QUANTITATIVE METHODS FOR ELECTRICITY TRADING AND RISK MANAGEMENT

QUANTITATIVE METHODS FOR ELECTRICITY TRADING AND RISK MANAGEMENT

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Quantitative Methods for Electricity Trading and Risk Management Advanced Mathematical and Statistical Methods for Energy Finance STEFANO FIORENZANI

Stefano Fiorenzani 2006 Softcover reprint of the hardcover 1st edition 2006 978-1-4039-4357-6 All rights reserved. No reproduction, copy or transmission of this publication may be made without written permission. No paragraph of this publication may be reproduced, copied or transmitted save with written permission or in accordance with the provisions of the Copyright, Designs and Patents Act 1988, or under the terms of any licence permitting limited copying issued by the Copyright Licensing Agency, 90 Tottenham Court Road, London W1T 4LP. Any person who does any unauthorized act in relation to this publication may be liable to criminal prosecution and civil claims for damages. The author has asserted his right to be identified as the author of this work in accordance with the Copyright, Designs and Patents Act 1988. First published 2006 by PALGRAVE MACMILLAN Houndmills, Basingstoke, Hampshire RG21 6XS and 175 Fifth Avenue, New York, N.Y. 10010 Companies and representatives throughout the world PALGRAVE MACMILLAN is the global academic imprint of the Palgrave Macmillan division of St. Martin s Press, LLC and of Palgrave Macmillan Ltd. Macmillan is a registered trademark in the United States, United Kingdom and other countries. Palgrave is a registered trademark in the European Union and other countries. ISBN 978-1-349-52221-7 DOI 10.1057/9780230598348 ISBN 978-0-230-59834-8 (ebook) This book is printed on paper suitable for recycling and made from fully managed and sustained forest sources. A catalogue record for this book is available from the British Library. A catalog record for this book is available from the Library of Congress. 10 9 8 7 6 5 4 3 2 1 15 14 13 12 11 10 09 08 07 06

Contents List of Tables List of Figures Introduction viii ix xi Part I Distributional and Dynamic Features of Electricity Spot Prices 1 Liberalized Electricity Markets Organization 3 1.1 The liberalization process 3 1.2 Spot electricity exchanges organization 4 1.3 Electricity derivatives markets: organized exchanges and OTC markets 6 2 Electricity Price Driving Factors 8 2.1 Price determination in a liberalized context 8 2.2 Electricity demand driving factors 12 2.3 Electricity supply driving factors 14 3 Electricity Spot Price Dynamics and Statistical Features 19 3.1 Preliminary data definitions 19 3.2 Detecting periodic components in electricity prices 22 3.3 Statistical properties of electricity prices 30 Part II Electricity Spot Price Stochastic Models 4 Electricity Modeling: General Features 39 4.1 Scope of a financial model 39 4.2 Econometric models versus purely probabilistic models 40 4.3 Characteristics of an ideal model and state of the art 41 v

vi CONTENTS 5 Econometric Modeling of Electricity Prices 43 5.1 Traditional dynamic regression models 44 5.2 Transfer function models 46 5.3 Capturing volatility effects: GARCH models 48 5.4 Capturing long-memory effects in electricity price level and volatility: fractionally integrated models 49 6 Probabilistic Modeling of Electricity Prices 51 6.1 Traditional stochastic models 52 6.2 More advanced and realistic models 57 Appendix Semimartingales in financial modeling 63 Part III Electricity Derivatives: Main Typologies and Evaluation Problems 7 Electricity Derivatives: Main Typologies 71 7.1 Exchange-traded derivatives and OTC derivatives 71 7.2 Exotic options 75 7.3 Options typically embedded in electricity physical contracts 79 8 Electricity Derivatives: Valuation Problems 83 8.1 Derivative pricing: the traditional approach 83 8.2 The spot-forward price relationship in traditional and electricity markets 85 8.3 Non-storability and market incompleteness 88 8.4 Pricing and hedging in incomplete markets: basic principles 89 8.5 Calibrating the pricing measure 92 Appendix An equilibrium principle for pricing electricity assets in incomplete markets 93 9 Electricity Derivatives: Numerical Methods for Derivatives Pricing 95 9.1 Monte Carlo simulations 95 9.2 The lattice approach 98 Appendix A Pricing electricity swaptions by means of Monte Carlo simulations 104 Appendix B Pricing swing options by means of trinomial tree forests 106

