E N E R GY
RISK
Valuing and Managing
Energy Derivatives
S E C O N D E D I T I O N
DRAGANA PILIPOVIC
McGraw-Hill
New York C...
Copyright © 2007 by Dragana Pilipovic. All rights reserved. Manufactured in the United States of America. Except as permit...
We hope you enjoy this
McGraw-Hill eBook! If
you’d like more information about this book,
its author, or related books and...
C O N T E N T S
PREFACE xiii
ACKNOWLEDGMENTS xv
Chapter 1
Energy Markets: Trading, Modeling, and Hedging 1
1.1. Introducti...
iv Contents
2.7.1. The Convenience Yield 29
2.7.2. Seasonality 30
2.8. Regulation and Illiquidity 31
2.9. Decentralization...
Contents v
3.9.4. Drawbacks of Single-Factor Non-Mean-Reverting Models 69
3.9.5. Volatility and Correlation Market Discove...
vi Contents
5.5. Performing Distribution Analysis 119
5.5.1. Implementation of Distribution Analysis 119
5.5.2. Results of...
Contents vii
7.3. Fitting the Modeling Needs to Trading Needs 182
7.3.1. Case of Trading Exchange-Traded Products Only 182...
viii Contents
8.5. Market-Implied Volatilities 224
8.5.1. Option-Implied Volatilities 224
8.5.2. Implied Volatilities from...
Contents ix
9.7. Option Valuation Process: What Should It Be? 270
9.7.1. Defining Underlying Market Price Behavior 270
9.7...
x Contents
11.3. Monthly Settled Options 313
11.3.1. Cash-Settled: Look-Back Monthly Settled Average
Price Options 314
11....
Contents xi
12.6. Portfolio Sensitivity: The “Greeks” 385
12.6.1. Delta: Sensitivity to Price Change 385
12.6.2. Vega: Sen...
xii Contents
14.3. Risk-Management Goals and Strategies 430
14.3.1. Speculation 431
14.3.2. Arbitrage 432
14.3.3. Market M...
P R E F A C E
Over the many years I have gained experiences in a wide variety of
derivative markets: from equities and int...
xiv Preface
during its dawn of deregulation and again in 1995 when I began mod-
eling electricity: they need practical ans...
A C K N O W L E D G M E N T S
I would like to thank many people for their help with this book. First
I want to thank John ...
xvi Acknowledgments
Dylan for his most recent work: Modern Times was my constant
companion during the writing of this seco...
C H A P T E R 1
Energy Markets: Trading,
Modeling, and Hedging
Reality is what we take to be true. What we take to be true...
2 Energy Risk
As Brian Hunter, the former trader at Amaranth Advisors, has been
quoted to say,
Every time you think you kn...
Energy Markets: Trading, Modeling, and Hedging 3
winter can result in sky-rocketing prices, sometimes to magnitudes
that a...
4 Energy Risk
danger of relying on reserve margins that are sufficient for average but
not necessarily above-average condi...
Energy Markets: Trading, Modeling, and Hedging 5
speculative trading in energy markets, the company must have pockets
deep...
6 Energy Risk
After the fact it is usually easy to understand why a company
might have lost huge amounts of money. Althoug...
Energy Markets: Trading, Modeling, and Hedging 7
The volatilities seen in California should not have been perceived as
bey...
8 Energy Risk
learning from mistakes other countries have made in the process of
deregulation. Still, it is no easy task:
...
Energy Markets: Trading, Modeling, and Hedging 9
cases, modeling begins with discerning between the important market
reali...
10 Energy Risk
the intellectual, and perhaps most importantly, the ignorance of both
“sides” regarding the value of knowle...
Energy Markets: Trading, Modeling, and Hedging 11
spark spreads, swing options and basis trades around these physical
play...
12 Energy Risk
Therefore, to think that a company is better off costwise to not put on
a hedge is to say (1) that the comp...
Energy Markets: Trading, Modeling, and Hedging 13
have had to respond to the changing market conditions through risk
manag...
14 Energy Risk
futures just began trading. Volatility for the longer-term futures was
comparable to the short-term futures...
Energy Markets: Trading, Modeling, and Hedging 15
the first edition was published there was not enough market
data to warr...
16 Energy Risk
15. “Structured Investment Vehicles: Trends, Truths and Myths of Complex Marketplace,”
Interview with Rober...
C H A P T E R 2
What Makes Energies
So Different?
America was changing. I had a feeling of destiny and I was riding the ch...
18 Energy Risk
Energy markets follow the same impulses: energy producers and
users alike wish to hedge their exposure to f...
What Makes Energies So Different? 19
2.2. WHAT MAKES ENERGIES SO DIFFERENT?
Energy markets are young maturing markets cont...
20 Energy Risk
fundamental differences between the energy and money markets.
Although these examples skim the surface and ...
What Makes Energies So Different? 21
Figures 2-1 and 2-2 show historical prices for Massachusetts Hub
power prices for bot...
22 Energy Risk
F I G U R E 2-2
Massachusetts Hub Off-Peak Power: Sample
Price History
F I G U R E 2-3
Massachusetts Hub Of...
What Makes Energies So Different? 23
Finally, Figure 2-4 shows the historical averages across the few
years of sample data...
24 Energy Risk
economic cycles, hence fundamental price drivers. The state of the econ-
omy as a fundamental driver can be...
What Makes Energies So Different? 25
F I G U R E 2-5
Natural Gas: Sample Price History
F I G U R E 2-6
Natural Gas: Sample...
26 Energy Risk
2.5. IMPACT OF SUPPLY DRIVERS
Energies function with supply drivers that do not exist in money mar-
kets: p...
What Makes Energies So Different? 27
F I G U R E 2-7
Massachusetts Hub On-Peak Power: Sample
Historical Volatility
F I G U...
2.7. IMPACT OF DEMAND DRIVERS
28 Energy Risk
2.6. ENERGIES HAVE A “SPLIT PERSONALITY”
F I G U R E 2-9
Massachusetts Hub Ho...
What Makes Energies So Different? 29
F I G U R E 2-10
NYMEX WTI Futures’ Prices 1992–1996
F I G U R E 2-11
NYMEX Natural G...
30 Energy Risk
price risk can be related to this function.) This urgency in maintaining
production gives the industrial us...
What Makes Energies So Different? 31
winter peaks—as clearly exhibited within the electricity forward price
curves—are a f...
32 Energy Risk
a Midwestern utility turn to hedge their price risk? If their risks are
localized, chances are that their h...
What Makes Energies So Different? 33
considered an “exotic” contract in mature money markets. Due largely
to the needs of ...
34 Energy Risk
4. Water reserves do represent a form of potential electricity storage for hydro plants;
several utilities ...
C H A P T E R 3
Modeling Principles and
Market Behavior
“Pooh’s found the North Pole,” said Christopher Robin. “Isn’t that...
36 Energy Risk
3.2. THE VALUE OF BENCHMARKS
Modeling is often left to itself in its struggle to arrive at pricing models
t...
Modeling Principles and Market Behavior 37
companies that have invested money in research development
and there is more th...
38 Energy Risk
3.3. THE IDEAL MODELING PROCESS
The recipe for efficient modeling as applied to a trading operation
include...
Modeling Principles and Market Behavior 39
forms the basis of quantitative analysis of option prices.2 One nice
feature of...
40 Energy Risk
Hence, the randomness that the stock prices exhibit is assumed to
always be of the same magnitude.
Although...
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  1. 1. E N E R GY RISK Valuing and Managing Energy Derivatives S E C O N D E D I T I O N DRAGANA PILIPOVIC McGraw-Hill New York Chicago San Francisco Lisbon London Madrid Mexico City Milan New Delhi San Juan Seoul Singapore Sydney Toronto
  2. 2. Copyright © 2007 by Dragana Pilipovic. All rights reserved. Manufactured in the United States of America. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written permission of the publisher. 0-07-159447-7 The material in this eBook also appears in the print version of this title: 0-07-148594-5. All trademarks are trademarks of their respective owners. Rather than put a trademark symbol after every occurrence of a trade- marked name, we use names in an editorial fashion only, and to the benefit of the trademark owner, with no intention of infringe- ment of the trademark. Where such designations appear in this book, they have been printed with initial caps. McGraw-Hill eBooks are available at special quantity discounts to use as premiums and sales promotions, or for use in corporate training programs. For more information, please contact George Hoare, Special Sales, at george_hoare@mcgraw-hill.com or (212) 904-4069. TERMS OF USE This is a copyrighted work and The McGraw-Hill Companies, Inc. (“McGraw-Hill”) and its licensors reserve all rights in and to the work. Use of this work is subject to these terms. Except as permitted under the Copyright Act of 1976 and the right to store and retrieve one copy of the work, you may not decompile, disassemble, reverse engineer, reproduce, modify, create derivative works based upon, transmit, distribute, disseminate, sell, publish or sublicense the work or any part of it without McGraw-Hill’s prior consent. You may use the work for your own noncommercial and personal use; any other use of the work is strictly prohibited. Your right to use the work may be terminated if you fail to comply with these terms. THE WORK IS PROVIDED “AS IS.” McGRAW-HILL AND ITS LICENSORS MAKE NO GUARANTEES OR WARRANTIES AS TO THE ACCURACY, ADEQUACY OR COMPLETENESS OF OR RESULTS TO BE OBTAINED FROM USING THE WORK, INCLUDING ANY INFORMATION THAT CAN BE ACCESSED THROUGH THE WORK VIA HYPERLINK OR OTHERWISE, AND EXPRESSLY DISCLAIM ANY WARRANTY, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMIT- ED TO IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. McGraw-Hill and its licensors do not warrant or guarantee that the functions contained in the work will meet your requirements or that its operation will be uninterrupted or error free. Neither McGraw-Hill nor its licensors shall be liable to you or anyone else for any inaccuracy, error or omission, regardless of cause, in the work or for any damages resulting therefrom. McGraw-Hill has no responsibility for the content of any information accessed through the work. Under no circumstances shall McGraw-Hill and/or its licensors be liable for any indirect, incidental, special, punitive, consequential or similar damages that result from the use of or inability to use the work, even if any of them has been advised of the possibility of such damages. This limitation of liability shall apply to any claim or cause whatsoever whether such claim or cause arises in contract, tort or --otherwise. DOI: 10.1036/0071485945
  3. 3. We hope you enjoy this McGraw-Hill eBook! If you’d like more information about this book, its author, or related books and websites, please click here. Professional Want to learn more?
