VaR Methodology for Non-Gaussian Finance
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...
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| Main Authors: | , , |
|---|---|
| Format: | eBook Book |
| Language: | English |
| Published: |
Newark
John Wiley & Sons, Incorporated
2013
ISTE Ltd/John Wiley and Sons Inc Wiley-Blackwell ISTE Press Wiley-ISTE |
| Edition: | 1 |
| Series: | Focus series in finance, business and management |
| Subjects: | |
| ISBN: | 1848214642, 9781848214644 |
| Online Access: | Get full text |
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Table of Contents:
- Cover -- Title Page -- Contents -- INTRODUCTION -- CHAPTER 1. USE OF VALUE-AT-RISK (VAR) TECHNIQUES FOR SOLVENCY II, BASEL II AND III -- 1.1. Basic notions of VaR -- 1.1.1. Definition -- 1.1.2. Calculation methods -- 1.1.3. Advantages and limits -- 1.2. The use of VaR for insurance companies -- 1.2.1. Regulatory approach -- 1.2.2. Risk profile approach -- 1.3. The use of VaR for banks -- 1.3.1. Basel II -- 1.3.2. Basel III -- 1.4. Conclusion -- CHAPTER 2. CLASSICAL VALUE-AT-RISK (VAR) METHODS -- 2.1. Introduction -- 2.2. Risk measures -- 2.3. General form of the VaR -- 2.4. VaR extensions: tail VaR and conditional VaR -- 2.5. VaR of an asset portfolio -- 2.5.1. VaR methodology -- 2.6. A simulation example: the rates of investment of assets -- CHAPTER 3. VAR EXTENSIONS FROM GAUSSIAN FINANCE TO NON-GAUSSIAN FINANCE -- 3.1. Motivation -- 3.2. The normal power approximation -- 3.3. VaR computation with extreme values -- 3.3.1. Extreme value theory -- 3.3.2. VaR values -- 3.3.3. Comparison of methods -- 3.3.4. VaR values in extreme theory -- 3.4. VaR value for a risk with Pareto distribution -- 3.4.1. Forms of the Pareto distribution -- 3.4.2. Explicit forms VaR and CVaR in Pareto case -- 3.4.3. Example of computation by simulation -- 3.5. Conclusion -- CHAPTER 4. NEW VAR METHODS OF NON-GAUSSIAN FINANCE -- 4.1. Lévy processes -- 4.1.1. Motivation -- 4.1.2. Notion of characteristic functions -- 4.1.3. Lévy processes -- 4.1.4. Lévy-Khintchine formula -- 4.1.5. Examples of Lévy processes -- 4.1.6. Variance gamma (VG) process -- 4.1.7. Risk neutral measures for Lévy models in finance -- 4.1.8. Particular Lévy processes: Poisson-Brownian model with jumps -- 4.1.9. Particular Lévy processes: Merton model with jumps -- 4.1.10. VaR techniques for Lévy processes -- 4.2. Copula models and VaR techniques -- 4.2.1. Introduction -- 4.2.2. Sklar theorem (1959)
- 4.2.3. Particular case and Fréchet bounds -- 4.2.4. Examples of copula -- 4.2.5. The normal copula -- 4.2.6. Estimation of copula -- 4.2.7. Dependence -- 4.2.8. VaR with copula -- 4.3. VaR for insurance -- 4.3.1. VaR and SCR -- 4.3.2. Particular cases -- CHAPTER 5. NON-GAUSSIAN FINANCE: SEMI-MARKOV MODELS -- 5.1. Introduction -- 5.2. Homogeneous semi-Markov process -- 5.2.1. Basic definitions -- 5.2.2. Basic properties [JAN 09] -- 5.2.3. Particular cases of MRP -- 5.2.4. Asymptotic behavior of SMP -- 5.2.5. Non-homogeneous semi-Markov process -- 5.2.6. Discrete-time homogeneous and non-homogeneous semi-Markov processes -- 5.2.7. Semi-Markov backward processes in discrete time -- 5.2.8. Semi-Markov backward processes in discrete time -- 5.3. Semi-Markov option model -- 5.3.1. General model -- 5.3.2. Semi-Markov Black-Scholes model -- 5.3.3. Numerical application for the semi-Markov Black-Scholes model -- 5.4. Semi-Markov VaR models -- 5.4.1. The environment semi-Markov VaR (ESMVaR) model -- 5.4.2. Numerical applications for the semi-Markov VaR model -- 5.4.3. Semi-Markov extension of the Merton's model -- 5.5. The Semi-Markov Monte Carlo Model in a homogeneous environment -- 5.5.1. Capital at Risk -- 5.5.2. A credit risk example -- CONCLUSION -- BIBLIOGRAPHY -- INDEX