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 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, L vy 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.

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.Contents1. 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.

INTRODUCTION ixCHAPTER 1. USE OF VALUE-AT-RISK (VAR) TECHNIQUES FOR SOLVENCYII, BASEL II AND III 11.1. Basic notions of VaR 11.2. The use of VaR for insurance companies 61.3. The use of VaR for banks 131.4. Conclusion 16CHAPTER 2. CLASSICAL VALUE-AT-RISK (VAR) METHODS 172.1. Introduction 172.2. Risk measures 182.3. General form of the VaR 192.4. VaR extensions: tail VaR and conditional VaR 252.5. VaR of an asset portfolio 282.6. A simulation example: the rates of investment of assets32CHAPTER 3. VAR EXTENSIONS FROM GAUSSIAN FINANCE TONON-GAUSSIAN FINANCE 353.1. Motivation 353.2. The normal power approximation 373.3. VaR computation with extreme values 403.4. VaR value for a risk with Pareto distribution 563.5. Conclusion 62CHAPTER 4. NEW VAR METHODS OF NON-GAUSSIAN FINANCE 634.1. Lévy processes 63 model with jumps 764.2. Copula models and VaR techniques 904.3. VaR for insurance 109CHAPTER 5. NON-GAUSSIAN FINANCE: SEMI-MARKOV MODELS1155.1. Introduction 1155.2. Homogeneous semi-Markov process 1165.3. Semi-Markov option model 1395.4. Semi-Markov VaR models 1435.5. The Semi-Markov Monte Carlo Model in a homogeneousenvironment 147CONCLUSION 159BIBLIOGRAPHY 161INDEX 165