  4. 4. C O N T E N T S PREFACE xiii ACKNOWLEDGMENTS xv Chapter 1 Energy Markets: Trading, Modeling, and Hedging 1 1.1. Introduction 1 1.2. Energy Trading 2 1.2.1. Understanding the Fundamentals 2 1.2.2. Liquidity, Volatility, and Intra-Market Correlations 4 1.2.3. Market Deregulation 6 1.3. Energy Modeling 8 1.3.1. Energies Are Still Unique 8 1.3.2. Model Complexity 8 1.3.3. Quants vs. Traders vs. Reality 9 1.4. Energy Hedging and Risk Management 10 1.4.1. Adding Financial Products to the Hedging Mix 10 1.4.2. Risk Management: A Profitable Business Function? 11 1.4.3. Hedging for the Little Guys 12 1.4.4. Assets as Hedges 12 1.4.5. Regulatory Response to “Bad” Stories 13 1.5. Conclusions 14 Chapter 2 What Makes Energies So Different? 17 2.1. Introduction 17 2.1.1. Quantitative and Fundamental Analysis 18 2.2. What Makes Energies So Different? 19 2.3. Energies Are Harder to Model 20 2.4. Market Response to Cycles and Events 23 2.5. Impact on Supply Drivers 26 2.6. Energies Have a “Split Personality” 28 2.7. Impact of Demand Drivers 28 iii For more information about this title, click here
  5. 5. iv Contents 2.7.1. The Convenience Yield 29 2.7.2. Seasonality 30 2.8. Regulation and Illiquidity 31 2.9. Decentralization of Markets and Expertise 31 2.10. Energies Require More Exotic Contracts 32 2.11. Conclusion 33 Chapter 3 Modeling Principles and Market Behavior 35 3.1. The Modeling Process 35 3.2. The Value of Benchmarks 36 3.2.1. Diffusing Personalized Attachments to Models 36 3.3. The Ideal Modeling Process 38 3.4. The Role of Assumptions: Market Before Theory 38 3.4.1. Typical Assumptions 39 3.4.2. Market Variable vs. Modeling Parameter 41 3.4.3. Testing Assumptions Through Benchmarks 42 3.4.4. Assumptions and Implementation 45 3.5. Contract Terms and Issues 45 3.5.1. Underlying Price or Market 45 3.5.2. Derivative Contract 46 3.5.3. Option Settlement Price 46 3.5.4. Delivery 46 3.5.5. Complexity of Contracts for Delivery 47 3.6. Modeling Terms and Issues 49 3.6.1. Price Returns 49 3.6.2. Elements of a Price Model 49 3.6.3. Convenience Yield 52 3.6.4. Cost of Risk 54 3.7. Quantitative Financial Models Across Markets 55 3.7.1. Lognormal Market 56 3.7.2. Mean-Reverting Market 60 3.8. The Taylor Series and Ito’s Lemma 63 3.8.1. The Taylor Series 63 3.8.2. Ito’s Lemma 64 3.9. Lessons from Money Markets 65 3.9.1. Modeling Price vs. Rate: Defining the Market Drivers 65 3.9.2. Yield vs. Forward Rate Curves 66 3.9.3. Drawbacks of Single-Factor Mean-Reverting Models 68
  6. 6. Contents v 3.9.4. Drawbacks of Single-Factor Non-Mean-Reverting Models 69 3.9.5. Volatility and Correlation Market Discovery 69 Chapter 4 Essential Statistical Tools 71 4.1. Introduction 71 4.2. Time Series and Distribution Analysis 72 4.2.1. Time Series Analysis 72 4.2.2. Distribution Analysis 75 4.3. Other Statistical Tests 81 4.3.1. The Q-Q Plot 81 4.3.2. The Autocorrelation Test 83 4.3.3. Measures of Fit 83 4.4. How Statistics Helps to Understand Reality 85 4.4.1. A Simple Case 85 4.4.2. The Difference Between Price and Return 86 4.4.3. Distinguishing Drift Terms 86 4.5. The Six-Step Model Selection Process 88 4.5.1. Step 1: An Informal Look 89 4.5.2. Step 2: A Shortlist of Possible Models 90 4.5.3. Step 3: Time Series Analysis 90 4.5.4. Step 4: From Underlying Price Models to Distributions 91 4.5.5. Step 5: Distribution Analysis 92 4.5.6. Step 6: Select the Most Appropriate Model 93 4.6. Relevance to Option Pricing 93 Chapter 5 Spot Price Behavior 95 5.1. Introduction 95 5.2. Looking at the Actual Market Data 96 5.3. A Shortlist of Possible Models 103 5.3.1. The Lognormal Price Model 103 5.3.2. Mean-Reverting Models 105 5.3.3. Cost-Based Models for Electric Utilities 111 5.3.4. Interest Rate Models 111 5.4. Calibrating Parameters Through Time Series Analysis 111 5.4.1. Incorporating Seasonality with Underlying Models 112 5.4.2. Results from Time Series Analysis 113
  7. 7. vi Contents 5.5. Performing Distribution Analysis 119 5.5.1. Implementation of Distribution Analysis 119 5.5.2. Results of Distribution Analysis 120 5.6. Analysis Summary 121 Chapter 6 The Forward Price Curve 127 6.1. Introduction 127 6.1.1. The Difference Between Forwards and Futures 128 6.2. Reading the Underlying Curve 129 6.3. Seasonality in the Forward Curve 132 6.4. Modeling Concepts Relating Spot, Forwards, and Seasonality 135 6.4.1. S&P 500 136 6.4.2. WTI Crude Oil 136 6.4.3. Seasonal Markets 137 6.5. Linking Spot Price Models to Forward Price Models 143 6.5.1. The Arbitrage-Free Condition 143 6.5.2. Capturing Market Characteristics Within the Model or During Implementation 145 6.5.3. Influence of the Convenience Yield 145 6.6. Modeling the Underlying Forward Price Curve 147 6.6.1. Difference Between Spot and Forward Prices 147 6.6.2. Going from Spot Price Models to Forward Price Models 150 6.6.3. The Risk-Free Portfolio 150 6.6.4. Effect of Dividends 153 6.6.5. Equivalence Between Dividends and the Convenience Yield 155 6.6.6. Adding a Second Factor 156 6.6.7. Seasonality 157 6.7. The Two-Factor Mean-Reverting Model (Pilipovic) 158 6.8. Testing the Spot Price Model on Forward Price Data 162 Chapter 7 Building Marked-to-Market Forward Price Curves: Implementing Forward Price Models 163 7.1. Introduction: What Is a Marked-to-Market Forward Price Curve? 164 7.2. Forward Price Contract Valuation 166 7.2.1. Simple Contract for One-Day Delivery 170 7.2.2. Contract for Delivery Over a Period 173 7.2.3. Bootstrapping and the Problem of Daily Price Discovery 179
  8. 8. Contents vii 7.3. Fitting the Modeling Needs to Trading Needs 182 7.3.1. Case of Trading Exchange-Traded Products Only 182 7.3.2. Case of Trading OTC 183 7.3.3. Case of Owning Power Production 184 7.4. Building Marked-to-Market Forward Price Curves: Issues to Consider 184 7.4.1. Quote Strips 184 7.4.2. Step-Function Treatment 187 7.4.3. Linear Interpolation 187 7.4.4. Applying Forward-Price Models Based on Spot-Price Analysis 188 7.4.5. Many Degrees of Freedom Within Implementation: Part Art, Part Science 189 7.4.6. From Events to Models 191 7.4.7. Parameter Calibration 192 7.5. Modeling Middle-Term Event Expectations 193 7.6. Modeling Forward Price Seasonality 195 7.6.1. Cosine Seasonality 196 7.6.2. Exponential Seasonality 197 7.6.3. Power-N Model—Flat Seasonality 201 7.6.4. Multiperiod Seasonality Treatment 201 7.7. Special Case of Basis Markets 205 7.8. Noise Versus Events 209 7.9. Markets with Little or No Market Discovery: Off-Peak and Hourly Forward Price Curves 211 7.10. Conclusion 212 Chapter 8 Volatilities 215 8.1. Introduction 215 8.2. Measuring Randomness 216 8.2.1. Standard Deviation and Variance 216 8.2.2. Volatility Defined 217 8.2.3. Comparing Variance and Volatility 218 8.2.4. Variance and Volatility in Spot Price Models 218 8.3. The Stochastic Term 220 8.3.1. Case of Constant Volatility 220 8.3.2. Case of Volatilities with Term Structure 221 8.4. Measuring Historical Volatilities 222 8.4.1. Simple Techniques 222 8.4.2. More Complex Techniques 223
  9. 9. viii Contents 8.5. Market-Implied Volatilities 224 8.5.1. Option-Implied Volatilities 224 8.5.2. Implied Volatilities from a Series of Options 225 8.5.3. Calibrating Caplet Volatility Term Structure 226 8.5.4. Implied Volatilities from Options on the Average of Price 230 8.5.5. The Volatility Smile 232 8.6. Model-Implied Volatilities 232 8.6.1. The Lognormal Model 233 8.6.2. The Log-of-Price Mean-Reverting Model 234 8.6.3. The Price Mean-Reverting Model 236 8.7. Building the Volatility Matrix 240 8.7.1. Introduction to the Forward Volatility Matrix 241 8.7.2. Discrete Volatilities 242 8.7.3. Tying In Caplet Volatilities 244 8.7.4. Two-Dimensional Approach to Volatility Term Structure 246 8.7.5. Tying In Historical Volatilities 249 8.7.6. Tying In Caplet and Swaption Prices 249 8.8. Implementing the Volatility Matrix 251 Chapter 9 Overview of Option Pricing for Energies 255 9.1. Introduction 255 9.2. Basic Concepts of Option Pricing 256 9.2.1. Parity Value 256 9.2.2. Settlement 258 9.3. Types of Options 258 9.3.1. European Options 259 9.3.2. American Options 259 9.3.3. Asian Options: Options on an Average of Price 259 9.3.4. Swing Options 260 9.4. Effect of Underlying Behavior 261 9.5. Option Pricing Implementation Techniques 263 9.5.1. Closed-Form Solutions 263 9.5.2. Simulations 265 9.5.3. Trees 266 9.5.4. Human Error in Implementation 267 9.6. Choosing the Right Option Pricing Model 267 9.6.1. Three Criteria for Evaluating Option Models 268 9.6.2. Investing in Pricing Model versus Implementation 269 9.6.3. A Model Is Only as Good as Its Implementation 270
  10. 10. Contents ix 9.7. Option Valuation Process: What Should It Be? 270 9.7.1. Defining Underlying Market Price Behavior 270 9.7.2. Testing Alternative Models 271 9.7.3. Selecting the Most Appropriate Option Model 272 9.8. Did That Option Make Money? 273 Chapter 10 Option Valuation 275 10.1. Introduction 275 10.2. Option Model Implementation 276 10.3. Closed-Form Solutions 276 10.3.1. Pros 276 10.3.2. Cons 277 10.3.3. The Black–Scholes Model 277 10.3.4. The Black Model 279 10.4. Approximations to Closed-Form Solutions 283 10.4.1. Pros 283 10.4.2. Cons 284 10.4.3. The Volatility Smile 284 10.4.4. The Edgeworth Series Expansion 285 10.4.5. Pulling It All Together 288 10.5. The Tree Approach 290 10.5.1. Pros 291 10.5.2. Cons 291 10.5.3. Binomial Trees 292 10.5.4. Trinomial Trees 292 10.5.5. Using a Tree to Value a European-Style Option 293 10.5.6. Using a Tree to Value an American-Style Option 295 10.5.7. Energy-Specific American-Style Options 295 10.6. Monte Carlo Simulations 300 10.7. Conclusions 302 Chapter 11 Valuing Energy Options 303 11.1. Introduction 303 11.2. Daily Settled Options 304 11.2.1. Extending Daily Methodology to Hourly Settled Options 312
  11. 11. x Contents 11.3. Monthly Settled Options 313 11.3.1. Cash-Settled: Look-Back Monthly Settled Average Price Options 314 11.3.2. Monthly-Settled (Look-Forward) Options on Monthly Forwards 317 11.3.3. Incorporating Price Mean Reversion (PMR) into Monthly Settled Options 326 11.3.4. Extending Monthly Methodology to Calendar Year Options 332 11.4. Optionality in Cheapest-to-Deliver Forward Prices 333 11.5. Types of Energy Swing Options 334 11.6. Demand Swing Contracts 336 11.6.1. Demand Swing Options 336 11.6.2. Demand Swing Forwards 339 11.6.3. Load Behavior 340 11.7. Price Swing Contracts 345 11.7.1. Multiple-Peaker Swing Options 346 11.7.2. Forward Starting Swing 358 11.7.3. Natural Gas Storage 360 11.8. Spread Options 361 11.8.1. Various Approximations to Spread Option Valuation 362 11.8.2. The Tree Approach 370 11.8.3. Crack Spread, Spark Spread, and Basis Spread Options 372 11.8.4. Valuing Power Plants and Transmission Lines 372 11.9. Conclusion 373 Chapter 12 Measuring Risk 375 12.1. Introduction 375 12.2. The Risk/Return Framework 375 12.3. Types of Risk 377 12.3.1. Market Risk 378 12.3.2. Commodity Risk 378 12.3.3. Human Error 378 12.3.4. Model Risk 379 12.4. Definition of a Portfolio 380 12.4.1. Change in Portfolio Value 381 12.4.2. Time Buckets 381 12.5. Measuring Changes in Portfolio Value 383 12.5.1. Taylor Series 383
