Weather derivatives : modeling and pricing weather-related risk

Cover......Page 1
Weather Derivatives......Page 4
Preface......Page 6
Contents......Page 10
List of Abbreviations......Page 14
1.1 Introduction......Page 17
1.2.1 The Purpose of Weather Derivatives\r......Page 18
1.2.2 The Weather Market History......Page 20
1.2.3 Market Participants......Page 22
1.2.4 Weather Securities......Page 24
1.2.5 Weather Derivatives and Insurance......Page 25
1.2.6 Basis Risk......Page 26
1.3.1 The Electricity Market......Page 27
1.3.2 The Oil and Gas Market......Page 29
1.4 Weather Derivatives Pricing and Other Issues......Page 30
1.5 Purpose of the Book and Readership Level......Page 31
1.6 Overview of the Book......Page 33
References......Page 34
2.1 Introduction......Page 37
2.2 Some Stochastic Processes......Page 38
2.3 Itô Integral......Page 40
2.4 Itô Formula......Page 41
2.5 Applications of Itô Formula......Page 45
2.6 Girsanov´s Theorem......Page 48
2.7 Esscher Transform......Page 49
2.8 Conclusions......Page 50
References......Page 51
3.1 Introduction......Page 52
3.2.1 Missing Values......Page 54
3.2.2 Erroneous Values......Page 55
3.2.3 Jump and Discontinuities Detection......Page 56
3.3.1.1 Urbanization......Page 58
3.3.2.1 Polynomial Trends......Page 59
3.3.2.3 Loess and Lowess Filtering Methods......Page 60
3.3.2.4 An Example of Fitting a Trend in Temperature......Page 61
3.4 Identifying and Removing Seasonalities......Page 62
3.5 El Niño and La Niña Effects......Page 63
3.6 Selection of the Length of Historical Data......Page 66
3.7 Conclusions......Page 68
References......Page 69
4.1 Introduction......Page 70
4.2 Actuarial Method......Page 71
4.3 Historical Burn Analysis......Page 73
4.4 Index Modeling......Page 74
4.5 Daily Modeling......Page 75
4.5.1 Discrete Process......Page 76
4.5.2 Continuous Process......Page 81
4.6 Alternative Methods......Page 95
4.7 Conclusions......Page 96
References......Page 97
5.1 Introduction......Page 101
5.2 Data Description......Page 102
5.3 Statistical Modeling of Daily Average Temperature......Page 114
5.4.1 The Linear Approach......Page 116
5.4.2 A More Advanced Approach: Wavelet Analysis......Page 118
5.5 The Speed of Mean Reversion......Page 123
5.5.1 The Linear Approach......Page 124
5.5.2 A More Advanced Approach: The Nonlinear Nonparametric Approach......Page 125
5.5.2.1 Variable Selection: Selecting the Significant Lags......Page 126
5.5.2.2 Model Selection: Selecting the Architecture of the Wavelet Network......Page 134
5.5.2.3 Initializing and Training the Wavelet Network......Page 135
5.5.2.4 The Wavelet Neural Networks Approach: Time-Dependent Mean Reversion Variable......Page 138
5.6 The Seasonal Variance......Page 144
5.7 Examination of the Residuals......Page 152
5.7.1 Testing the Normality Hypothesis......Page 153
5.7.2 In-Sample Comparison......Page 156
5.7.3 Testing Alternative Distributions for the Residuals......Page 160
5.8 The Forecasting Ability of the Daily Models......Page 164
5.9 Conclusions......Page 176
References......Page 177
6.1 Introduction......Page 179
6.2 Temperature Derivatives Traded in the CME......Page 180
6.3 Solving the Temperature Stochastic Differential Equation......Page 181
6.4 Pricing Under the Normal Assumption......Page 185
6.4.1 CAT and Pacific Rim: Futures and Options......Page 186
6.4.2 HDD and CDD Indices: Futures and Options......Page 191
6.5 Pricing Under the Assumption of a Lévy Noise Process......Page 196
6.6 The Market Price of Risk......Page 202
6.7 Conclusions......Page 203
References......Page 204
7.1 Introduction......Page 205
7.2 Numerical Weather Prediction......Page 207
7.3 Ensemble Forecasts......Page 208
7.4 Probabilistic Forecasts and Scenario Analysis......Page 209
7.5 Meteorological Forecasts and Pricing......Page 212
7.6 Conclusions......Page 213
References......Page 214
8.1 Introduction......Page 216
8.2 Weather Risk Management and the Geographical/Spatial Risk......Page 217
8.2.1 A Spatial Model for Temperature......Page 221
8.3 Weather Risk Management and the Basis Risk......Page 222
8.4 Conclusions......Page 226
References......Page 227
9.1 Introduction......Page 229
9.2 Modeling the Daily Average Wind Speed......Page 231
9.2.1 The Linear ARMA Model......Page 234
9.2.2 Wavelet Networks for Wind Speed Modeling......Page 237
9.2.3 Forecasting Daily Average Wind Speeds......Page 240
9.3 Pricing Wind Derivatives......Page 243
9.3.1 The Cumulative Average Wind Speed Index......Page 245
9.3.2 The Nordix Wind Speed Index......Page 247
9.4 Conclusions......Page 248
References......Page 249
10.1 Introduction......Page 252
10.2.1 Annual Rainfall......Page 255
10.2.2 Monthly Rainfall......Page 256
10.2.3 Daily Rainfall......Page 258
10.3 A Daily Rainfall Process......Page 260
10.3.1.1 A Two-State, First-Order Markov Chain......Page 261
10.3.1.2 A Higher-Order Markov Chain......Page 264
10.3.1.3 Selecting the Order of the Markov Chain......Page 265
10.3.1.4 An Example of Selecting the Order of the Markov Chain......Page 266
10.3.1.5 Time-Varying Transition Probabilities......Page 267
10.3.2 Magnitude Modeling......Page 269
10.3.2.1 The Gamma Distribution......Page 270
10.3.2.2 The Exponential Distribution......Page 272
10.3.2.4 An Example of Magnitude Modeling......Page 273
10.4 Pricing Precipitation Derivatives......Page 274
10.4.1 Indifference Pricing for Rainfall Derivatives......Page 275
10.4.2 Limitations of Indifference Pricing Method......Page 277
10.4.3 Hedging Effectiveness......Page 278
10.5 Conclusions......Page 279
References......Page 280
A.1 Introduction\r......Page 282
A.2.1 Structure of a Wavelet Network\r......Page 284
A.2.2 Initialization of the Parameters of the Network\r......Page 285
A.2.3 Training a Wavelet Network with Back-Propagation\r......Page 288
A.3 Model Selection for Weather Time-Series Modeling\r......Page 289
A.4 Selecting the Significant Lags of the Weather Variables\r......Page 291
A.4.1 An Algorithm for Selecting the Significant Lags in Modeling of Weather Processes\r......Page 292
A.5 Modeling the Uncertainty of the Weather Predictions\r......Page 294
A.5.1 Confidence Intervals\r......Page 296
A.5.2 Prediction Intervals\r......Page 298
A.6 Conclusions\r......Page 299
B.1 Partial Derivatives w.r.t. the Bias Term\r......Page 303
B.4 Partial Derivatives w.r.t. the Translation Parameters\r......Page 304
B.6 Partial Derivatives w.r.t. the Input Variables\r......Page 305
Index......Page 306