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Full Description
With the impact of the recent financial crises, more attention must be given to new models in finance rejecting "Black-Scholes-Samuelson" assumptions leading to what is called non-Gaussian finance. With the growing importance of Solvency II, Basel II and III regulatory rules for insurance companies and banks, value at risk (VaR) - one of the most popular risk indicator techniques plays a fundamental role in defining appropriate levels of equities. The aim of this book is to show how new VaR techniques can be built more appropriately for a crisis situation.
VaR methodology for non-Gaussian finance looks at the importance of VaR in standard international rules for banks and insurance companies; gives the first non-Gaussian extensions of VaR and applies several basic statistical theories to extend classical results of VaR techniques such as the NP approximation, the Cornish-Fisher approximation, extreme and a Pareto distribution. Several non-Gaussian models using Copula methodology, Lévy processes along with particular attention to models with jumps such as the Merton model are presented; as are the consideration of time homogeneous and non-homogeneous Markov and semi-Markov processes and for each of these models.
Contents
1. Use of Value-at-Risk (VaR) Techniques for Solvency II, Basel II and III.
2. Classical Value-at-Risk (VaR) Methods.
3. VaR Extensions from Gaussian Finance to Non-Gaussian Finance.
4. New VaR Methods of Non-Gaussian Finance.
5. Non-Gaussian Finance: Semi-Markov Models.
Contents
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