  12. 12. Contents xi 12.6. Portfolio Sensitivity: The “Greeks” 385 12.6.1. Delta: Sensitivity to Price Change 385 12.6.2. Vega: Sensitivity to Volatility Change 386 12.6.3. Theta: Sensitivity to Time 388 12.6.4. Rho: Sensitivity to Discounting Rates 391 12.6.5. Gamma: Sensitivity to Changes in Delta 391 12.6.6. Quantity-Specific Risks 394 12.6.7. Sensitivity to Correlation Change 394 12.7. Hedging 395 12.8. Marking-to-Market 396 12.8.1. Information for Marking-to-Market 396 12.8.2. Mark-to-Market Valuation 397 12.8.3. Testing the Mark-to-Market Process 398 Chapter 13 Portfolio Analysis 401 13.1. Introduction 401 13.2. Applications of Portfolio Analysis 402 13.3. Analyzing the Change in Portfolio Value 402 13.4. The Minimum-Variance Method 404 13.4.1. The Hedged Portfolio 405 13.4.2. Per-Deal Hedges 406 13.4.3. Portfolio with Options 410 13.4.4. Lessons from Inadequate Hedging Policies 411 13.5. The Generalized Minimum-Variance Model 417 13.6. Correlations 417 13.7. Value-at-Risk (VAR) Analysis 418 13.7.1. Fixed-Scenario Stress Simulations 420 13.7.2. Monte Carlo Simulations 420 13.7.3. Estimated Variance–Covariance Method 422 13.7.4. Historical “Simulations” 422 13.8. The Special Case of Electricity 423 13.9. The Corporate Utility Function 424 Chapter 14 Risk Management Policies 427 14.1. Introduction 427 14.2. The Case for a Risk-Management Policy 428 14.2.1. Horror Stories 429
  13. 13. xii Contents 14.3. Risk-Management Goals and Strategies 430 14.3.1. Speculation 431 14.3.2. Arbitrage 432 14.3.3. Market Maker 433 14.3.4. Treasury 434 14.3.5. Mixed Strategies 434 14.4. Initial Evaluation Checklist 435 14.4.1. Diagnosing and Selecting Trading Strategies 437 14.4.2. Gaps Between Existing and Desired Market Position 438 14.4.3. Corporate Culture 438 14.5. The “Front/Middle/Back Office” Paradigm 439 14.5.1. Conflicts Between Offices 440 14.5.2. Interoffice Committees 441 14.6. The Energy Team 441 14.6.1. Appropriate Knowledge by Organizational Level and Functions 444 14.6.2. Management Issues 445 14.6.3. Common Management Misconceptions 450 14.7. Implementation of Risk-Management Policies 453 Appendix A: Mathematical and Statistical Notes 455 Appendix B: Models from Interest Rate and Bond Markets 463 Appendix C: Analysis of Markets Published in the First Edition of Energy Risk 467 Glossary of Energy Risk Management Terms 485 Select Bibliography 499 INDEX 503
  14. 14. P R E F A C E Over the many years I have gained experiences in a wide variety of derivative markets: from equities and interest rates to natural gas and electricity. With every new market, I discovered further proof of some- thing that I had only sensed at the very first: markets differ significantly from each other through differences in the types of fundamental price drivers and how they impact the market prices. Each market follows its own unique price behavior: a summer event in the electricity markets is caused by an unexpected tempera- ture spike that typically keeps the prices up for a week or so; a stock price jumps up on news of a take-over and remains at the newly reached levels unless there is further news that the take-over failed. Then why, I ask you, do the pricing experts insist on using the same set of models in markets that are so very different? This question inspired this book. My motivation is to explain why energy markets are so different from the more traditional derivatives markets. My objective is to provide tools capable of handling these differences. Energy risk managers, particularly in the still young power markets, need a comprehensive guide. This book is a practitioner’s book, not an academic one. Energy Risk: Valuing and Managing Energy Derivatives is the product of my years of being a “rocket scientist”—an ex-physicist working in finan- cial markets. I faced all the questions in this book first hand, “on the trading desk” as a quantitative analyst, trader, and consultant. The problems always resembled a double-headed guard dog: first I had to determine a good analytical answer, then I faced the problem of imple- mentation. I approached the problems by establishing benchmarks, setting standards of acceptability, and at the end of the day settled for ideas and technology that got the job done. With the amazing growth of today’s energy markets, particularly in electricity and power, I suspect there are many professionals who now find themselves in a position similar to mine in 1989 when I began trading, natural gas xiii Copyright © 2007 by Dragana Pilipovic. Click here for terms of use.
  15. 15. xiv Preface during its dawn of deregulation and again in 1995 when I began mod- eling electricity: they need practical answers to derivatives and risk management issues. This book is intended as a single-source, desk-top manual for getting reasonable answers to actual modeling and implementation problems surfacing in today’s energy markets. Dragana Pilipovi´c
  16. 16. A C K N O W L E D G M E N T S I would like to thank many people for their help with this book. First I want to thank John Wengler, Chief Risk Officer of Entergy Services, Inc., who first conceived of this book and then spent many sleepless nights helping me write and edit the first edition. He was also critical in the editing of this new edition, providing many ideas and helpful comments. Thank you, John! I want to thank many professionals in chronological order for their help in developing the concepts and materials for this book: Harvard University’s Deborah Hughes-Hallet for giving me my first job, teach- ing a course for people scared of math at the college and the wonderful cast of characters attending the Kennedy School of Government sum- mer program; Brown University’s graduate school of physics Professor Augustine Falieros for the joy of applied mathematics and Professor Dave Cutts for giving me the chance to move to Chicago’s Fermilab and understanding why I had to leave physics; Mike Parkinson of the former O’Connor & Associates for giving me my first job in finance and David Weinberger for supporting my research style; Continental Bank’s Ken Cunningham and Philippe Comer for allowing me to form my ideas freely; Linda Rudnick of Harris Bank for providing a safe haven and one of my first consulting contracts; Kay Rigney of the First National Bank of Chicago’s women’s banking unit for invaluable support and advice; Southern Energy Marketing’s Sean Murphy and Jeff Roark for inviting me into the world of electricity; Cinergy Corporation’s Ken Leong and Paul Zhang for helping market-test my theories; the partic- ipants in the Chicago, Houston and Aspen seminars that served as the basis for this book; the forward-thinking professionals at Dayton Power & Light, Sonat Marketing and NESI Power Marketing for their special participation in the seminars; Stephen Isaacs of McGraw-Hill for agreeing that the market needed a book like this; Adrian D’Silva of the Federal Reserve Bank of Chicago and his bookshelf; Professor John Bilson of the Illinois Institute of Technology’s Master’s in Financial Markets and Trading for providing a teaching podium; and, last but not least, Rick Dennis of Southern Corp. for suggestions and challenging requests within risk management implementation. Also, thanks to Bob xv Copyright © 2007 by Dragana Pilipovic. Click here for terms of use.
  17. 17. xvi Acknowledgments Dylan for his most recent work: Modern Times was my constant companion during the writing of this second edition. A special thanks goes to Entergy Services, Inc., and Francis H. Wang, the Director of Commercial Analytics, for providing invaluable market data for this new edition. Many additional thanks to Francis for also contributing the discussion on Locational Marginal Pricing in Chapter 5. Finally, I would like to thank my family: my children, Sasha and Nevena, for being the wonderful, loving, and positive creatures that they are: your athletic prowess is an incredible motivation in every- thing I do! My parents, Vera and Nikola, for their labors of love. And my husband, John, for always believing in me.
  18. 18. C H A P T E R 1 Energy Markets: Trading, Modeling, and Hedging Reality is what we take to be true. What we take to be true is what we believe. What we believe is based upon our perceptions. What we perceive depends upon what we look for. What we look for depends upon what we think. What we think depends upon what we perceive. What we perceive determines what we believe. What we believe determines what we take to be true. What we take to be true is our reality . . . Gary Zukav, The Dancing Wu Li Masters1 1 1.1. INTRODUCTION . . . until it starts hurting. As a little girl perhaps I did not know very much about the world at large, but I knew that I did not like going to the dentist. One of my teeth started hurting. I did not like it, I did not enjoy it, but I was going to stand it for as long as I could. I was going to pretend that it was not happening, assume everything was fine—just to avoid the dreaded dentist. In the end, the tooth caught up with me. Once the pain got so bad that I could no longer run out to play, I had to tell my mother. Sure enough, the visit to the dentist was not a pleasant one; the baby tooth was at this point so far gone that it could not be saved, and had to be pulled. The moral of the story is not that you should go to the dentist (although you should!), but rather, that the truth will catch up to you, sooner or later, like it or not. As much as we all have our own realities, our own ways of looking and experiencing the world around us, there are sometimes moments of truth forced upon us. This is a good thing—it is a chance for recalibration of reality, a chance for new growth and new paradigms of thought and experience, much as the process might hurt. In the energy markets there have been many painful lessons since I wrote the first edition of this book in 1997, with some serious moments of truth forced upon us, and there are probably many more awaiting us. But that is what makes the energy business so interesting. Copyright © 2007 by Dragana Pilipovic. Click here for terms of use.
