Var Methodology for Non-Gaussian Finance (Hardcover)

INTRODUCTION ix

CHAPTER 1. USE OF VALUE-AT-RISK (VAR) TECHNIQUES FOR SOLVENCY II, BASEL II AND III 1

1.1. Basic notions of VaR 1

1.2. The use of VaR for insurance companies 6

1.3. The use of VaR for banks 13

1.4. Conclusion 16

CHAPTER 2. CLASSICAL VALUE-AT-RISK (VAR) METHODS 17

2.1. Introduction 17

2.2. Risk measures 18

2.3. General form of the VaR 19

2.4. VaR extensions: tail VaR and conditional VaR 25

2.5. VaR of an asset portfolio 28

2.6. A simulation example: the rates of investment of assets 32

CHAPTER 3. VAR EXTENSIONS FROM GAUSSIAN FINANCE TO NON-GAUSSIAN FINANCE 35

3.1. Motivation 35

3.2. The normal power approximation 37

3.3. VaR computation with extreme values 40

3.4. VaR value for a risk with Pareto distribution 56

3.5. Conclusion 62

CHAPTER 4. NEW VAR METHODS OF NON-GAUSSIAN FINANCE 63

4.1. Lévy processes 63 model with jumps 76

4.2. Copula models and VaR techniques 90

4.3. VaR for insurance 109

CHAPTER 5. NON-GAUSSIAN FINANCE: SEMI-MARKOV MODELS 115

5.1. Introduction 115

5.2. Homogeneous semi-Markov process 116

5.3. Semi-Markov option model 139

5.4. Semi-Markov VaR models 143

5.5. The Semi-Markov Monte Carlo Model in a homogeneous environment 147

CONCLUSION 159

BIBLIOGRAPHY 161

INDEX 165