CONTENTS vii Part IV Real Asset Modeling and Real Options: Theoretical Framework and Numerical Methods 10 Financial Optimization of Power Generation Activity 111 10.1 Optimization problems and the real option approach 111 10.2 Generation asset modeling: the spark spread method 116 10.3 Generation asset modeling: the stochastic dynamic optimization approach 117 Appendix Discrete time stochastic dynamic programing 123 11 Framing and Solving the Optimization Problem 127 11.1 Optimization problems in a deterministic environment 127 11.2 Naïve application of Monte Carlo methods 129 11.3 Solving Bellman s problem 130 11.4 Alternative solution methods: ordinal optimization 134 Appendix Generation asset modeling: numerical results 136 Part V Electricity Risk Management: Risk Control Principles and Risk Measurement Techniques 12 Risk Definition and Mapping 145 12.1 Market risk definition and basic principles 145 12.2 Different risk factors and their mapping onto the company value-creation chain 146 12.3 Risk and opportunity (enterprise risk attitude) 150 13 Risk Measurement Methods 152 13.1 Risk measures for financial trading portfolios 152 13.2 Risk measures for physical trading portfolios 161 Appendix On the coherence of risk measures 163 14 Risk-Adjusted Planning in the Electricity Industry 165 14.1 Production value and risk return measures 166 14.2 Survival performance level and extreme market events 170 14.3 A practical application 172 Bibliography 176 Index 179

List of Tables 3.1 Powernext de-structured time series correlogram analysis 34 3.2 Powernext de-structured time series unit root test 34 3.3 Powernext squared de-structured price time series correlogram analysis 36 5.1 Dynamic regression model estimation results 45 5.2 Transfer function model estimation results 47 9A.1 Simulation experiment results 105 9A.2 Sensitivity experiment result 106 11A.1 Summary of test case characteristics 136 11A.2 Production value and risk measure versus spark spread 137 11A.3 Power production value versus volatility 140 11A.4 Worst case value versus volatility 140 14.1 Power plant physical characteristics used in the example 168 14.2 Price model characteristics used in the example 168 14.3 Empirical experiments results 173 viii

List of Figures 2.1 Alberta power exchange merit order, 12 November 1999, 13.06 9 2.2 Demand/supply schematic representation 10 2.3 Demand shock in normal load regime 11 2.4 Demand shock in high load regime 11 2.5 Supply local shock 12 2.6 Italian national load (April 04 April 05) 13 2.7 Typical daily max load and daily max temperature 14 2.8 Mean hourly consumption of two European countries (Italy and France) 15 2.9 Mean monthly consumption of two European countries (Italy and France) 16 2.10 Powernext and EEX base load daily prices (546 observations 2003 04) 18 3.1 Daily base-load prices from major European and American electricity exchanges (546 observations from 11-01-02 to 16-03-04) 20 3.2 IPEX (Italian Power Exchange) hourly electricity spot price matrix (1 Jan. 2005 16 Mar. 2005) 22 3.3 EEX (German market) historical hourly prices, Oct. 2000 Oct. 2003 23 3.4 EEX periodogram calculated with hourly prices, Oct. 2000 Oct. 2003 26 3.5 EEX seasonal component y(t) 27 3.6 EEX intra-week shaping component w(t) 28 3.7 New South Wales electricity spot prices (Jan. 1998 Aug. 1998): original series denoised by means of wavelets (two examples) 30 ix

x LIST OF FIGURES 3.8 Powernext hourly spot prices distributional analysis (8,784 observations from 1 Jan. 2004 31 Dec. 2004) 32 3.9 Powernext hourly spot prices structural and unpredictable components 32 3.10 Powernext hourly spot de-structured prices distributional analysis 33 5.1 Dynamic regression model graphical representation 45 5.2 Powernext daily price (base load) 47 5.3 Transfer function model graphical representation 48 7.1 Tolling contract scheme 81 9.1 Lattice approach schematic representation 99 9.2 State price aggregation scheme 103 9A.1 Barlow process simulated price paths 104 9B.1 Trinomial tree forest scheme 107 10.1 Power generation/marketing decisional process 115 10.2 Diagrammatic representation of the dynamic equation (10.14) 122 11.1 Trinomial lattice scheme 133 11A.1 Production value versus spark spread (case 1) 138 11A.2 Production value versus spark spread (case 2) 138 11A.3 Production value versus spark spread (case 3) 139 11A.4 Production value versus spark spread (relative differences from case 1) 139 11A.5 Production value versus volatility 140 11A.6 Worst case versus volatility 141 12.1 Company risk map 147 13.1 Thick loss function vs normal 158 13.2 Non-monotonic loss function vs normal 159 13.3 Discontinuous loss function vs normal 159 13.4 Graphical representation of VaR, ES and CVaR 161 14.1 Asset optimization scheme 166 14.2 Power generation economic performance distribution 168 14.3 Power generation performance risk measure 169 14.4 Portfolio s economic performance distribution 171 14.5 A portfolio s economic performance survival risk measure 171 14.6 Distributional results from first experiment 174 14.7 Distributional results from second experiment 175