  19. 19. 2 Energy Risk As Brian Hunter, the former trader at Amaranth Advisors, has been quoted to say, Every time you think you know what these markets can do, something else happens.2 With this second edition, we continue exploring energy markets and solutions to valuing energy derivatives and their potential risks. In addition to an all new introduction, there are two new much needed chapters covering forward price curve building and option valuation, plus expanded derivations, explanations, and updates to the original chapters. Many readers over the years had comments and requests for more detailed explanations and I have tried to include these as much as possible. Before we get to the math, let us take some time for a high- level look at some of the major events through which we have learned and re-learned important risk management lessons during the decade since Energy Risk was first published. 1.2. ENERGY TRADING 1.2.1. Understanding the Fundamentals Energy markets continue to grow and develop as a function of funda- mentals. Perhaps some early players underestimated the impact of fun- damentals, but by now most energy participants understand first hand just how volatile and eventful these markets can be. The BP Statistical Review of World Energy recap of 2005 energy markets ticks off the kind of fundamentals that continue to drive the market: 2005 was a third consecutive year of rising energy prices. Tight capacity, extreme weather, continued conflict in the Middle East, civil strife elsewhere and growing interest in energy among financial investors led to rising prices ... World primary energy consumption in 2005 increased by 2.7% ... World natural gas consumption grew by 2.3% ... Coal was again the world’s fastest-growing fuel, with global consumption rising by 5% ...3 Weather is one of the main fundamental price drivers in the energy markets. A heat wave in the summer or a cold spell in the
  20. 20. Energy Markets: Trading, Modeling, and Hedging 3 winter can result in sky-rocketing prices, sometimes to magnitudes that are hard to believe. However, even on a day-to-day basis, weather is a dominant player in the market place that has everyone’s attention, as evidenced by the following dispatch in a daily newsletter: In the Midcontinent, the National Weather Service issued a heat advisory for the Oklahoma City area until Thursday evening, with heat indices expected to approach 110 degrees through the end of the week. The oppressive heat continued to test local power generators as they pulled gas supplies from storage and from Western production basins. Natural Gas Pipeline Co. of America’s Midcontinent zone shot up nearly 60 cents, while Natural’s Texok zone added about 50 cents and CenterPoint’s East zone gained more than 45 cents.4 Weather events in the energy markets can easily go both ways. After a price spike due to a large weather event, such as that experi- enced in the south U.S. markets due to Hurricane Katrina, the market participants become quite weary of the possibility of another such event, particularly given the reality of hurricane seasons and expected long-term hurricane weather patterns. The following magazine excerpt captures how past pain can infuse future expectations: The catastrophic damage to Gulf of Mexico oil facilities wrought by Hurricane Katrina last year leaves the industry extremely jittery as the start of the 2006 hurricane season approaches. So far, most weather predictions do not bode well ... Worryingly, it is also evident that any new storms are likely to have a bigger impact than in 2005, because the region’s infrastructure is only just recovering from last year.5 These fears were justified during the spring and summer of 2006, despite the fact that prices had been dropping since their post-Katrina highs. But then no serious storms hit the United States, despite the conditions being ripe for a repeat of 2005. In a market with such an event expectation looming large over all the market participants, for the hurricane season to not realize itself is also a huge event, sending prices tumbling down. Although the market participants have to worry about short-term events, trading, and hedging, the long-term market outlook can be just as complex: Consulting company Weed Mackenzie concluded that there is a serious risk of power shortages and extreme price volatility if electricity demand growth is higher than expected during the next five or six years. The record demand peaks of the summer 2006 highlight the
  21. 21. 4 Energy Risk danger of relying on reserve margins that are sufficient for average but not necessarily above-average conditions, according to the company’s report, “A Crisis in the Making?”6 It goes without saying, because we cannot expect the weather to stabilize anytime soon, the need for proper volatility analysis and risk management will continue for years to come! 1.2.2. Liquidity, Volatility, and Intra-Market Correlations As a trader in any market will tell you, liquidity issues are a part of a traders’ life. When events hit, even the best-covered markets experi- ence illiquidity, as summarized by a risk manager with a hedge fund: One can never guarantee liquidity in the markets. When events happen, bid–offer spreads widen, volume might decrease. That is just the nature of trading.7 In energy markets, the frequency and magnitude of events can be captured by the high volatility. To make things more complicated, the forward price curves remain imperfectly correlated as the short- and long-term portions of the energy forward price curves tend to be driven by different market factors with usually very little or no relationship.The eventful nature of energy markets, coupled with physical limitations in responding to events, and with relatively limited market participation, can result in what is beginning to appear as a never ending sequence of horror stories for the even highly knowledgeable traders: MotherRock, an energy trading hedge fund led by former Nymex President J. Robert “Bo” Collins, is imploding ... MotherRock’s troubles stemmed from a series of bad bets on natural gas prices made with leverage, or borrowed money, sources say. Natural gas prices have been volatile in recent months ... In a May investor update, MotherRock the hedge fund’s “natural gas book was hurt primarily by a loss on volatility spread trading.”8 Understanding the appropriate trading strategy for both the mar- ket conditions and the company’s depth of pocket and corporate culture is key to avoiding a market-driven tragedy. When participating in
  22. 22. Energy Markets: Trading, Modeling, and Hedging 5 speculative trading in energy markets, the company must have pockets deep enough to cover the types of risk levels the management approves for the traders. In the case of speculative position taking, given excellent traders, a company should expect to see both high profits as well as occasional large losses—this is simply the reality of speculative position taking. One would have thought that investors would eventually take to heart the caveat that appears in most prospectuses: “past results do not guarantee future results,” especially when the promise of success is linked with an individual superstar. The story of Long-Term Capital Management (LTCM), with its array of luminaries, should have proven that hiring the smartest folks does not necessarily guarantee that gambles will always win. And yet, as the Wall Street Journal reported in 2006, we witnessed the same sad story repeated again: ... Mr. Hunter headed the energy desk for a Connecticut hedge fund called Amaranth Advisors. At the end of August, trading natural gas, he was up roughly $2 billion for the year. Then he lost approximately $5 billion—in about a week. ... “The cycles that play out in the oil market can take several years, whereas in natural gas, cycles take several months,” Mr. Hunter said in an interview late in July, when his returns were looking rosy ...9 By all accounts, it appears that Mr. Hunter speculated on the spread between certain months of natural gas delivery. Perhaps this was pre- sented to management and/or investors as an arbitrage strategy based on the idea that positions can be taken to take advantage of market mispricing in such a manner that risks are ideally neutralized but usually minimized. One of the areas in energy trading that require quite a bit of thought both in terms of valuation and hedging are the intra-market correlations: the correlations between forward prices in the same market place but covering different periods of delivery. In these murky correlation waters it is easy to disguise speculation under arbitrage, resulting in potentially miscalculating the market risks and therefore not matching the actual market risks to the depth of the company’s pockets. As the Wall Street Journal noted: Mr. Hunter’s bets ultimately went bad because he misjudged the movement of the difference between prices for different month contracts, known as the spread.10
  23. 23. 6 Energy Risk After the fact it is usually easy to understand why a company might have lost huge amounts of money. Although misjudging the intra-market correlations between the natural gas futures can result in a tragic loss, it is also important to remember that getting these correlations right can earn loads of money as well. However, very rarely do the investors ask for a review of trading strategies when a company makes lots of money: LTCM experienced huge losses on stable correlations that suddenly changed. As in the case of LTCM, and probably Amaranth, when a company makes lots of money, usually the investors indirectly encourage it to invest even more into the strategy. Ultimately, this can be a bad strategy, not because of the strategy itself, but because at some point the company’s pockets may not be able to sustain the magni- tudes of risks taken. 1.2.3. Market Deregulation It would not be a “decade in review” chapter without revisiting California. One obvious mistake of the California legislators was assuming that they were in a closed system comparable to that of an island, for example, England, a framework that—by the way— the California utilities strongly supported. PG&E valued their plants under the assumption of a closed market. Despite other experts’ voices, cobwebbed within their wishful thinking about the future, and spurred on by the lack of both research and understanding regarding the rest of the U.S. power markets at the time, both the California legislators and the California utilities decided to utterly ignore the existing nature of power markets in the rest of the United States and instead to bury their heads in the sand and pretend that they were just like England. John Wengler summarized the situation at the time: The California experiment with deregulation made two fatal errors early on. First, they looked to England rather than Ohio for inspiration. Prior to liberalization, the British market was far more centralized than California—their solutions simply could not fit our problems ... California’s other mistake involved promising lower prices rather than price transparency ...11
  24. 24. Energy Markets: Trading, Modeling, and Hedging 7 The volatilities seen in California should not have been perceived as beyond the possible by any of the California utilities prior to deregula- tion—but in fact, that is exactly what they were. It is funny that the California utilities and the legislators engaged in a legal battle over whose fault it was in the end, when the truth is that both were equally ignorant and irresponsible. Perhaps PG&E did perform mark to market valuations of their plants prior to selling them—perhaps the problem is that they marked to the wrong market! While certainly one could easily argue that the California utilities should not have been forced to sell their plants in order to encourage market competition, it is also true that California utilities did not perform a proper valuation of their plants taking into account the power market price behavior already observed in other parts of the country, and all the potential market states post-deregulation. The local paper summed it up as follows: “There are a lot of smart people at PG&E, but they aren’t exactly creative,” said Harry Snyder, a lawyer for Consumers Union in San Francisco. “So Duke Power, Enron and the other independents came in and ate PG&E’s lunch.” “Those companies paid three times the book value for those PG&E generating plants and PG&E thought they were taking these guys,” he said. “In fact, those independents knew the value of those generating plants, and PG&E sold off way too many of them, so they couldn’t govern their own destiny.”12 You would think that PG&E would have thought twice about why it is that independents were coming in and offering them three times the book value for their plants. PG&E could not possibly have under- stood the possible energy prices to be seen soon after in California with- out understanding energy market price behavior outside their own region, just over the Rocky Mountains. Apparently they did not under- stand price volatility (hence how could they possibly value their assets correctly?) and so—perhaps—it is no surprise that they did not even understand demand volatility. Good intentions, unfortunately, are not enough. Risk management requires both accepting and understanding market price behavior. Sometimes it is good to be the first, but quite often it is much better to be the second, or third, or fourth . . . Eastern European and Asian markets are opening up to power trading, and have the benefit of
  25. 25. 8 Energy Risk learning from mistakes other countries have made in the process of deregulation. Still, it is no easy task: The fledgling electricity markets of central eastern Europe have developed rapidly since liberalization spread to the region at the start of the decade. Some of the incumbent state-run utilities developed sophisticated trading teams from scratch in a remarkably short period of time, and the area has attracted investment from large western European utilities as well ... The greatest frustrations surround cross-border trading, the lack of transparency around transmission system operators (TSOs), and a prevalence of long-term contracts.13 1.3. ENERGY MODELING 1.3.1. Energies Are Still Unique The “old days” of energy markets saw quite a few agnostics regarding price mean reversion and multifactor energy price modeling. It appears that, over time, the market has more or less accepted the notion that energy markets are indeed different from the financial markets (i.e., interest rate, FX, and stock markets) in some fundamental ways, that indeed the energy markets appear to be driven by more than a single factor (such as spot), and that there is such a thing as mean reversion present in the energy price behavior: Unlike the financial markets, where current and future prices are linked, it is not possible to determine forward electricity prices from present ones. It is also not safe to assume a relationship between forward prices at two adjacent dates, or to rely on price changes between those dates occurring in a predictable manner. To make matters more complex, pricing methods used in the finan- cial markets often break down when applied to the electricity markets ... ... Pricing methods must take into account factors such as the mean- reversion behavior of electricity prices, price spikes, and non-constant volatility. Modeling future prices via stochastic processes represents one way of including these factors in calculation.14 1.3.2. Model Complexity All markets can be quite complex, and even the simpler markets can have extremely complex option valuation problems to solve. In all these
