Modeling and Pricing in Financial Markets for Weather Derivatives

Modeling and Pricing in Financial Markets for Weather Derivatives

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Overview

Modeling and Pricing in Financial Markets for Weather Derivatives by Jurate Saltyte-benth, Fred Espen Benth, Jurate Saltyte-Benth

Weather derivatives provide a tool for weather risk management, and the markets for these exotic financial products are gradually emerging in size and importance. This unique monograph presents a unified approach to the modeling and analysis of such weather derivatives, including financial contracts on temperature, wind and rain. Based on a deep statistical analysis of weather factors, sophisticated stochastic processes are introduced modeling the time and space dynamics. Applying ideas from the modern theory of mathematical finance, weather derivatives are priced, and questions of hedging analyzed. The treatise contains an in-depth analysis of typical weather contracts traded at the Chicago Mercantile Exchange (CME), including so-called CDD and HDD futures. The statistical analysis of weather variables is based on a large data set from Lithuania. The monograph includes the research done by the authors over the last decade on weather markets. Their work has gained considerable attention, and has been applied in many contexts.

Product Details

ISBN-13: 9789814401845
Publisher: World Scientific Publishing Company, Incorporated
Publication date: 10/28/2012
Series: Advanced Series On Statistical Science And Applied Probability Series
Pages: 256
Product dimensions: 6.10(w) x 9.10(h) x 0.70(d)

Table of Contents

Preface vii

1 Financial markets for weather 1

1.1 The use of weather derivatives 1

1.2 Markets for weather derivatives 4

1.2.1 Temperature derivatives 4

1.2.2 Derivatives on wind speed 7

1.2.3 Precipitation derivatives 8

1.2.4 Other weather derivatives 9

1.3 A brief outlook of the monograph 11

Statistics of weather 15

2 Data description and exploratory analysis 17

2.1 Data 17

2.2 Temperature 18

2.3 Wind 19

2.4 Precipitation 22

2.5 Spatial statistics and spatial-temporal modelling 24

2.6 Stochastic weather modelling - literature overview 29

2.6.1 Temperature 30

2.6.2 Wind 31

2.6.3 Precipitation 33

3 Spatial-temporal modelling 35

3.1 The modelling approach 35

3.2 Spatial-temporal model for temperature and wind speed 37

3.2.1 Marginal modelling of temperature and wind speed 39

3.2.2 Spatial modelling of temperature and wind speed 40

3.2.3 Estimation of the marginal temperature model 40

3.2.4 Estimation of spatial temperature model 48

3.2.5 A critical view on temporal temperature modelling 51

3.2.6 Estimation of wind speed model 54

3.3 Temporal modelling of precipitation 66

3.3.1 Estimation of precipitation time series model 67

3.3.2 Validation of precipitation time series model 70

Weather derivatives 75

4 Continuous-time models for temperature and wind speed 77

4.1 CARMA models 77

4.2 Simulation of CARMA processes 82

4.3 Linking CARMA to ARMA 85

4.4 Recovering the states I: the Kalman filter 88

4.5 Recovering the states II: an approximative L1-filter 91

4.6 CARMA models for temperature and wind speed 96

4.6.1 A model for temperature 97

4.6.2 A model for wind speed 99

4.7 Speed of reversion to the mean: the half-life 103

5 Pricing of forward contracts on temperature and wind speed 107

5.1 Theory on pricing forwards 107

5.1.1 Pricing by burn analysis 110

5.2 A structure preserving class of measure changes 111

5.3 Pricing temperature forwards 118

5.4 Analysis of temperature futures prices 124

5.4.1 Temperature futures prices and the states of temperature 124

5.4.2 The theoretical risk premium of temperature 128

5.4.3 The Samuelson effect 132

5.5 Pricing wind speed forwards 134

6 Extensions of temperature and wind speed models 139

6.1 Stochastic temperature volatility 139

6.2 Brownian semistationary processes 143

6.3 Fractional models 147

7 Options on temperature and wind 157

7.1 Options on temperature futures 157

7.2 Options on wind speed futures 166

7.3 Geographical hedging 170

7.3.1 A simple spatial-temporal model for temperature 172

7.3.2 Computation of the optimal geographical hedge 174

8 Precipitation derivatives 179

8.1 A continuous-time model for precipitation 179

8.1.1 A class of independent increment processes 180

8.1.2 A stochastic model of precipitation 182

8.2 Pricing derivatives on precipitation 188

8.2.1 The Esscher transform for independent increment processes 189

8.2.2 Pricing 192

9 Utility-based approaches to pricing weather derivatives 197

9.1 Indifference pricing 197

9.1.1 Application to the pricing of rainfall derivatives 209

9.2 Fair pricing by benchmarking to a reference index 214

9.3 Pricing by marginal utility 216

9.4 The equilibrium approach by Cao and Wei 226

Appendix A List of abbreviations 229

Bibliography 231

Index 241

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