Introduction The electricity sector is traditionally a business sector with a strong industrial connotation. Due to regimes of strong national or regional protection under which the power sector in many countries has been born and developed, not much effort has been traditionally put into developing methods to increase the level of competitiveness of operators. Among such competitiveness weapons we may also consider all those merely financial issues related to the management and control of economic risks. The progressive liberalization process which has characterized many countries in recent years, and is developing in many others now, has led to the fragmentation of big national power operators and the entrance of new players into the different sectors of the electricity market. The increase in the number of players has obviously been accompanied by an increase in the level of competitiveness in all branches of the power sector: generation, marketing and distribution. Competition has also stimulated many players to look at and experiment with new business developments, and attention towards financial trading and risk-management issues has registered a significant increase such that today they play a central role in business practice. The same persons who, until few years ago, used to deal only with problems related to generation efficiency, transmission loads or power tariffs, are today asked to manage complex problems typically belonging to the financial area such as: financial trading, risk management, derivative products and portfolio optimization. The need to manage the problems of a market in rapid and strong evolution brings with it the need to integrate standard business and analysis tools with new methods more suitable to tackle this new set of problems. Hence we have observed massive efforts towards applying traditional methods of financial analysis to the new exigencies of the electricity market. Quantitative finance methods are now used not only for xi

xii INTRODUCTION financial risk assessment or for derivatives trading; real asset valuation with real options methodology and commercial deal structuring are also potential fields of application. A first problem is that of inducting non-experts to the application of mathematical and statistical tools for energy finance problems. This has been the focus of the biggest part of the specific scientific literature in the last few years. Initially we did not observe the development of specific models or methodologies for the power market, but rather the straightforward transposition to the electricity sector of instruments traditionally used in more mature financial sectors such as fixed-income or foreign-exchange markets. Often, this straightforward transposition has not given balanced attention to the potential dangers which may arise from a limited consideration of the physical peculiarities which characterize electricity markets. This book has been conceived and written as a natural continuation of the above approach. Following the traditional scientific literature of the sector, I also introduce some elements of discontinuity with the past tradition in the hope that they may help to inaugurate a new and independent field of research in the area of mathematical finance. I shall review the existing literature with a critical eye, emphasizing the limits and dangers of a straightforward application of traditional mathematical models in the peculiar environment represented by power markets. Advanced modeling approaches and mathematical tools are introduced to enhance the cultural and technical background of the reader. The necessary increase in complexity of the whole analysis is the price we have to pay in order to develop realistic and ad hoc analysis tools for the electricity world. Economics concepts such as that of market incompleteness or mathematical methods such as stochastic dynamic programing are introduced in this spirit. In addition, I want to give space to some extremely interesting and innovative research initiatives that have characterized the specialist literature in very recent years. Mainly I am referring to mathematical or statistical methods developed by researchers working in the field, with the precise scope of solving typical valuation or analysis problems of the electricity business. The reason for this choice lies in the need to stimulate the academic world also, too often concentrated on theoretical issues, towards real business problems. The book is more inclined towards practical issues than theoretical ones, although theoretical issues are considered if and when they are functional to business practice. The book is essentially dedicated to two groups of people: electricity market operators willing to enlarge their cultural and technical backgrounds concerning quantitative methods; and quantitative analysts actively working in traditional financial sectors curious to approach the fantastic world of power markets.

INTRODUCTION xiii Nevertheless, I strongly recommend the use of the book to all postgraduate students who are considering research in the energy finance sector. The contents of the book are essentially the fruits of my personal professional and academic experience, but I do not want to forget the contributions in terms of ideas and professional experiences that many people I have worked with or had the pleasure to meet in recent years have been able to transfer to me. STEFANO FIORENZANI