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Table of Contents Preface Acknowledgements About the Author 1 Chapter 1 Energy Markets: Trading, Modeling, and Hedging 1.1. Introduction 1.2. Energy Trading 1.2.1. Understanding The Fundamentals 1.2.2. Liquidity, Volatility, and Intra-market Correlations 1.2.3. Market Deregulation 1.3. Energy Modeling 1.3.1. Energies Are Still Unique 1.3.2. Model Complexity 1.3.3. Quants vs. Traders vs. Reality 1.4. Energy Hedging And Risk Management 1.4.1. Adding Financial Products To The Hedging Mix 1.4.2. Risk Management: A Profitable Business Function? 1.4.3. Hedging For The Little Guys 1.4.4. Assets As Hedges 1.4.5. Regulatory Response To ¿Bad¿ Stories 1.5. Conclusion 2 Chapter 2 What Makes Energies So Different? 2.1 Introduction 2.1.1. Quantitative and Fundamental Analysis 2.2 What Makes Energies So Different? 2.3 Energies Are Harder to Model 2.4 Market Response to Cycles and Events 2.5 Impact on Supply Drivers 2.6 Energies Have a ¿Split Personality¿ 2.7 Impact of Demand Drivers 2.7.1 The Convenience Yield 2.7.2 Seasonality 2.8 Regulation and Illiquidity 2.9 Decentralization of Markets and Expertise 2.10 Energies Require More Exotic Contracts 2.11 Conclusion and Organization of the Book 3 Chapter 3 Modeling Principles and Market Behavior 3.1 2.1 The Modeling Process 3.2 The Value of Benchmarks 3.2.1 Defusing Personal Attachments to Models 3.3 The Ideal Modeling Process 3.4 The Role of Assumptions: Market Before Theory 3.4.1 Typical Assumptions 3.4.2 Market Variable vs. Modeling Parameter 3.4.3 Testing Assumptions through Benchmarks 3.4.4 Assumptions and Implementation 3.5 Contract Terms and Issues 3.5.1 Underlying Price (or Market) 3.5.2 Derivative Contract 3.5.3 Option Settlement Price 3.5.4 Delivery 3.5.5 Complexity of Contracts for Delivery 3.6 Modeling Terms and Issues 3.6.1 Price Returns 3.6.2 Elements of a Price Model 3.6.3 Convenience Yield 3.6.4 Cost of Risk 3.7 Quantitative Financial Models Across Markets 3.7.1 Log-Normal Market 3.7.2 Mean-Reverting Market 3.8 The Taylor Series and Ito¿s Lemma 3.8.1 Taylor Series 3.8.2 Ito¿s Lemma 3.9 Lessons From Money Markets 3.9.1 Modeling Price vs. Rate: Defining the Market Drivers 3.9.2 Yield vs. Forward Rate Curves 3.9.3 Drawbacks of Single-Factor Mean-Reverting Models 3.9.4 Drawbacks of Single-Factor Non-Mean-Reverting Models 3.9.5 Volatility Market Discovery 4 Chapter 4 Essential Statistical Tools 4.1 Introduction 4.2 Time Series and Distribution Analysis 4.2.1 Time Series Analysis 4.2.2 Distribution Analysis 4.3 Other Statistical Tests 4.3.1 The Q-Q Plot 4.3.2 The Autocorrelation Test 4.3.3 Measures of Fit 4.4 How Statistics Helps to Understand Reality 4.4.1 A Simple Case 4.4.2 The Difference Between Price and Return 4.4.3 Distinguishing Drift Terms 4.5 The Six-Step Model Selection Process 4.5.1 Step 1: An Informal Look 4.5.2 Step 2: A Short List of Possible Models 4.5.3 Step 3: Time Series Analysis 4.5.4 Step 4: From Underlying Price Models to Distributions 4.5.5 Step 5: Distribution Analysis 4.5.6 Step 6: Select the Most Appropriate Model 4.6 Relevance to Option Pricing 5 Chapter 5 Spot Price Behavior 5.1 Introduction 5.2 Looking at the Actual Market Data 5.3 A Short List of Possible Models 5.3.1 The Lognormal Price Model 5.3.2 Mean-Reverting Models 5.3.3 Cost-Based Models for Electric Utilities 5.3.4 Interest Rate Models 5.4 Calibrating Parameters Through Time Series Analysis 5.4.1 Incorporating Seasonality With Underlying Models 5.4.2 Results from Time Series Analysis 5.5 Performing Distribution Analysis 5.5.1 Implementation of Distribution Analysis 5.5.2 Results of Distribution Analysis 5.6 Conclusion ¿Introduction To Locational Marginal Pricing¿, by Francis H. Wang 6. Chapter 6 The Forward Price Curve 6.1. Introduction 6.1.1. The Difference between Forwards and Futures 6.2. Reading the Underlying Curve 6.3. Seasonality in the Forward Curve 6.4. Modeling Concepts Relating Spot, Forwards, and Seasonality 6.4.1. S&P 500 6.4.2. WTI Crude Oil 6.4.3. Seasonal Markets 6.5. Linking Spot Price Models To Forward Price Models 