Skip to main content

VaR Methodology for Non-Gaussian Finance

VaR Methodology for Non-Gaussian Finance

Marine Habart-Corlosquet, Jacques Janssen, Raimondo Manca

ISBN: 978-1-848-21464-4

Apr 2013, Wiley-ISTE

176 pages

In Stock

$86.00

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.

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