  26. 26. Energy Markets: Trading, Modeling, and Hedging 9 cases, modeling begins with discerning between the important market realities and those that can be assumed away or perhaps handled within the model implementation stage. The process of understanding the market realities and simplifying them in order to come up with models that can be feasibly implemented on a trading floor for a value- added use by traders becomes all the more important the more complex the market behavior. Energy markets perhaps offer the biggest chal- lenge of all. This is perhaps one reason why simulations are so popular in energy markets. Experts today clearly appreciate elegant simplicity, as demonstrated in the following statement by Robert Bothwell in a GARP magazine interview: Lacking intuitive understanding of which aspects of a problem are important and which may be safely ignored, modelers often err on the side of caution and build excessively complex models.15 Another expert, in the same interview, summarizes how simulations and other complex methodologies incorporating numerous degrees of freedom have their limitations: ... there comes a point when additional complexity begins to reduce rather than enhance a model’s utility. More complex models are slow, and this makes them less useful for real-time decision making. Complexity also increases the risk that the model contains errors. Finally, and most importantly, complexity makes it more difficult to understand why the model produces the results that it does. In other words, it contributes to the black-box syndrome.16 Where does that leave us, because energy markets are unquestion- ably complex and we will always need complex models? Ultimately, there is no way of getting around the basic problem of understanding which market drivers are the most important and should be included within the modeling process and which can be treated within the imple- mentation stage. Also, once the models are built, we need to make sure that they appeal to both the intuition of the traders, the intellect of the quants, and the proof-hungry skepticisms of true engineers. 1.3.3. Quants vs. Traders vs. Reality The walls dividing quants and traders are often quite thick. The differ- ent “languages,” the spectrum of response spanning the instinctive and
  27. 27. 10 Energy Risk the intellectual, and perhaps most importantly, the ignorance of both “sides” regarding the value of knowledge on the other side of this wall contribute to building these walls quite thick. The paradox of the situ- ation is that the higher the market complexity, the more transparent these walls must be in order to most realistically model the market. In an article entitled “Quant doublespeak,” Neil Palmer put it this way: If you are on the lookout for obscure and perverse language, then look no further than the theory of option pricing. Not even George Orwell could have devised a more intimidating form of doublespeak. It’s ironic that the principle underlying this terrifying subject—first articulated by Black, Scholes & Merton—is beautifully simple ... This language has come from finance, and now we’re using it in energy. If you think in terms of a nice easy slogan like “risk-neutral expectation,” then you might just be forgetting about what really lies behind it. In fact, there are some extremely strong assumptions behind the idea of pricing via this method. Continuous trading with no costs is a key requirement. There are many energy markets where this is a remote dream. ... If you can’t directly compete for attention with the hotshot traders, maybe it pays to be just a little mysterious.17 1.4. ENERGY HEDGING AND RISK MANAGEMENT 1.4.1. Adding Financial Products to the Hedging Mix The decade of energy trading has seen continued use of physical stor- age as a means of hedging energy exposure, but also an increase in both the availability and use of cash-settled products: ... Because of high natural gas prices, the summer–winter spread— injecting natural gas into storage when prices are low and withdrawing in winter when prices are high—is not profitable, [Glen] Sudler says ... With natural gas prices forecasted to remain high, more utilities are buying their own storage facilities, enabling them to swing in and out to meet load demands as needed. The financial markets, says [Keith] Kelly, offer an alternative to physical storage capacity to hedge natural gas prices. Signing long-term contracts and buying storage assets are still mainstays. But the market has more actively traded storage spreads,
  28. 28. Energy Markets: Trading, Modeling, and Hedging 11 spark spreads, swing options and basis trades around these physical plays. On the gas side, American Gas Association (AGA) reports local gas distribution companies use financial derivatives to hedge 70% of their physical portfolio, up from 55% just two years ago [2002].18 1.4.2. Risk Management: A Profitable Business Function? Risk management should be just risk management. To expect risk man- agement to be a profit function is to disguise other trading strategies under the guise of risk management. This should be a very scary prac- tice for any company. And yet, the idea of risk management adding value outside of reducing risk keeps popping up in the market place every now and then: Utilities and regulators often disagree over the purpose of energy price risk management ... should utility hedging simply smooth out rates for consumers or actively reduce them?19 The risk management experts, however, know better: “The suggestion that utilities should try to beat the market is just plain wrong,” says a risk manager at another Canadian utility who asked not to be named. “It goes against the purpose of risk management.”20 There is also often a notion of putting a hedge at a right or wrong time encouraging the idea of risk management for profit, resulting in regulators encouraging position taking based on market timing: But a regulator has to monitor hedging programmes continuously to ensure they make sense with regard to costs and rates, says Gerry Gaudreau, secretary to the MPUB (Manitoba Public Utility Board). Moreover, if a utility uses a mechanistic hedging programme at times of unusually high gas prices—such as now—it may be locking in prices that are too high. As a result, the company should use its discretion, he says: a large utility that delivers a lot of gas to its customers should be able to take a relatively educated price view.21 Although it certainly is true that there are times when the hedges are less expensive than other times, it should also be true that the mar- ket is pricing all the real market costs in its hedges and who can say that high prices cannot go even higher (or low prices go even lower)?
  29. 29. 12 Energy Risk Therefore, to think that a company is better off costwise to not put on a hedge is to say (1) that the company knows better than the market, and (2) that the company would rather take the “price” of market risk than the price of the hedge. In the case of the first point, if every com- pany knew better than the market, then the market as a whole would converge towards this greater knowledge (making it ultimately impos- sible for any particular company to know better than the market). The second point is based on whether or not the company has based this fact on the cost analysis of risk or pure conjecture. There is no question that there is such a thing as good hedging vs. bad hedging (as is discussed in Chapter 13 on issues of correlations and proper hedges), it is also true that certain companies do not possess core competencies for speculation. You would be asking for big trouble by asking a utility or a non-trading corporate function that aims at reducing risk to take on speculative views on the market! 1.4.3. Hedging for the Little Guys Even the little guys are becoming a part of the traded energy markets. Innovations in price hedging are beginning to reach all the way to the small individual users: Gasoline retailers are exploring ways of enabling customers to personally manage their gasoline price risk, through prepaid cards and price caps. From October this year, Gulf Oil will allow consumers to buy prepaid cards for a fixed amount of gasoline at a prevailing market price—so if the price dips to $2, for example, customers can go online and buy 200 gallons for $200, to be delivered at any time from any Gulf gas station. The firm will also allow holders of its branded credit cards cap their gas prices on any gas purchases made with the credit card, in exchange for a nominal per-gallon fee. Gulf Oil will track what prices its customers are locking in, and then hedge this exposure in the futures market.22 1.4.4. Assets as Hedges Although physical assets have always been the necessary and therefore natural hedge for the energy service providers, the energy houses
  30. 30. Energy Markets: Trading, Modeling, and Hedging 13 have had to respond to the changing market conditions through risk management via their asset base: Following the demise of Enron, companies that retreated from trading to more asset-based activities, such as generation, are now faced with different market circumstances than a few year ago, when fuel and electricity markets were less volatile. The withdrawal of many companies from trading, combined with considerable M&A activity, has created a shortage of liquidity in many markets. This, in turn, has been partly responsible for increased prices and volatility, and the inability to manage risk through the markets. Some retail suppliers of energy responded several years ago by vertical integration into upstream generation or production activities, which may offset supply risk to some degree but increases the challenge of portfolio management.23 Of course, the financial trading houses conveniently had the capital to buy some distressed generation assets following the post-Enron era. (It reminded me of the movie “It’s a Wonderful Life” when Mr. Potter went about buying bank shares during a panic.) There’s even talk about the financial houses owning their own nuclear power plants. This evolution makes sense because the volatility of power markets carries so much risk that deep pockets and generation may be necessary to stabilize portfolios through the highs and lows. 1.4.5. Regulatory Response to “Bad” Stories Huge profits do not occur without huge risks—you can never make as much money in arbitrage as you can in pure bets—but if you know what you are doing, you are taking very little risk of the downside. When companies report large losses, it catches the eye of politicians and they often have an instinctive rather than educated response. The Wall Street Journal reported in 2006: Congress, meanwhile, is jumping in to debate whether hedge funds are to blame for all the volatility.24 Illiquidity contributes to volatility . . . just take a look at the longer- term natural gas futures prices on NYMEX in the late 1980s when the
  31. 31. 14 Energy Risk futures just began trading. Volatility for the longer-term futures was comparable to the short-term futures contracts, in the 60–70% range! Perhaps this is nothing impressive right now, but back then this was a huge volatility driven directly by illiquidity. As soon as the market saw more participants, the volatility of these longer-term natural gas futures dropped down to the 15% range, where, in fact, it remained for quite a few years. The bottom line is, illiquidity adds volatility, not due to the actual price behavior, or market fundamentals, but due to the lack of price discovery (or rather, counterparty discovery). More participants means more liquidity, means less volatility due to price discovery. Energy markets have enough volatility to go around without issues of illiquidity, thank you very much! For Congress to now jump on hedge funds for helping markets reduce illiquidity (for their own gain, of course) is absolutely the wrong response. 1.5. CONCLUSIONS I wrote the first edition of Energy Risk because my publisher agreed that the fledgling energy market needed its own guidebook. Now that we are ten years down the path, we agree that the guidebook is still needed but with the requisite updates. The balance of this book explores the specifics of modeling and managing the complex task of quantitative and fundamental analysis of the energy derivatives and risk management market. We will follow a progressive path. ● Chapter 2 introduces the fundamental supply and demand market drivers. ● Chapters 3 and 4 cover the type of modeling principles and skills demanded by the complexities of the energy markets. ● Chapters 5 and 6 describe how to model the underlying price behavior of the spot and forward price markets. The behavioral characteristics of these markets act both as an end to them- selves and as valuable inputs for the quantitative analysis cov- ered in the remaining chapters. These chapters were exten- sively expanded to include some new ideas, such as on distribu- tion analysis, and updated with new market data. ● Chapter 7 is an entirely new chapter. It goes into the details of building marked-to-market forward price curves. At the time
  32. 32. Energy Markets: Trading, Modeling, and Hedging 15 the first edition was published there was not enough market data to warrant such a chapter, but now it is much needed. ● Chapter 8 explains volatility and introduces a comprehensive method for its modeling. ● Chapters 9 and 10 cover energy option pricing modeling and implementation. ● Chapter 11 is another new chapter discussing the many differ- ent types of energy options. Since the publishing of the first edi- tion of this book, traded energy options markets were still in their infancy in comparison to today. ● Finally Chapters 12, 13, and 14 pull together the fundamental and quantitative analysis of market behavior into the context of risk management and portfolio analysis. ENDNOTES 1. Gary Zukav, The Dancing Wu Li Masters (New York: William Morrow and Company, Inc., 1979) p. 328. 2. “How Giant Bets on Natural Gas Sank Brash Hedge-Fund Trader,” Wall Street Journal, Dow Jones & Company, September 19, 2006. 3. “Quantifying Energy, BP Statistical Review of World Energy,” BP, June 2006. 4. “Heat Drives Power Demand in Midcontinent,” Platt’s Gas Daily, McGraw-Hill Companies, August 10, 2006. 5. Zachary Simecek, “Weathering the Impact of Stormy Price Hikes,” Energy Risk, June 2006. 6. “Consultant Warns that High Demand Growth Could Strain Power Markets and Add Volatility,” Power Markets Week, October 23, 2006. 7. “Hedge Fund Risk: Insights From a Well-Traveled Mind,” interview with Gloria Pilz, Global Association of Risk Professionals, January/February 2006. 8. Matthew Goldstein, Lauren Rae Silva and Melissa Davis, MotherRock Cries Uncle, August 18, 2006, TheStreet.com. 9. “How Giant Bets on Natural Gas Sank Brash Hedge-Fund Trader,” Wall Street Journal, Dow Jones & Company, September 19, 2006. 10. “What Went Wrong At Amaranth,” Wall Street Journal, Dow Jones & Company, September 20, 2006. 11. John Wengler, “Avoid Monday Morning Quarterbacking in California,” Energy Informer, September 2001. 12. Susan Sward and David Lazarus, “How PG&E Missteps Preceded Crisis,” San Francisco Chronicle, January 22, 2001. 13. James Ockenden, “Growing Pains,” Energy Risk, September 2006. 14. Aarzoo Ahah, Riccardo Anacar and Antony Kakoudakis, “The Price Is Right?” Energy Risk, June 2006.