6.5.1. The Arbitrage-Free Condition 6.5.2. Capturing Market Characteristics Within The Model Or During Implementation 6.5.3. Influence of the Convenience Yield 6.6. Modeling the Underlying Forward Price Curve 6.6.1. Difference Between Spot and Forward Prices 6.6.2. Going from Spot Price Models to Forward Price Models 6.6.3. The Risk-Free Portfolio 6.6.4. Effect of Dividends 6.6.5. Equivalence Between Dividends and the Convenience Yield 6.6.6. Adding A Second Factor 6.6.7. Seasonality 6.7. The Two-Factor Mean-Reverting (Pilipovic) Model 6.8. Testing the Spot Price Model on Forward Price Data 7 Chapter 7 Building Marked To Market Forward Price Curves: Implementing Forward Price Models 7.1 Introduction: What Is A Marked-To-Market Forward Price Curve? 7.2 Forward Price Contact Valuation 7.2.1 Simple Contract For 1-Day Delivery 7.2.2 Contract For Delivery Over A Period 7.2.3 Bootstrapping and the Problem of Daily Price Discovery 7.3 Fitting The Modeling Needs To Trading Needs 7.3.1 Case Of Trading Exchange-Traded Products Only 7.3.2 Case Of Trading OTC 7.3.3 Case Of Owning Power Production 7.4 Building Marked-To-Market Forward Price Curves: Issues To Consider 7.4.1 Quote Strips 7.4.2 Step-Function Treatment 7.4.3 Linear Interpolation 7.4.4 Applying Forward-Price Models Based On Spot Price Analysis 7.4.5 Many Degrees Of Freedom Within Implementation: Part Art, Part Science 7.4.6 From Events To Models 7.4.7 Parameter Calibration 7.5 Modeling Middle Term Event Expectations 7.6 Modeling Forward Price Seasonality 7.6.1 Cosine Seasonality 7.6.2 Exponential Seasonality 7.6.3 Power N Model ¿ Flat Seasonality 7.6.4 Multi-Period Seasonality Treatment 7.7 Special Case Of Basis Markets 7.8 Noise vs. Events 7.9 Markets With Little Or No Market Discovery: Off-Peak and Hourly Forward Price Curves 7.10 Conclusion 8. Chapter 8 Volatilities 8.1. 8.1 Introduction 8.2. Measuring Randomness 8.2.1. Standard Deviation and Variance 8.2.2. Volatility Defined 8.2.3. Comparing Variance and Volatility 8.2.4. Variance and Volatility in Spot Price Models 8.3. The Stochastic Term 8.3.1. Case of Constant Volatility 8.3.2. Case of Volatilities with Term Structure 8.4. Measuring Historical Volatilities 8.4.1. Simple Techniques 8.4.2. More-Complex Techniques 8.5. Market-Implied Volatilities 8.5.1. Option-Implied Volatilities 8.5.2. Implied Volatilities from a Series of Options 8.5.3. Calibrating Caplet Volatility Term Structure 8.5.4. Implied Volatilities from Options on the Average of Price 8.5.5. The Volatility Smile 8.6. Model-Implied Volatilities 8.6.1. The Lognormal Model 8.6.2. The Log-of-Price Mean-Reverting Model 8.6.3. The Price Mean-Reverting Model 8.7. Building the Volatility Matrix 8.7.1. Introduction to the Forward Volatility Matrix 8.7.2. Discrete Volatilities 8.7.3. Tying In Caplet Volatilities 8.7.4. Two-Dimensional Approach to Volatility Term Structure 8.7.5. Tying in Historical Volatilities 8.7.6. Tying in Caplet and Swaption Prices 8.8. Implementing the Volatility Matrix 9. Chapter 9 Overview of Option Pricing for Energies 9.1. Introduction 9.2. Basic Concepts of Option Pricing 9.2.1. Parity Value 9.2.2. Settlement 9.3. Types of Options 9.3.1. European Options 9.3.2. American Options 9.3.3. Asian Options: Options on an Average of Price 9.3.4. Swing Options 9.4. Effects of Underlying Behavior 9.5. Option Pricing Implementation Techniques 9.5.1. Close-Form Solutions 9.5.2. Simulations 9.5.3. Trees 9.5.4. Human Error in Implementation 9.6. Choosing the Right Option Pricing Model 9.6.1. Three Criteria for Evaluating Option Models 9.6.2. Investing in Pricing Model vs. Implementation 9.6.3. A Model Is Only As Good as Its Implementation 9.7. Option Valuation Process: What Should It Be? 9.7.1. Defining Underlying Market Price Behavior 9.7.2. Testing Alternative Models 9.7.3. Selecting Most Appropriate Option Model 9.8. Did That Option Make Money? 