Modeling and Valuation of Energy Structures (eBook)

Dan Mahoney has over 17 years of experience as an energy quant in support of trading, structuring, and origination. He has extensive experience in mathematical and financial modeling with an emphasis on the valuation of volatility-related structures. He has held positions at Mirant, FPL, Sempra, Societe Generale, Trafigura, Swiss Re, and Citigroup, where he has been responsible for model development and infrastructure. His background covers a wide range of deals, both physical and financial, including tolling, full requirements, gas storage, and transport. He holds degrees from Caltech and MIT, US.

Cover 1
Half-Tile 2
Title 4
Contents 8
List of Figures 12
List of Tables 14
Preface 15
Acknowledgments 19
1 Synopsis of Selected EnergyMarkets and Structures 20
1.1 Challenges of modeling in energy markets 20
1.1.1 High volatilities/jumps 20
1.1.2 Small samples 21
1.1.3 Structural change 22
1.1.4 Physical/operational constraints 23
1.2 Characteristic structured products 23
1.2.1 Tolling arrangements 23
1.2.2 Gas transport 25
1.2.3 Gas storage 26
1.2.4 Load serving 28
1.3 Prelude to robust valuation 30
2 Data Analysis and StatisticalIssues 31
2.1 Stationary vs. non-stationary processes 31
2.1.1 Concepts 31
2.1.2 Basic discrete time models: AR and VAR 41
2.2 Variance scaling laws and volatilityaccumulation33 48
2.2.1 The role of fundamentals and exogenous drivers 50
2.2.2 Time scales and robust estimation 52
2.2.3 Jumps and estimation issues 53
2.2.4 Spot prices 58
2.2.5 Forward prices 61
2.2.6 Demand side: temperature 62
2.2.7 Supply side: heat rates, spreads, and productionstructure 65
2.3 A recap 66
3 Valuation, Portfolios, andOptimization 67
3.1 Optionality, hedging, and valuation 67
3.1.1 Valuation as a portfolio construction problem 67
3.1.2 Black Scholes as a paradigm 71
3.1.3 Static vs. dynamic strategies 77
3.1.4 More on dynamic hedging: rolling intrinsic 87
3.1.5 Market resolution and liquidity 94
3.1.6 Hedging miscellany: greeks, hedge costs, and discounting 98
3.2 Incomplete markets and the minimal martingale measure$^61$ 104
3.2.1 Valuation and dynamic strategies 105
3.2.2 Residual risk and portfolio analysis 107
3.3 Stochastic optimization 120
3.3.1 Stochastic dynamic programming and HJB 120
3.3.2 Martingale duality 125
3.4 Appendix 130
3.4.1 Vega hedging and value drivers 130
3.4.2 Value drivers and information conditioning 132
4 Selected Case Studies 137
4.1 Storage 137
4.2 Tolling 140
4.3 Appendix 147
4.3.1 (Monthly) Spread option representation of storage 147
4.3.2 Lower-bound tolling payoffs 148
5 Analytical Techniques 150
5.1 Change of measure techniques 150
5.1.1 Review/main ideas 150
5.1.2 Dimension reduction/computation facilitation/estimation robustness 154
5.1.3 Max/min options 158
5.1.4 Quintessential option pricing formula 159
5.1.5 Symmetry results: Asian options 161
5.2 Affine jump diffusions/characteristic function methods 164
5.2.1 L?y processes 164
5.2.2 Stochastic volatility 168
5.2.3 Pseudo-unification: affine jump diffusions 174
5.2.4 General results/contour integration 176
5.2.5 Specific examples 180
5.2.6 Application to change of measure 185
5.2.7 Spot and implied forward models 188
5.2.8 Fundamental drivers and exogeneity 193
5.2.9 Minimal martingale applications 197
5.3 Appendix 203
5.3.1 More Asian option results 203
5.3.2 Further change-of-measure applications 206
6 Econometric Concepts 210
6.1 Cointegration and mean reversion 210
6.1.1 Basic ideas 210
6.1.2 Granger causality 216
6.1.3 Vector Error Correction Model (VECM) 218
6.1.4 Connection to scaling laws 224
6.2 Stochastic filtering 226
6.2.1 Basic concepts 226
6.2.2 The Kalman filter and its extensions 228
6.2.3 Heston vs. generalized autoregressive conditional heteroskedasticity (GARCH) 239
6.3 Sampling distributions 244
6.3.1 The reality of small samples 244
6.3.2 Wishart distribution and more general sampling distributions 245
6.4 Resampling and robustness 250
6.4.1 Basic concepts 250
6.4.2 Information conditioning 251
6.4.3 Bootstrapping 254
6.5 Estimation in finite samples 256
6.5.1 Basic concepts 256
6.5.2 MLE and QMLE 261
6.5.3 GMM, EMM, and their offshoots 263
6.5.4 A study of estimators in small samples 266
6.5.5 Spectral methods 274
6.6 Appendix 277
6.6.1 Continuous vs. discrete time 277
6.6.2 Estimation issues for variance scaling laws 279
6.6.3 High-frequency scaling 287
7 Numerical Methods 291
7.1 Basics of spread option pricing 291
7.1.1 Measure changes 291
7.1.2 Approximations 294
7.2 Conditional expectation as a representationof value 298
7.3 Interpolation and basis function expansions 298
7.3.1 Pearson and related approaches 299
7.3.2 The grid model$^16$ 304
7.3.3 Further applications of characteristic functions 319
7.4 Quadrature 323
7.4.1 Gaussian 324
7.4.2 High dimensions 332
7.5 Simulation 337
7.5.1 Monte Carlo 338
7.5.2 Variance reduction 342
7.5.3 Quasi-Monte Carlo 352
7.6 Stochastic control and dynamic programming 356
7.6.1 Hamilton-Jacobi-Bellman equation 357
7.6.2 Dual approaches 357
7.6.3 LSQ 358
7.6.4 Duality (again) 363
7.7 Complex variable techniques for characteristic function applications 365
7.7.1 Change of contour/change of measure 365
7.7.2 FFT and other transform methods 372
8 Dependency Modeling 378
8.1 Dependence and copulas 378
8.1.1 Concepts of dependence 378
8.1.2 Classification 384
8.1.3 Dependency: continuous vs. discontinuous processes 393
8.1.4 Consistency: static vs. dynamic 395
8.1.5 Wishart processes 400
8.2 Signal and noise in portfolio construction 402
8.2.1 Random matrices 403
8.2.2 Principal components and related concepts 408
Notes 410
1 Synopsis of Selected Energy Markets andStructures 410
2 Data Analysis and Statistical Issues 412
3 Valuation, Portfolios, and Optimization 417
4 Selected Case Studies 428
5 Analytical Techniques 429
6 Econometric Concepts 437
7 Numerical Methods 444
8 Dependency Modeling 452
Bibliography 456
Index 470