  33. 33. 16 Energy Risk 15. “Structured Investment Vehicles: Trends, Truths and Myths of Complex Marketplace,” Interview with Robert Bothwell, GARP Risk Review, May/June 2006. 16. “Structured Investment Vehicles: Trends, Truths and Myths of Complex Marketplace,” Interview with Nels Anderson, GARP Risk Review, May/June 2006. 17. Neil Palmer, “Quant Doublespeak,” Energy Risk, April 2005. 18. Catherine Lacoursiere, “Storing up Trouble,” Energy Risk, September 2004. 19. “A Look in the Rear View,” Energy Risk, December 2005. 20. Ibid. 21. Ibid. 22. “Hedging for Drivers,” Energy Risk, June 2006. 23. Colin Cooper, “Optimal Results,” Energy Risk, June 2006. 24. “How Giant Bets on Natural Gas Sank Brash Hedge-Fund Trader,” Wall Street Journal, Dow Jones & Company, September 19, 2006.
  34. 34. C H A P T E R 2 What Makes Energies So Different? America was changing. I had a feeling of destiny and I was riding the changes. New York was as good a place to be as any. My consciousness was beginning to change, too, change and stretch. One thing for sure, if I wanted to compose folk songs I would need some kind of new template, some philosophical identity that wouldn’t burn out. It would have to come on its own from the outside. Without knowing it in so many words, it was beginning to happen. Bob Dylan1 17 2.1. INTRODUCTION Energy markets remain a relatively new world. In dealing with this extraordinary market environment we need all the skills and experi- ence of other, more mature markets, plus some new ways of looking at market behaviors including via volatilities and price distributions. Our learning path should begin with the market, encompass study and research of market variables, in order to ultimately loop back to the market, hopefully with new understanding and knowledge. Throughout this process, our emphasis should be on the managerial and implemen- tation aspects of “quantitative analysis.” Quantitative analysis creates models that reflect market behavior in order to support trading in the actual market. If this book helps a novice build a first forward price curve, or inspires an expert to update a favorite model, then this book, Energy Risk, will have served its purpose. The origin of quantitative analysis is rooted in the concept of “risk” itself. Since the days of the Romans, and perhaps even before then, peo- ple have “hedged their bets” against the unknowns of the future by entering into primitive futures and options contracts. Intuition, com- mon sense, and experience probably served as the first quantitative tools for setting prices. (All three remain equally valid tools today!) Copyright © 2007 by Dragana Pilipovic. Click here for terms of use.
  35. 35. 18 Energy Risk Energy markets follow the same impulses: energy producers and users alike wish to hedge their exposure to future uncertainty, or to obtain a particular risk/return strategy. Fortunately, in valuing these products, our task will be easier than that of the Romans, thanks to modern mathematics and statistics, and the advent of computers. 2.1.1. Quantitative and Fundamental Analysis In addition to quantitative analysis, a second discipline forms the basis of derivatives valuation and risk management: fundamental analysis. Fundamental analysis is an attempt to understand and describe mar- ket behavior in terms of the economics of supply and demand. Fundamental analysts attempt to identify, measure, and understand the relationship between the “fundamental price drivers” that cause markets to move up and down.2 Quantitative analysis, on the other hand, attempts to replicate or model market behavior through mathe- matical models and statistical methodologies. In this book, quantitative analysis plays the leading role, and fundamental analysis contributes to the motivation and the intuition behind the models. The interplay between fundamental and quantitative analysis is very much like the interplay between macroeconomics and micro- economics. Macroeconomics is the study of the forces and causes of economic fluctuations and their relationships. Microeconomics, on the other hand, is the study of the behavior of individual consumers and firms. The two are very much related, as assumptions about the economy depend on the assumptions about the individual players within the econ- omy. A thorough understanding of macroeconomics requires a thorough understanding of microeconomics, and vice versa. Similarly, although fundamental analysts try to understand general price drivers, the quan- titative analyst imposes the condition of rational market players who will not allow price arbitrage, resulting in an efficient marketplace. In this sense, fundamental analysis can be likened to macroeconomics, and quantitative analysis can be likened to microeconomics. This book attempts to describe quantitative issues and techniques with very much a fundamental flavor. Every quantitative approach and result is evaluated against the standard of consistency with the funda- mental drivers of a marketplace. Therefore, understanding both the quantitative methodologies and the fundamentals of a marketplace is extremely important.
  36. 36. What Makes Energies So Different? 19 2.2. WHAT MAKES ENERGIES SO DIFFERENT? Energy markets are young maturing markets continuing their trans- formation by the derivatives and risk management industry. In com- parison, the money markets stand as mature markets with relatively few modeling mysteries left to conquer. Bookstores already offer full shelves of excellent introductory and specialized books on fundamental and quantitative analysis for the mature financial markets. Energy markets are slowly catching up. At the time of the first publishing of Energy Risk, there were no other energy market books available. Now, there are a number of excellent energy-specific books. Energies remain very different from money markets (Table 2-1). Fundamental analysis tells us that energy markets respond to under- lying price drivers that differ dramatically from interest rates and other well-developed money markets. More importantly, quantitative analysis tells us that the differences in fundamental price drivers can exert a dramatic domino effect as they are applied to pricing and hedg- ing models. The remainder of this chapter will introduce some of the energy market’s fundamental price drivers and cite several examples of T A B L E 2-1 What Makes Energies Different? Issue In Money Markets In Energy Markets Maturity of market Several decades Relatively new Fundamental price drives Few, simple Many, complex Impact of economic cycles High Low Frequency of events Low High Impact of storage and delivery; None Significant the convenience yield Correlation between short- High Lower, “split personality” and long-term pricing Seasonality None Key to natural gas and electricity Regulation Little Varies from little to very high Market activity (“liquidity”) High Lower Market centralization Centralized Decentralized Complexity of derivative contracts Majority of contracts Majority of contracts are are relatively simple relatively complex
  37. 37. 20 Energy Risk fundamental differences between the energy and money markets. Although these examples skim the surface and the individual chapters provide the necessary details for true understanding, we offer these examples in the spirit of market-driven modeling that we hope perme- ates the entire book. 2.3. ENERGIES ARE HARDER TO MODEL The interest rate and equity markets are “lucky.” Their fundamental drivers number relatively few and easily translate into quantitative pricing models. For example, the deliverables in money markets consist of “a piece of paper” or its electronic equivalent, which are easily stored and transferred and are insensitive to weather conditions.3 Energy mar- kets paint a more complicated picture. Energies respond to the dynamic interplay between producing and using, transferring and storing, buying and selling, and ultimately “burning” actual physical products. Issues of storage, transport, weather, and technological advances play a major role. In the energy markets, the supply side concerns not only the storage and transfer of the actual commodity, but also how to get the actual commodity out of the ground. The end user truly consumes the asset. Residential users need energy for heating in the winter and cooling in the summer, and industrial users’ own production continually depends on energy to keep the plants running and to avoid the high costs of stopping and restarting them. Each of these energy market participants—be they producers or end users—deals with a different set of fundamental drivers, which in turn affect the behavior of energy markets. These problems lead directly to the need for derivatives contracts. Nothing even approaches these problems in money markets. What makes energies so different is the excessive number of fun- damental price drivers, which cause extremely complex price behavior. This complexity frustrates our ability to create simple quantitative models that capture the essence of the market. A hurricane in the Gulf of Mexico will send traders in Toronto into a tailspin. An anticipated technological advance in extracting natural gas could be influencing the forward price curve. How would you go about capturing these kinds of resulting price behaviors into a quantitative model that is also sim- ple enough for quick and efficient everyday use on the trading desk?
  38. 38. What Makes Energies So Different? 21 Figures 2-1 and 2-2 show historical prices for Massachusetts Hub power prices for both the On-Peak and Off-Peak markets (see Chapter 7 for details on contract specifications for both On-Peak and Off-Peak markets). As you can see from the several years of price data in these figures, power prices are not shy in jumping to very high levels during events. Generally speaking, these are upward jumps followed by quick mean reversion back to a more reasonable price level. Also, note that winters and summers tend to be periods of more probable (and serious!) price spikes. Note that the off-peak price history appears quite a bit more volatile, day to day, than even the on-peak power prices, which is counterintuitive; off-peak power is for delivery during the hours of the business day when the demand is less (hence the name “off-peak”) and includes around-the-clock (i.e., all hours of the day) delivery of power on Saturdays, Sundays, and holidays. The large amounts of price volatility we see in Figure 2-2 are a result of the fact that we are “mixing” full days of delivery on weekends and holidays with only a segment of the day for delivery during business days. By separating the two, we obtain Figure 2-3, which shows the price history of off-peak prices only on business days, and is clearly less volatile. F I G U R E 2-1 Massachusetts Hub On-Peak Power: Sample Price History
  39. 39. 22 Energy Risk F I G U R E 2-2 Massachusetts Hub Off-Peak Power: Sample Price History F I G U R E 2-3 Massachusetts Hub Off-Peak Power: Sample Price History with Weekends Excluded
  40. 40. What Makes Energies So Different? 23 Finally, Figure 2-4 shows the historical averages across the few years of sample data of hourly power prices. As you can see from these graphs, not only do power prices exhibit calendar year seasonality, but they also show a strong price term structure across the hours of the day. F I G U R E 2-4 Massachusetts Hub Hourly Power: Sample Price History Averages across Hours of Delivery 2.4. MARKET RESPONSE TO CYCLES AND EVENTS In the broadest sense, the traditional financial markets demonstrate an almost seamless transition from fundamental to quantitative analysis, but energies do not. The relative impact of economic cycles and frequency of events in the two markets demonstrates this difference. Generally speaking, most economic markets appear to move “up” and “down” around some sort of equilibrium level. This equilibrium level could be a historical interest rate, return on equity, or commodity price. The equilibrium may also be called the “average” or “mean” level. The process of a market returning to its equilibrium level is termed “mean reversion.” Mean reversion will be a recurring theme in this book, because it describes a critical difference between the energy and financial markets. Interest rate markets exhibit relatively weak mean reversion. The actual rate of mean reversion in interest rates appears to be related to
  41. 41. 24 Energy Risk economic cycles, hence fundamental price drivers. The state of the econ- omy as a fundamental driver can be directly translated into financial models through the inclusion of mean reversion. In the case of energies, however, we see stronger mean reversion, and for dramatically different reasons than those that apply to interest rates. The mean reversion in energy commodities appears to be a function of either how quickly the supply side of the market can react to “events” or how quickly the events go away. Droughts, wars, and other news-making events create new and unexpected supply-and-demand imbalances. Mean reversion measures how quickly it takes for these events to dissipate or for supply and demand to return to a balanced state. The Gulf War in the late 1980s and early 1990s, for example, greatly affected crude oil prices. The market forward prices of crude oil contained information on how long it would take the production side to respond to the sudden imbalance between supply and demand. Spot and short-term forward prices spiked, but longer-term futures remained relatively stable. In this case, the mean reversion—as exhib- ited in forward prices—was tied to how quickly the production side could bring the system back into balance. In another example, summer heat waves over the years have caused electricity prices to jump to multiples of their average price levels. However, in many of the weather-caused events, temperatures spiked only for several days and prices rapidly reverted to equilibrium as the temperatures reverted to their more normal levels. In this case, the mean reversion was related to the dissipation of an event. Figure 2-5 shows quite a few years of natural gas spot price history. Different events tend to have different effects on an energy market. In the case of natural gas, we have observed quite a few event- ful situations during this new century. Natural gas prices in the United States appeared to abandon their long-term historical levels for much higher prices under the occasional effects of storage concerns, the longer-term supply problems caused by the Iraq war, seasonal events such as extremely damaging hurricanes, and, perhaps most impor- tantly, the emergence of new agressive players spiking the natural gas prices to a level that could not possibly be understood in the prior years of trading. Natural gas spot prices have always exhibited a high volatility (Figure 2-6). (Many of the natural gas contracts traded are contingent on monthly price averages; the volatility of these monthly-based con- tracts is smaller, diluted by the averaging effects.) Given the levels of
  42. 42. What Makes Energies So Different? 25 F I G U R E 2-5 Natural Gas: Sample Price History F I G U R E 2-6 Natural Gas: Sample Historical Volatility these historical volatilities you might conclude that this is a market where just about anything could happen! Understanding the possible “anythings” becomes crucial to the risk management of a portfolio in natural gas.
