Stochastic Modelling of Electricity and Related Markets

by Benth, Fred Espen; Benth, Jurate Saltyte; Koekebakker, Steen

• ISBN13: 9789812812308
• ISBN10: 981281230X
• Format: Hardcover
• Copyright: 2008-04-14
• Publisher: World Scientific Pub Co Inc

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.

Table of Contents

Preface	p. vii
A Survey of Electricity and Related Markets	p. 1
The electricity markets	p. 3
Electricity contracts with physical delivery	p. 3
Financial electricity contracts	p. 5
The gas market	p. 8
Futures and options on gas	p. 10
The temperature market	p. 11
Other related energy markets	p. 14
Stochastic modelling of energy markets	p. 18
Spot price modelling	p. 19
Forward and swap pricing in electricity and related markets	p. 24
Outline of the book	p. 32
Stochastic Analysis for Independent Increment Processes	p. 37
Definitions	p. 37
Stochastic integration with respect to martingales	p. 41
Random jump measures and stochastic integration	p. 43
The Levy-Kintchine decomposition and semimartingales	p. 45
The Ito Formula for semimartingales	p. 48
Examples of independent increment processes	p. 49
Time-inhomogeneous compound Poisson process	p. 49
Models based on the generalized hyperbolic distributions	p. 51
Models based on the Variance-Gamma and CGMY distributions	p. 55
Stochastic Models for the Energy Spot Price Dynamics	p. 59
Introduction	p. 59
Spot price modelling with Ornstein-Uhlenbeck processes	p. 60
Geometric models	p. 66
Arithmetic models	p. 74
The autocorrelation function of multi-factor Ornstein-Uhlenbeck processes	p. 78
Simulation of stationary Ornstein-Uhlenbeck processes: a case study with the arithmetic spot model	p. 82
Pricing of Forwards and Swaps Based on the Spot Price	p. 89
Risk-neutral forward and swap price modelling	p. 89
Risk-neutral probabilities and the Esscher transform	p. 95
The Esscher transform for some specific models	p. 99
Currency conversion for forward and swap prices	p. 100
Pricing of forwards	p. 104
The geometric case	p. 104
The arithmetic case	p. 114
Pricing of swaps	p. 118
The geometric case	p. 119
The arithmetic case	p. 122
Applications to the Gas Markets	p. 129
Modelling the gas spot price	p. 129
Empirical analysis of UK gas spot prices	p. 130
Residuals modelled as a mixed jump-diffusion process	p. 136
NIG distributed residuals	p. 139
Pricing of gas futures	p. 142
Inference for multi-factor processes	p. 146
Kalman filtering	p. 147
Inference using forward and swap data	p. 150
Modelling Forwards and Swaps Using the Heath-Jarrow-Morton Approach	p. 155
The HJM modelling idea for forward contracts	p. 156
HJM modelling of forwards	p. 160
HJM modelling of swaps	p. 164
Swap models based on forwards	p. 168
The market models	p. 172
Modelling with jump processes	p. 176
Constructing Smooth Forward Curves in Electricity Markets	p. 181
Swap and forward prices	p. 183
Basic relationships	p. 183
A continuous seasonal forward curve	p. 184
Maximum smooth forward curve	p. 187
A smooth forward curve constrained by closing prices	p. 187
A smooth forward curve constrained by bid and ask spreads	p. 190
Putting the algorithm to work	p. 191
Nord Pool example I: A smooth curve	p. 191
Nord Pool example II: Preparing a data set and analysing volatility	p. 195
Modelling of the Electricity Futures Market	p. 203
The Nord Pool market and financial contracts	p. 205
Preparing data sets	p. 206
Descriptive statistics	p. 208
A market model for electricity futures	p. 214
Principal component analysis	p. 215
Principal component analysis of the total data set	p. 217
Principal component analysis for individual market segments	p. 220
Estimating a parametric multi-factor market model	p. 224
Seasonal volatility	p. 226
Maturity volatilities	p. 227
Normalised logreturns and heavy tails	p. 231
Final remarks	p. 235
Pricing and Hedging of Energy Options	p. 237
Pricing and hedging options on forwards and swaps	p. 238
The case of no jumps - the Black-76 Formula	p. 238
The case of jumps	p. 247
Exotic Options	p. 254
Spread options	p. 254
Asian options	p. 260
Case Study: Valuation of spark spread options - a direct approach	p. 262
Modelling and analysis of spark spread options	p. 264
Empirical analysis of UK gas and electricity spread	p. 268
Analysis of Temperature Derivatives	p. 277
Some preliminaries on temperature futures	p. 277
Modelling the dynamics of temperature	p. 280
The CAR(p) model with seasonality	p. 281
A link to time series	p. 283
Empirical analysis of Stockholm temperature dynamics	p. 285
Description of the data	p. 285
Estimating the CAR(p) models	p. 287
Fitting an AR(1) model	p. 289
Fitting an AR(3) model	p. 296
Identification of the parameters in the CAR(p) model	p. 300
Temperature derivatives pricing	p. 301
CAT futures	p. 302
HDD/CDD futures	p. 305
Frost Day index futures	p. 312
Application to futures on temperatures in Stockholm	p. 314
List of abbreviations	p. 319
Bibliography	p. 321
Index	p. 333
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