Stochastic modelling of electricity and related markets / Fred Espen Benth, Jūratė Šaltytė Benth, Steen Koekebakker.

Format:

Book

Author/Creator:

Benth, Fred Espen, 1969-

Contributor:

Saltyte Benth, Jurate.

Koekebakker, Steen.

Series:

Advanced series on statistical science & applied probability ; v. 11.

Advanced series on statistical science & applied probability ; v. 11

Language:

English

Subjects (All):

Electric utilities--Mathematical models.

Electric utilities.

Energy industries--Mathematical models.

Energy industries.

Stochastic models.

Physical Description:

xiv, 337 pages : illustrations ; 24 cm.

Place of Publication:

Singapore ; Hackensack, N.J. : World Scientific, [2008]

Summary:

The markets for electricity, gas and temperature have distinctive features, which provide the focus for countless studies. For instance, electricity and gas prices may soar several magnitudes above their normal levels within a short time due to imbalances in supply and demand, yielding what is known as spikes in the spot prices. The markets are also largely influenced by seasons, since power demand for heating and cooling varies over the year. The incompleteness of the markets, due to nonstorability of electricity and temperature as well as limited storage capacity of gas, makes spot-forward hedging impossible. Moreover, futures contracts are typically settled over a time period rather than at a fixed date. All these aspects of the markets create new challenges when analyzing price dynamics of spot, futures and other derivatives.

This book provides a concise and rigorous treatment on the stochastic modelling of energy markets. Ornstein-Uhlenbeck processes are described as the basic modelling tool for spot price dynamics, where innovations are driven by time-inhomogeneous jump processes. Temperature futures are studied based on a continuous higher-order autoregressive model for the temperature dynamics. The theory presented here pays special attention to the seasonality of volatility and the Samuelson effect. Empirical studies using data from electricity, temperature and gas markets are given to link theory to practice. Book jacket.

Contents:

1 A Survey of Electricity and Related Markets 1

1.1 The electricity markets 3

1.1.1 Electricity contracts with physical delivery 3

1.1.2 Financial electricity contracts 5

1.2 The gas market 8

1.2.1 Futures and options on gas 10

1.3 The temperature market 11

1.4 Other related energy markets 14

1.5 Stochastic modelling of energy markets 18

1.5.1 Spot price modelling 19

1.5.2 Forward and swap pricing in electricity and related markets 24

2 Stochastic Analysis for Independent Increment Processes 37

2.2 Stochastic integration with respect to martingales 41

2.3 Random jump measures and stochastic integration 43

2.4 The Levy-Kintchine decomposition and semimartingales 45

2.5 The Ito Formula for semimartingales 48

2.6 Examples of independent increment processes 49

2.6.1 Time-inhomogeneous compound Poisson process 49

2.6.2 Models based on the generalized hyperbolic distributions 51

2.6.3 Models based on the Variance-Gamma and CGMY distributions 55

3 Stochastic Models for the Energy Spot Price Dynamics 59

3.2 Spot price modelling with Ornstein-Uhlenbeck processes 60

3.2.1 Geometric models 66

3.2.2 Arithmetic models 74

3.3 The autocorrelation function of multi-factor Ornstein-Uhlenbeck processes 78

3.4 Simulation of stationary Ornstein-Uhlenbeck processes: a case study with the arithmetic spot model 82

4 Pricing of Forwards and Swaps Based on the Spot Price 89

4.1 Risk-neutral forward and swap price modelling 89

4.1.1 Risk-neutral probabilities and the Esscher transform 95

4.1.2 The Esscher transform for some specific models 99

4.2 Currency conversion for forward and swap prices 100

4.3 Pricing of forwards 104

4.3.1 The geometric case 104

4.3.2 The arithmetic case 114

4.4 Pricing of swaps 118

4.4.1 The geometric case 119

4.4.2 The arithmetic case 122

5 Applications to the Gas Markets 129

5.1 Modelling the gas spot price 129

5.1.1 Empirical analysis of UK gas spot prices 130

5.1.2 Residuals modelled as a mixed jump-diffusion process 136

5.1.3 NIG distributed residuals 139

5.2 Pricing of gas futures 142

5.3 Inference for multi-factor processes 146

5.3.1 Kalman filtering 147

5.3.2 Inference using forward and swap data 150

6 Modelling Forwards and Swaps Using the Heath-Jarrow-Morton Approach 155

6.1 The HJM modelling idea for forward contracts 156

6.2 HJM modelling of forwards 160

6.3 HJM modelling of swaps 164

6.3.1 Swap models based on forwards 168

6.4 The market models 172

6.4.1 Modelling with jump processes 176

7 Constructing Smooth Forward Curves in Electricity Markets 181

7.1 Swap and forward prices 183

7.1.1 Basic relationships 183

7.1.2 A continuous seasonal forward curve 184

7.2 Maximum smooth forward curve 187

7.2.1 A smooth forward curve constrained by closing prices 187

7.2.2 A smooth forward curve constrained by bid and ask spreads 190

7.3 Putting the algorithm to work 191

7.3.1 Nord Pool example I: A smooth curve 191

7.3.2 Nord Pool example II: Preparing a data set and analysing volatility 195

8 Modelling of the Electricity Futures Market 203

8.1 The Nord Pool market and financial contracts 205

8.2 Preparing data sets 206

8.3 Descriptive statistics 208

8.4 A market model for electricity futures 214

8.5 Principal component analysis 215

8.5.1 Principal component analysis of the total data set 217

8.5.2 Principal component analysis for individual market segments 220

8.6 Estimating a parametric multi-factor market model 224

8.6.1 Seasonal volatility 226

8.6.2 Maturity volatilities 227

8.7 Normalised logreturns and heavy tails 231

9 Pricing and Hedging of Energy Options 237

9.1 Pricing and hedging options on forwards and swaps 238

9.1.1 The case of no jumps - the Black-76 Formula 238

9.1.2 The case of jumps 247

9.2 Exotic Options 254

9.2.1 Spread options 254

9.2.2 Asian options 260

9.3 Case Study: Valuation of spark spread options - a direct approach 262

9.3.1 Modelling and analysis of spark spread options 264

9.3.2 Empirical analysis of UK gas and electricity spread 268

10 Analysis of Temperature Derivatives 277

10.1 Some preliminaries on temperature futures 277

10.2 Modelling the dynamics of temperature 280

10.2.1 The CAR(p) model with seasonality 281

10.2.2 A link to time series 283

10.3 Empirical analysis of Stockholm temperature dynamics 285

10.3.1 Description of the data 285

10.3.2 Estimating the CAR(p) models 287

10.3.2.1 Fitting an AR(1) model 289

10.3.2.2 Fitting an AR(3) model 296

10.3.2.3 Identification of the parameters in the CAR(p) model 300

10.4 Temperature derivatives pricing 301

10.4.1 CAT futures 302

10.4.2 HDD/CDD futures 305

10.4.3 Frost Day index futures 312

10.4.4 Application to futures on temperatures in Stockholm 314.

Notes:

Includes bibliographical references (pages 321-331) and index.

ISBN:

9789812812308

981281230X

OCLC:

191024116