VaR Methodology for Non-Gaussian Finance

Marine Habart-Corlosquet is a Qualified and Certified Actuary at BNP Paribas Cardif, Paris, France. She is co-director of EURIA (Euro-Institut d'Actuariat, University of West Brittany, Brest, France), and associate researcher at Telecom Bretagne (Brest, France) as well as a board member of the French Institute of Actuaries. She teaches at EURIA, Telecom Bretagne and Ecole Centrale Paris (France). Her main research interests are pandemics, Solvency II internal models and ALM issues for insurance companies.Jacques Janssen is now Honorary Professor at the Solvay Business School (ULB) in Brussels, Belgium, having previously taught at EURIA (Euro-Institut d'Actuariat, University of West Brittany, Brest, France) and Telecom Bretagne (Brest, France) as well as being a director of Jacan Insurance and Finance Services, a consultancy and training company.Raimondo Manca is Professor of mathematical methods applied to economics, finance and actuarial science at University of Roma "La Sapienza" in Italy. He is associate editor for the journal Methodology and Computing in Applied Probability. His main research interests are multidimensional linear algebra, computational probability, application of stochastic processes to economics, finance and insurance and simulation models.

• INTRODUCTION ixCHAPTER 1. USE OF VALUE-AT-RISK (VAR) TECHNIQUES FOR SOLVENCY II, 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 assets 32CHAPTER 3. VAR EXTENSIONS FROM GAUSSIAN FINANCE TO NON-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 MODELS 1155.1. 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 homogeneous environment 147CONCLUSION 159BIBLIOGRAPHY 161INDEX 165