  43. 43. 26 Energy Risk 2.5. IMPACT OF SUPPLY DRIVERS Energies function with supply drivers that do not exist in money mar- kets: production and storage. Consider the issue of longer-term effects, which have to do with expectations of market production capacity and cost in the long run. Effects of expectations of improvements in the technology of drawing natural gas from the ground will not be seen in the historical data, but—if we are lucky—may be expressed by knowl- edgeable traders in determining forward prices. Their views would be captured through the levels or yields of long-term forward prices. Similarly, the effects of overcapacity in electricity markets, and how long the overcapacity is expected to last, impact the price over a longer period of time. This “storage limitation” problem creates volatile day-to-day behavior of varying degrees for electricity, natural gas, heating oil, and crude oil. Another consequence of limited storage is that although the spot prices exhibit extremely high volatility, the forward prices show volatilities that decrease significantly as the forward price expirations increase. The latter volatility characteristic has to do with the fact that, in the long run, we expect the supply and demand to be balanced, resulting in long-term forward prices that reflect this relatively stable equilibrium price level. Ultimately, when discussing energy commodi- ties, we are forced to confront the issue of storage capacity. Storage lim- itations cause energy markets to have much higher spot price volatility than is seen in money markets. Electricity markets represent the extreme case of storage limita- tion issues. In fact, electricity cannot be readily stored.4 When power plants reach maximum allowable base-load and marginal capacity, there is no more “juice” to go around. While there is no more new elec- tricity to sell, the same unit of electricity may be bought and sold, and hence you may still be able to obtain market price quotes. It should not come as a surprise that such extreme market conditions can cause elec- tricity prices to easily reach levels in multiples of mean price levels. As can be seen from Figures 2-7 and 2-8, power spot prices are even more volatile than natural gas prices, with short-term volatility hitting over 1000% at times! In this sample power market the average on-peak power volatility over the few years of historical data measured 207% and the off-peak prices had an average volatility not too far off at 188%. By comparison—as you can see from Figure 2-9—the average hourly power prices are even more volatile.
  44. 44. What Makes Energies So Different? 27 F I G U R E 2-7 Massachusetts Hub On-Peak Power: Sample Historical Volatility F I G U R E 2-8 Massachusetts Hub Off-Peak Power: Sample Historical Volatility (Using Weekday Price Returns)
  45. 45. 2.7. IMPACT OF DEMAND DRIVERS 28 Energy Risk 2.6. ENERGIES HAVE A “SPLIT PERSONALITY” F I G U R E 2-9 Massachusetts Hub Hourly Power: Average Sample Historical Volatility (2003–2006) From the big picture, the issue of storage accounts for energy prices exhibiting a “split personality.” Energy prices are driven both by the short-term conditions of storage and by the long-term conditions of future potential energy supply. Energy forward prices reflect these two drivers, resulting in short-term forward prices with very different behavior from long-term forward prices. Figures 2-10 and 2-11 show a sample historical behavior of the one-month and one-year forward price points of the West Texas Intermediate (WTI) and natural gas forward price curves, respectively. Short-term forward prices reflect the energy currently in storage, and long-term forward prices exhibit the behavior of future potential energy, that is, energy “in the ground,” capturing the energy markets’ “split personality.”5 If supply constraints can “shock” the system, demand exerts its own fundamental price drivers. In energies, demand drivers introduce the issues of convenience yield and seasonality that have no parallel in money markets.
  46. 46. What Makes Energies So Different? 29 F I G U R E 2-10 NYMEX WTI Futures’ Prices 1992–1996 F I G U R E 2-11 NYMEX Natural Gas Futures’ Prices 1992–1996 2.7.1. The Convenience Yield On the industrial user side, the explicit purpose of derivative contracts is to keep plants running. These industrial users drive the market value of convenience yield. Factories seek to minimize their cost of pro- duction by avoiding the cost of shutting down and restarting the factory due to high prices or lack of available supply. (In a sense, minimizing
  47. 47. 30 Energy Risk price risk can be related to this function.) This urgency in maintaining production gives the industrial users an incentive to pay a premium to have the energy necessary to run their plants delivered now, today. This is not because they are being financially inefficient. Quite the contrary; they are factoring in the opportunity cost of having their production stopped while waiting around to get a better deal on energy or waiting for energy to become available. The premium they are willing to pay (or not, depending on the immediate abundance of supply relative to demand) is factored into something called the “convenience yield.” An analogy can be made between the concept of convenience yield and a stock dividend. Consider a shareholder who buys the stock prior to the ex-dividend date. When the dividend is paid, the new shareholder will capture the value of that dividend. But that shareholder would have had to pay a higher price—relative to the price paid post ex-dividend date—which would have included the dividend value. Similarly, the industrial users capture the value of their own production by purchasing energy before they run out of their supply. In doing so, they willingly pay a higher price for this immediate energy supply in order to capture their own, very specific in-house dividend. In the end, the markets will, given spe- cific industrial user demand, reflect a premium of near-term forward prices relative to the longer-term forward prices. To be more specific, the convenience yield is the net benefit minus the cost—other than financing costs—of holding the energy “in your hands.” The benefits include the user-specific value defined above, and the costs include storage. 2.7.2. Seasonality On the demand side we have to consider the significant seasonality effects of the residential users. Aggregate residential demand creates seasonality. For example, the United States consumes heating oil mostly during the winter; hence, heating oil prices tend to peak during winter and then drop to their annual lows in the summer months. Electricity, on the contrary, powers air conditioners in the summer months and is used less during winter for heating; its prices tend to reach highest peaks during the summer months, with semi-annual humps during the winter.6 The relative highs of the summer and
  48. 48. What Makes Energies So Different? 31 winter peaks—as clearly exhibited within the electricity forward price curves—are a function of the geographic regions within the United States. These seasonality effects can be seen and measured not only through historical spot price data, but also by observing the forward price markets. 2.9. DECENTRALIZATION OF MARKETS AND EXPERTISE When one thinks of financial markets, Wall Street shines at the center. Companies throughout the nation list their stocks on the New York Stock Exchange, and New York also hosts most of the major U.S. banks. Of course, cities outside the Empire State play important roles, but major local and regional banks and financial institutions still turn to Wall Street, Chicago, and other major trading centers to hedge their portfolios. Thus, the financial markets are essentially centralized in terms of location, capital, and expertise. Energy markets, on the other hand, are highly decentralized. To be sure, Houston serves as a mecca, as does Calgary. Energy producers and end users, however, spread from sea to shining sea. To whom does 2.8. REGULATION AND ILLIQUIDITY When modeling energies, we must always remember their relative youth in terms of derivatives and risk management. Natural gas dereg- ulated over a decade ago, and Eastern European and Asian govern- ments are deregulating electricity as this book is being re-written. Even the relatively older markets of heating oil and crude oil took root in the 1980s and continue to evolve in terms of theoretical sophistica- tion and contract complexity and standardization. Although the money markets took decades to evolve, energies are in some ways replicating this evolution in a shorter period. Clearly, lessons from deregulated markets have accelerated the trip up the learning curve. Unfortunately, human character flaws have slowed down the process somewhat. The California crisis and the Enron scandal had wide-felt market effects, dampening energy markets’ development for a period of time.
  49. 49. 32 Energy Risk a Midwestern utility turn to hedge their price risk? If their risks are localized, chances are that their hedges will also be localized. Although many producers and end users may actively use futures contracts in New York and Kansas City, these contracts represent prices at specific delivery points that may behave very differently from the local market being hedged. Decentralization introduces geographic “basis risk,” which is unique to energies. In financial markets, today’s dollar is worth a dollar anywhere in the country. In energy markets, price depends on location. A megawatt of electricity is priced according to delivery point; the same holds true for natural gas. Location is a funda- mental driver of price. At the most human level, even the jobs of energy risk managers are more decentralized than in financial markets. Throughout North America, large end users and even moderate sized utilities maintain energy purchasing officers and wholesale analysts at the least, and full trading and risk management staffs at the extreme. Even the people working the energy desks are diverse. These profes- sionals come from a wide variety of backgrounds, including trading, risk management, corporate treasury departments, and even engineering. Not surprisingly, their voices often conflict, sending mixed messages (and occasionally mis-pricing) to the market. These market inefficiencies are being resolved with time, of course, as growth of market understanding (and knowledge transfer, as exemplified by a growing number of energy books) occurs. 2.10. ENERGIES REQUIRE MORE EXOTIC CONTRACTS The final factor that makes energies so different can be found in the type of financial contracts required by the end users of derivatives. In interest rates, contracts tend to be standardized and relatively easy to model. For the most part, end users of financial derivatives find that relatively simple forwards, swaps, caps, floors, and swaptions suit the majority of their needs. (Not surprisingly, these contracts are made in highly liquid financial markets as compared to energies.) The market even uses the term “vanilla” for these simple contracts; traders imme- diately term non-vanilla contracts as “exotic.” What makes energy con- tracts so different is that energy’s typical “vanilla” contract would be
  50. 50. What Makes Energies So Different? 33 considered an “exotic” contract in mature money markets. Due largely to the needs of end users, energy contracts often exhibit a complexity of price averaging and customized characteristics of commodity delivery. The combination of a relatively young derivatives market in develop- ment, supporting very sophisticated contracts, presents a terrific challenge to quantitative analysts and risk managers in the energy markets. 2.11. CONCLUSION Energies differ from nonphysical markets for both fundamental and quantitative reasons. Compared to the traditional markets of interest rates and equities, energies react differently to such fundamental vari- ables as macroeconomic cycles and events. The energy markets suffer from supply-and-demand constraints that dramatically influence both the valuation and management of energy risk. The differences even spread to the company level, where firms that would be considered small by financial market standards must still support trading and risk management operations never seen in like-sized banks. In summary, this chapter introduced energy derivatives and risk management through a comparison of the quantitative differences between energy and money markets. The markets also share many characteristics. The main outcome of these parallel differences and sim- ilarities is that the energy markets demonstrate a “split personality.” Energies exhibit some behaviors of traditional financial markets, in particular within long-term price behavior, but at the same time they have their own unique and challenging behavioral intricacies. ENDNOTES 1. Bob Dylan, Chronicles, Volume One, p. 73. (New York: Simon & Schuster, 2004). 2. Hall & Taylor, pp. 3, 4. Macroeconomics: Theory, Performance, and Policy (New York: W.W. Norton & Company, 1988). 3. However, this was not always so. Remember the gold standard? In the gold standard days, the interest rate markets acted much more like today’s energy markets than like today’s interest rate markets.