10. Chapter 10 Option Valuation 10.1. Introduction 10.2. Option Model Implementation 10.3. Closed-Form Solutions 10.3.1. Pros 10.3.2. Cons 10.3.3. The Black-Scholes Model 10.3.4. The Black Model 10.4. Approximations to Closed-Form Solutions 10.4.1. Pros 10.4.2. Cons 10.4.3. The Volatility Smile and Term Structure 10.4.4. The Edgeworth Series Expansion 10.4.5. Pulling It All Together 10.5. The Tree Approach 10.5.1. Pros 10.5.2. Cons 10.5.3. Binomial Trees 10.5.4. Trinomial Trees 10.5.5. Using A Tree To Value A European Style Option 10.5.6. Using A Tree To Value An American Style Option 10.5.7. Energy-Specific American-Style Options 10.6. Monte Carlo Simulations 10.7. Conclusion 11. Chapter 11 Valuing Energy Options 11.1. Introduction 11.2. Daily Settled Options 11.2.1. Extending Daily Methodology To Hourly Settled Options 11.3. Monthly Settled Options 11.3.1. Cash-Settled: Look-Back Monthly Settled Average Price Options 11.3.2. Monthly-Settled (Look-Forward) Options On Monthly Forwards 11.3.3. Incorporating Price Mean-Reversion (PMR) Into Monthly-Settled Options 11.3.4. Extending Monthly Methodology To Calendar Year Options 11.4. Optionality In Cheapest-To-Deliver Forward Prices 11.5. Types Of Energy Swing Options 11.6. Demand-Swing Contracts 11.6.1. Demand-Swing Options 11.6.2. Demand-Swing Forwards 11.6.3. Load Behavior 11.7. Price-Swing Contracts 11.7.1. Multiple-Peaker Swing Options 11.7.2. Forward-Starting Swing 11.7.3. Natural Gas Storage 11.8. Spread Options 11.8.1. Various Approximations To Spread Option Valuation 11.8.2. Tree Approach 11.8.3. Crack Spread, Spark Spread and Basis Spread Options 11.8.4. Valuing Power Plants And Transmission Lines 11.9. Conclusion 12. Chapter 12 Measuring Risk 12.1. Introduction 12.2. The Risk/Return Framework 12.3. Types of Risk 12.3.1. Market Risk 12.3.2. Commodity Risk 12.3.3. Human Error 12.3.4. Model Risk 12.4. Definition of a Portfolio 12.4.1. Change in Portfolio Value 12.4.2. Time Buckets 12.5. Measuring Changes in Portfolio Value 12.5.1. Taylor Series 12.6. Portfolio Sensitivity: The ¿Greeks¿ 12.6.1. Delta: Sensitivity to Price Change 12.6.2. Vega: Sensitivity to Volatility Change 12.6.3. Theta: Sensitivity to Time 12.6.4. Rho: Sensitivity to Discounting Rates 12.6.5. Gamma: Sensitivity to Changes in Delta 12.6.6. Quantity-Specific Risks 12.6.7. Sensitivity to Correlation Change 12.7. Hedging 12.8. Marking-to-Market 12.8.1. Information for Marking-to-Market 12.8.2. Mark-to-Market Valuation 12.8.3. Testing the Mark-to-Market Process 13. Chapter 13 Portfolio Analysis 13.1. Introduction 13.2. Application of Portfolio Analysis 13.3. Analyzing the Change in Portfolio Value 13.4. The Minimum-Variance Method 13.4.1. The Hedged Portfolio 13.4.2. Per-Deal Hedges 13.4.3. Portfolio with Options 13.4.4. Lessons from Inadequate Hedging Policies 13.5. The Generalized Minimum-Variance Model 13.6. Correlations 13.7. Value-at-Risk (VAR) Analysis 13.7.1. Fixed-Scenario Stress Simulations 13.7.2. Monte Carlo Simulations 13.7.3. Estimated Variance-Covariance Method 13.7.4. Historical ¿Simulations¿ 13.8. The Special Case of Electricity 13.9. The Corporate Utility Function 14. Chapter 14 Risk Management Policies 14.1. Introduction 14.2. The Case for a Risk Management Policy 14.2.1. Horror Stories 14.3. Risk Management Goals and Strategies 14.3.1. Speculation 14.3.2. Arbitrage 14.3.3. Market Maker 14.3.4. Treasury 14.3.5. Mixed Strategies 14.4. Initial Evaluation Checklist 14.4.1. Diagnosing and Selecting Trading Strategies 14.4.2. Gaps between Existing and Desired Market Position 14.4.3. Corporate Culture 14.5. The ¿Front/Middle/Back Office¿ Paradigm 14.5.1. Conflicts between Offices 14.5.2. Interoffice Committees 14.6. The Energy Team 14.6.1. Appropriate Knowledge by Organizational Level and Functions 14.6.2. Management Issues 14.6.3. Common Management Misconceptions 14.7. Implementation of Risk Management Policies Appendix A: Mathematical and Statistical Notes Appendix B: Models from Interest Rate and Bond Markets Appendix C: Analysis of Markets Published In The First Version Of ¿Energy Risk¿ Glossary of Energy Risk Management Terms Select Bibliography Index
Library of Congress Subject Headings for this publication:
Electric utilities.
Energy industries.
Commodity futures.
Derivative securities.