CASE OF NO JUMPS - THE BLACK-76 FORMULA . . . . 238 9.1.2
THE CASE OF JUMPS 247 XIV STOCHASTIC MODELLING OF ELECTRICITY AND
RELATED MARKETS 9.2 EXOTIC OPTIONS 254 9.2.1 SPREAD OPTIONS 254 9.2.2
ASIAN OPTIONS 260 9.3 CASE STUDY: VALUATION OF SPARK SPREAD OPTIONS - A
DIRECT APPROACH 262 9.3.1 MODELLING AND ANALYSIS OF SPARK SPREAD OPTIONS
. . . 264 9.3.2 EMPIRICAL ANALYSIS OF UK GAS AND ELECTRICITY SPREAD .
268 10. ANALYSIS OF TEMPERATURE DERIVATIVES 277 10.1 SOME PRELIMINARIES
ON TEMPERATURE FUTURES 277 10.2 MODELLING THE DYNAMICS OF TEMPERATURE
280 10.2.1 THE CAR(P) MODEL WITH SEASONALITY 281 10.2.2 A LINK TO TIME
SERIES 283 10.3 EMPIRICAL ANALYSIS OF STOCKHOLM TEMPERATURE DYNAMICS . .
. 285 10.3.1 DESCRIPTION OF THE DATA 285 10.3.2 ESTIMATING THE CAR(P)
MODELS 287 10.3.2.1 FITTING AN AR(1) MODEL 289 10.3.2.2 FITTING AN AR(3)
MODEL 296 10.3.2.3 IDENTIFICATION OF THE PARAMETERS IN THE CAR(P) MODEL
300 10.4 TEMPERATURE DERIVATIVES PRICING 301 10.4.1 CAT FUTURES 302
10.4.2 HDD/CDD FUTURES 305 10.4.3 FROST DAY INDEX FUTURES ' 312 10.4.4
APPLICATION TO FUTURES ON TEMPERATURES IN STOCKHOLM 314 APPENDIX A LIST
OF ABBREVIATIONS 319 BIBLIOGRAPHY 321 INDEX 333 |
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| author | Benth, Fred Espen Saltyte Benth, Jurate Koekebakker, Steen |
| author_GND | (DE-588)171901983 (DE-588)137396937 |
| author_facet | Benth, Fred Espen Saltyte Benth, Jurate Koekebakker, Steen |
| author_role | aut aut aut |
| author_sort | Benth, Fred Espen |
| author_variant | f e b fe feb b j s bj bjs s k sk |
| building | Verbundindex |
| bvnumber | BV035040165 |
| callnumber-first | H - Social Science |
| callnumber-label | HD9685 |
| callnumber-raw | HD9685.A2 |
| callnumber-search | HD9685.A2 |
| callnumber-sort | HD 49685 A2 |
| callnumber-subject | HD - Industries, Land Use, Labor |
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| ctrlnum | (OCoLC)191024116 (DE-599)BVBBV035040165 |
| dewey-full | 333.793/20151922 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 333 - Economics of land and energy |
| dewey-raw | 333.793/20151922 |
| dewey-search | 333.793/20151922 |
| dewey-sort | 3333.793 820151922 |
| dewey-tens | 330 - Economics |
| discipline | Energietechnik, Energiewirtschaft Elektrotechnik Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Energietechnik, Energiewirtschaft Elektrotechnik Mathematik Wirtschaftswissenschaften |
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| id | DE-604.BV035040165 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:52:55Z |
| indexdate | 2024-09-12T00:03:35Z |
| institution | BVB |
| isbn | 9789812812308 981281230X |
| language | English |
| lccn | 2008002489 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016709006 |
| oclc_num | 191024116 |
| open_access_boolean | |
| owner | DE-945 DE-91G DE-BY-TUM DE-11 DE-384 DE-634 DE-355 DE-BY-UBR |
| owner_facet | DE-945 DE-91G DE-BY-TUM DE-11 DE-384 DE-634 DE-355 DE-BY-UBR |
| physical | XIV, 337 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | World Scientific |
| record_format | marc |
| series | Advanced series on statistical science and applied probability |
| series2 | Advanced series on statistical science and applied probability |
| spelling | Benth, Fred Espen Verfasser (DE-588)171901983 aut Stochastic modelling of electricity and related markets Fred Espen Benth ; Jūratė Šaltytė Benth ; Steen Koekebakker Singapore [u.a.] World Scientific 2008 XIV, 337 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Advanced series on statistical science and applied probability 11 Hier auch später erschienene, unveränderte Nachdrucke Mathematisches Modell Electric utilities Mathematical models Energy industries Mathematical models Stochastic models Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf Energiemarkt (DE-588)4014712-5 gnd rswk-swf Energiemarkt (DE-588)4014712-5 s Stochastisches Modell (DE-588)4057633-4 s DE-604 Saltyte Benth, Jurate Verfasser (DE-588)137396937 aut Koekebakker, Steen Verfasser aut Advanced series on statistical science and applied probability 11 (DE-604)BV011932321 11 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016709006&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Benth, Fred Espen Saltyte Benth, Jurate Koekebakker, Steen Stochastic modelling of electricity and related markets Advanced series on statistical science and applied probability Mathematisches Modell Electric utilities Mathematical models Energy industries Mathematical models Stochastic models Stochastisches Modell (DE-588)4057633-4 gnd Energiemarkt (DE-588)4014712-5 gnd |
| subject_GND | (DE-588)4057633-4 (DE-588)4014712-5 |
| title | Stochastic modelling of electricity and related markets |
| title_auth | Stochastic modelling of electricity and related markets |
| title_exact_search | Stochastic modelling of electricity and related markets |
| title_exact_search_txtP | Stochastic modelling of electricity and related markets |
| title_full | Stochastic modelling of electricity and related markets Fred Espen Benth ; Jūratė Šaltytė Benth ; Steen Koekebakker |
| title_fullStr | Stochastic modelling of electricity and related markets Fred Espen Benth ; Jūratė Šaltytė Benth ; Steen Koekebakker |
| title_full_unstemmed | Stochastic modelling of electricity and related markets Fred Espen Benth ; Jūratė Šaltytė Benth ; Steen Koekebakker |
| title_short | Stochastic modelling of electricity and related markets |
| title_sort | stochastic modelling of electricity and related markets |
| topic | Mathematisches Modell Electric utilities Mathematical models Energy industries Mathematical models Stochastic models Stochastisches Modell (DE-588)4057633-4 gnd Energiemarkt (DE-588)4014712-5 gnd |
| topic_facet | Mathematisches Modell Electric utilities Mathematical models Energy industries Mathematical models Stochastic models Stochastisches Modell Energiemarkt |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016709006&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011932321 |
| work_keys_str_mv | AT benthfredespen stochasticmodellingofelectricityandrelatedmarkets AT saltytebenthjurate stochasticmodellingofelectricityandrelatedmarkets AT koekebakkersteen stochasticmodellingofelectricityandrelatedmarkets |