Handbook of Heavy Tailed Distributions in Finance

Table of contents

1. Cover image
2. Title page
3. Table of Contents
4. Copyright page
5. Introduction to the Series
6. Contents of the Handbook
7. Preface
8. Chapter 1: Heavy Tails in Finance for Independent or Multifractal Price Increments
   1. Abstract
   2. 1 Introduction: A path that led to model price by Brownian motion (Wiener or fractional) of a multifractal trading time
   3. 2 Background: the Bernoulli binomial measure and two random variants: shuffled and canonical
   4. 3 Definition of the two-valued canonical multifractals
   5. 4 The limit random variable Ω = µ ([0,1]), its distribution and the star functionalequation
   6. 5 The function τ(q): motivation and form of the graph
   7. 6 When u > 1, the moment > 1, the moment EΩq diverges if q exceeds a critical exponent qcritsatisfying τ(q) = 0; Ω follows a power-law distribution of exponent qcrit
   8. 7 The quantity α: the original Hölder exponent and beyond
   9. 8 The full function f(α) and the function ρ(α)
   10. 9 The fractal dimension D = τ′(1) = 2[– pu log2 u – (1 – p)v log2 v] and multifractal concentration
   11. 10 A noteworthy and unexpected separation of roles, between the “dimensionspectrum” and the total mass Ω; the former is ruled by the accessible α forwhich f(α) &gt; 0, the latter, by the inaccessible ) > 0, the latter, by the inaccessible α for which f(α) &lt; 0) < 0
   12. 11 A broad form of the multifractal formalism that allows α &lt; 0 and < 0 and f(α) &lt; 0) < 0
   13. Acknowledgments
9. Chapter 2: Financial Risk and Heavy Tails
   1. Abstract
   2. Contents
   3. 1 Introduction
   4. 2 Historical perspective
   5. 3 Value at risk
   6. 4 Risk measures
   7. 5 Portfolios and dependence
   8. 6 Univariate extreme value theory
   9. 7 Stable Paretian models
   10. Acknowledgments
10. Chapter 3: Modeling Financial Data with Stable Distributions
    1. Abstract
    2. 1 Basic facts about stable distribution
    3. 2 Appropriateness of stable models
    4. 3 Computation, simulation, estimation and diagnostics
    5. 4 Applications to financial data
    6. 5 Multivariate stable distributions
    7. 6 Multivariate computation, simulation, estimation and diagnostics
    8. 7 Multivariate application
    9. 8 Classes of multivariate stable distributions
    10. 9 Operator stable distributions
    11. 10 Discussion
11. Chapter 4: Statistical issues in modeling multivariate stable portfolios
    1. Abstract
    2. 1 Introduction
    3. 2 Multivariate stable laws
    4. 3 Estimation of the index of stability
    5. 4 Estimation of the stable spectral measure
    6. 5 Estimation of the scale parameter
    7. 6 Extensions to other stable models
    8. 7 Applications
    9. Acknowledgment
12. Chapter 5: Jump-diffusion models
    1. Abstract
    2. 1 Introduction
    3. 2 Preliminaries
    4. 3 Market models with jump-diffusions
    5. 4 Martingale measures: Existence and uniqueness (Market price of risk and market completion)
    6. 5 Hedging jump-diffusion market models
    7. 6 Pricing in jump-diffusion models
13. Chapter 6: Hyperbolic Processes in Finance
    1. Abstract
    2. 1 Hyperbolic and related distributions
    3. 2 Lévy processes
    4. 3 Stochastic differential equations
    5. 4 Stochastic volatility models
    6. Acknowledgment
    7. Appendix
14. Chapter 7: Stable Modeling of Market and Credit Value at Risk
    1. Abstract
    2. 1 Introduction
    3. 2 “Normal” modeling of VaR
    4. 3 A finance-oriented description of stable distributions
    5. 4 VaR estimates for stable distributed financial returns
    6. 5 Stable modeling and risk assessment for individual credit returns
    7. 6 Portfolio credit risk for independent credit returns
    8. 7 Stable modeling of portfolio risk for symmetric dependent credit returns
    9. 8 Stable modeling of portfolio risk for skewed dependent credit returns
    10. 9 One-factor model of portfolio credit risk
    11. 10 Credit risk evaluation for portfolio assets
    12. 11 Portfolio credit risk
    13. 12 Conclusions
    14. Appendix A Stable modeling of credit returns in figures
    15. Appendix B Tables
    16. Appendix C OLS credit risk evaluation for portfolio assets in figures
    17. Appendix D GARCH credit risk evaluation for portfolio assets in figures
    18. Acknowledgments
15. Chapter 8: Modelling dependence with copulas and applications to risk management
    1. 1 Introduction
    2. 2 Copulas
    3. 3 Dependence concepts
    4. 4 Marshall-Olkin copulas
    5. 5 Elliptical copulas
    6. 6 Archimedean copulas
    7. 7 Modelling extremal events in practice
16. Chapter 9: Prediction of Financial Downside-Risk with Heavy-Tailed Conditional Distributions
    1. Abstract
    2. 1 Introduction
    3. 2 GARCH-stable processes
    4. 3 Modeling exchange-rate returns
    5. 4 Prediction of densities and downside risk
    6. 5 Conclusions
17. Chapter 10: Stable Non-Gaussian Models for Credit Risk Management
    1. Abstract
    2. 1 Stable modeling in credit risk – recent advances
    3. 2 A one-factor model for stable credit returns
    4. 3 Comparison of empirical results
    5. 4 The detection and measurement of long-range dependence
    6. 5 Conclusion
18. Chapter 11: Multifactor stochastic variance models in risk management Maximum entropy approach and Lévy processes*
    1. Abstract
    2. 1 Review of market risk models
    3. 2 Single-factor stochastic variance model
    4. 3 Multifactor stochastic variance model
    5. Acknowledgment
19. Chapter 12: Modelling the Term Structure of Monetary Rates*
    1. Abstract
    2. 1 Introduction
    3. 2 The mathematical framework
    4. 3 The tree representation
    5. 4 The econometric analysis
    6. 5 Conclusions
20. Chapter 13: Asset Liability Management: A Review and Some New Results in the Presence of Heavy Tails
    1. Abstract
    2. 1 Introduction
    3. Part I: Review of the stochastic programming ALM literature
    4. Part II: Stable asset allocation
21. Chapter 14: Portfolio Choice Theory With Non-Gaussian Distributed Returns
    1. Abstract
    2. 1 Introduction
    3. 2 Choices determined by a finite number of parameters
    4. 3 The asymptotic distributional classification of portfolio choices
    5. 4 A first comparison between the normal multivariate distributional assumption and the stable sub-Gaussian one
    6. 5 Conclusions
    7. Acknowledgment
    8. Appendix A: Proofs
    9. Appendix B: Tables
22. Chapter 15: Portfolio Modeling With Heavy Tailed Random Vectors
    1. Abstract
    2. 1 Introduction
    3. 2 Heavy tails
    4. 3 Central limit theorems
    5. 4 Matrix scaling
    6. 5 The spectral decomposition
    7. 6 Sample covariance matrix
    8. 7 Dependent random vectors
    9. 8 Tail estimation
    10. 9 Tail estimator proof for dependent random vectors
    11. 10 Conclusions
23. Chapter 16: Long Range Dependence in Heavy Tailed Stochastic Processes
    1. Abstract
    2. 1 Introduction
    3. 2 What is long range dependence?
    4. 3 Tails and rare events
    5. 4 Some classes of heavy tailed processes
    6. 5 Rare events, associated functionals and long range dependence
24. Author Index
25. Subject Index