  51. 51. 34 Energy Risk 4. Water reserves do represent a form of potential electricity storage for hydro plants; several utilities employ off-peak power to pump water up to a reservoir, only to reverse the flow to capture the potential energy during peak periods. 5. “In the ground” is used here as an expression of speech. In the case of electricity, it is not that simplistic. 6. Ironically, most of the residential demand remains in the regulated portion of electricity generation, although this is currently changing.
  52. 52. C H A P T E R 3 Modeling Principles and Market Behavior “Pooh’s found the North Pole,” said Christopher Robin. “Isn’t that lovely?” Pooh looked modestly down. “Is that it?” said Eeyore. “Yes,” said Christopher Robin. “Is that what we were looking for?” A. A. Milne1 35 3.1. THE MODELING PROCESS Modeling market behavior should be approached like any business: with a good amount of common sense. It should not be some mysterious process that Ph.D.s perform in isolation, with no view of the overall trading business goals. The full energy team of managers, traders, quantitative analysts, and engineers should be able to understand the basics of modeling principles and market behavior. This way, modeling can become a well-defined process, with goals and procedures that are discussed, set up, and agreed upon by several key players in a company structure, just like any other business branch of a company. The first step in getting the full energy team to communicate is to define the modeling process, which should include both trader insights about the markets and expert insights about quantifying and valuing the products in that marketplace. In the spirit of developing a stan- dardized language that both traders and valuation experts can use to better define the modeling business goals, this chapter will define the basics of modeling and some common-sense requirements that the modeling process ought to satisfy. Copyright © 2007 by Dragana Pilipovic. Click here for terms of use.
  53. 53. 36 Energy Risk 3.2. THE VALUE OF BENCHMARKS Modeling is often left to itself in its struggle to arrive at pricing models that traders can use. The beginning of the modeling process should consist of an analysis of the available models and their appropriateness for the particular product. Hence, the beginning should be the bench- marking between active market behavior and the modeling choices, resulting in a final choice of a model, given possible implementation con- straints. The middle should be the actual development of the chosen model, and the end should be the implementation of the chosen model. The most difficult and also the most important part of this process is the first, the beginning. If the model chosen is not appropriate for the product, given the market in which the product is traded, then the last part of the process, the implementation, is likely to drag on—sometimes for months and even years. Quite often the critical first step of the process, the model bench- marking, is not performed. This can be a very costly mistake. Although the company is paying its valuation experts a good deal of money to finish the long-awaited implementation of the choice model, it is also paying a price for not being able to participate in the trading of the product because the traders cannot yet price it. It is often such poor modeling management (and poor management in general) that results in the traders coming up with their own—however simplistic and maybe even inappropriate—spreadsheets for pricing products. What we are really talking about here is the cost a trading business has to pay for not benchmarking and testing between the models in the laboratory before bringing them out onto the trading desk. If you were to buy a new suit, and you decided to spend a good amount of money on it, surely you would shop around and try on different suits for fit and look? Then why would a company that wants to invest a good amount of money in a modeling methodology not do the same? 3.2.1. Diffusing Personalized Attachments to Models I would like to discuss an important issue, which I like to refer to as the “my model, your model” problem. This problem often arises in trading
  54. 54. Modeling Principles and Market Behavior 37 companies that have invested money in research development and there is more than one modeling expert, but each is driven by a separate system of beliefs about modeling. Hence, it would not be surprising to find these valuation experts in what might appear as lethal warfare with no real means of conclusion. Unfortunately, the valuation experts, just like most of us when it comes to something that we know a great deal about and have been working on for years, tend to take the modeling issues very personally. (As hard as I try to be objective, I remain aware of this weakness in myself.) The problem is not that the experts might have different opinions; in fact, this is rather a good thing, as they could probably learn quite a bit from each other. The problem is that they have not agreed on modeling benchmarks and have had no help from the trading or management sides in deciding what benchmarks really ought to be used, given the trading strategies and business goals of the company. Even worse than the “my model, your model” problem is the problem of having a single expert who has a favorite model that the company decides to implement without any benchmarking and testing. The typical story goes as follows: The expert’s favorite model is implemented, but because it might not be appropriate for the market in question, any implementation and new product problems are dealt with using “modeling Band-Aids.” The resulting valuation system very quickly becomes cumbersome if not impossible to use, not to mention that the cost of maintaining it can become quite high. As well as introducing modeling benchmarks, the trading organi- zation must also approach the modeling side with the spirit of always searching for a better understanding of the marketplace and its prod- ucts. This means that managers, traders, and valuation experts should form a team, which provides a framework for sharing knowledge, and sets the team’s valuation goals, including determining the benchmarks for deciding on methodology routes. With all the above said, I recognize that this book in fact intro- duces you to one particular view on modeling. However, if the book achieves its purpose, you will not walk away from it thinking about the author’s modeling views. Instead, you will walk away empowered to form your own views and you will encourage others around you to do the same.
  55. 55. 38 Energy Risk 3.3. THE IDEAL MODELING PROCESS The recipe for efficient modeling as applied to a trading operation includes five steps: 1. Establish corporate goals that are within the context of the risk/return framework and are expressed through the risk management policy (see Chapters 12 and 14). 2. Prioritize the market characteristics, which should be captured by the model. Define the benchmarks that describe the market against which any model will be judged. 3. Select the models to be tested and evaluated against the benchmarks. Perform time series analysis and distribution analysis for comparison. The models should be selected in the order of the evaluation results. 4. Estimate the implementation constraints and costs for each model. 5. Finally, identify the model that best satisfies both the market benchmarks and the implementation requirements. This process would require the participation of at least the producers (the valuation experts and implementers) and the users (the traders). Ideally, the management also has a representative who adds the nec- essary degree of management support, understanding, and guidance from a higher level of the trading business goals. 3.4. THE ROLE OF ASSUMPTIONS: MARKET BEFORE THEORY The goal of quantitative analysis is to develop and implement models that reflect market behavior. The process forces us to make some fun- damental assumptions about the marketplace and the products we are trying to model. For example, the famous Black–Scholes differential equation for option prices is based on the fundamental assumption that a hedged portfolio consisting of an option, a stock, and a bond must earn the risk-free rate of return because we have eliminated all the stock price risk by hedging the option with the stock. Expressed in terms of partial differential equations, this fundamental assumption
  56. 56. Modeling Principles and Market Behavior 39 forms the basis of quantitative analysis of option prices.2 One nice feature of making unrealistic assumptions is that we can enforce them to simplify a problem, and then later relax the assumption for a more general, realistic solution. Similarly, if we make the fundamental assumption that electricity prices are related to coal and natural gas prices, we can arrive at a solu- tion for electricity prices by assuming that we can create a risk-free portfolio consisting of electricity, coal, and natural gas. On the other hand, we may assume that electricity prices tend to revert to equilib- rium price levels, which are determined by supply-and-demand condi- tions. In these cases, our different fundamental assumptions would possibly lead us to very different solutions. Fundamental assumptions about the marketplace dramatically influence quantitative models developed and implemented for pricing and risk management purposes. Every quantitative result ought to be consistent with the characteristics the fundamental drivers ultimately give to the behavior of the marketplace. Therefore, understanding the fundamental drivers of the marketplace as well as how these drivers are captured in the behavior of the market is extremely important in arriving at models that reflect market reality. Furthermore, in order to arrive at such models we need not only to understand the fundamental drivers of the marketplace, but also to translate these fundamental drivers into pricing models that are both arbitrage free and practical for implementation onto a trading desk. This is by no means an easy task. 3.4.1. Typical Assumptions Some typical assumptions are that the markets are efficient and arbi- trage free. In money markets, prices are often assumed to be lognormal. Through such assumptions, we define our version of reality. One person may assume that volatilities are constant, while another may assume the volatilities vary along different points of the forward price curve (i.e., have “term structure”). It is also common to assume continuous hedging. Everyone has probably heard of the Black–Scholes option pricing model.3 While valuing European options on stocks, Black and Scholes assumed that stock prices are lognormal and have constant volatilities.
  57. 57. 40 Energy Risk Hence, the randomness that the stock prices exhibit is assumed to always be of the same magnitude. Although most people agree that stock prices are indeed lognormal, most disagree that the volatilities remain constant. In reality, the randomness of the stock price behavior is not constant, and volatilities do possess term structure. Black and Scholes were forced to make this unrealistic assumption because allowing the volatility to also exhibit a nonconstant behavior made solving for the option price far too difficult. After all, one of the best features of the resulting model is its ease of use. This is a terrific example of how unrealistic assumptions might help to create practical solutions. An important consideration in making assumptions is that they be correctly implemented within models. For example, consider the assumption that price mean reversion exists in interest rates. Although most people believe this to be true, when this assumption is imple- mented within a single-factor model, the result is a volatility term structure that goes to zero over time. Because most interest rate models are, in fact, single-factor, and because the volatility’s term structure does not in fact go to zero over time, we see a potential conflict.4 The lesson that can be learned from Black–Scholes and similar modeling experiences is that some assumptions that reflect market reality should be relaxed in order to arrive at a workable valuation model. However, when we relax assumptions but recognize them to be true in the real world, we should make sure that the valuation method- ology’s implementation captures the assumption—even though the valuation methodology itself does not. So, in the case of Black–Scholes, we can correct for the constant volatility assumption by allowing each option price of different maturity to have a different volatility value. Thus we somewhat capture market reality of the marketplace (at least allowing for marked-to-market option prices), not in the valuation model, but rather in its implementation. If we had just ignored the fact that in reality energy volatilities, intermarket and intramarket correlations are not constant, we could be making a grave mistake, perhaps costing the trading operation a great deal of money. Hence, here is an excellent example of why it is very impor- tant to have traders communicating with the valuation experts, particu- larly when the implementation is very informal. If they do not understand the model assumptions, they may end up using the models blindly and without the appropriate checks on implementation assumptions.

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