Efnisyfirlit

• Title
• Copyright
• Dedication
• Contents
• Preface
• I An Introduction to Quantitative Risk Management
• 1 Risk in Perspective
• 1.1 Risk
• 1.1.1 Risk and Randomness
• 1.1.2 Financial Risk
• 1.1.3 Measurement and Management
• 1.2 A Brief History of Risk Management
• 1.2.1 From Babylon to Wall Street
• 1.2.2 The Road to Regulation
• 1.3 The Regulatory Framework
• 1.3.1 The Basel Framework
• 1.3.2 The Solvency II Framework
• 1.3.3 Criticism of Regulatory Frameworks
• 1.4 Why Manage Financial Risk?
• 1.4.1 A Societal View
• 1.4.2 The Shareholder’s View
• 1.5 Quantitative Risk Management
• 1.5.1 The Q in QRM
• 1.5.2 The Nature of the Challenge
• 1.5.3 QRM Beyond Finance
• 2 Basic Concepts in Risk Management
• 2.1 Risk Management for a Financial Firm
• 2.1.1 Assets, Liabilities and the Balance Sheet
• 2.1.2 Risks Faced by a Financial Firm
• 2.1.3 Capital
• 2.2 Modelling Value and Value Change
• 2.2.1 Mapping Risks
• 2.2.2 Valuation Methods
• 2.2.3 Loss Distributions
• 2.3 Risk Measurement
• 2.3.1 Approaches to Risk Measurement
• 2.3.2 Value-at-Risk
• 2.3.3 VaR in Risk Capital Calculations
• 2.3.4 Other Risk Measures Based on Loss Distributions
• 2.3.5 Coherent and Convex Risk Measures
• 3 Empirical Properties of Financial Data
• 3.1 Stylized Facts of Financial Return Series
• 3.1.1 Volatility Clustering
• 3.1.2 Non-normality and Heavy Tails
• 3.1.3 Longer-Interval Return Series
• 3.2 Multivariate Stylized Facts
• 3.2.1 Correlation between Series
• 3.2.2 Tail Dependence
• II Methodology
• 4 Financial Time Series
• 4.1 Fundamentals of Time Series Analysis
• 4.1.1 Basic Definitions
• 4.1.2 ARMA Processes
• 4.1.3 Analysis in the Time Domain
• 4.1.4 Statistical Analysis of Time Series
• 4.1.5 Prediction
• 4.2 GARCH Models for Changing Volatility
• 4.2.1 ARCH Processes
• 4.2.2 GARCH Processes
• 4.2.3 Simple Extensions of the GARCH Model
• 4.2.4 Fitting GARCH Models to Data
• 4.2.5 Volatility Forecasting and Risk Measure Estimation
• 5 Extreme Value Theory
• 5.1 Maxima
• 5.1.1 Generalized Extreme Value Distribution
• 5.1.2 Maximum Domains of Attraction
• 5.1.3 Maxima of Strictly Stationary Time Series
• 5.1.4 The Block Maxima Method
• 5.2 Threshold Exceedances
• 5.2.1 Generalized Pareto Distribution
• 5.2.2 Modelling Excess Losses
• 5.2.3 Modelling Tails and Measures of Tail Risk
• 5.2.4 The Hill Method
• 5.2.5 Simulation Study of EVT Quantile Estimators
• 5.2.6 Conditional EVT for Financial Time Series
• 5.3 Point Process Models
• 5.3.1 Threshold Exceedances for Strict White Noise
• 5.3.2 The POT Model
• 6 Multivariate Models
• 6.1 Basics of Multivariate Modelling
• 6.1.1 Random Vectors and Their Distributions
• 6.1.2 Standard Estimators of Covariance and Correlation
• 6.1.3 The Multivariate Normal Distribution
• 6.1.4 Testing Multivariate Normality
• 6.2 Normal Mixture Distributions
• 6.2.1 Normal Variance Mixtures
• 6.2.2 Normal Mean–Variance Mixtures
• 6.2.3 Generalized Hyperbolic Distributions
• 6.2.4 Empirical Examples
• 6.3 Spherical and Elliptical Distributions
• 6.3.1 Spherical Distributions
• 6.3.2 Elliptical Distributions
• 6.3.3 Properties of Elliptical Distributions
• 6.3.4 Estimating Dispersion and Correlation
• 6.4 Dimension-Reduction Techniques
• 6.4.1 Factor Models
• 6.4.2 Statistical Estimation Strategies
• 6.4.3 Estimating Macroeconomic Factor Models
• 6.4.4 Estimating Fundamental Factor Models
• 6.4.5 Principal Component Analysis
• 7 Copulas and Dependence
• 7.1 Copulas
• 7.1.1 Basic Properties
• 7.1.2 Examples of Copulas
• 7.1.3 Meta Distributions
• 7.1.4 Simulation of Copulas and Meta Distributions
• 7.1.5 Further Properties of Copulas
• 7.2 Dependence Concepts and Measures
• 7.2.1 Perfect Dependence
• 7.2.2 Linear Correlation
• 7.2.3 Rank Correlation
• 7.2.4 Coefficients of Tail Dependence
• 7.3 Normal Mixture Copulas
• 7.3.1 Tail Dependence
• 7.3.2 Rank Correlations
• 7.3.3 Skewed Normal Mixture Copulas
• 7.3.4 Grouped Normal Mixture Copulas
• 7.4 Archimedean Copulas
• 7.4.1 Bivariate Archimedean Copulas
• 7.4.2 Multivariate Archimedean Copulas
• 7.5 Fitting Copulas to Data
• 7.5.1 Method-of-Moments Using Rank Correlation
• 7.5.2 Forming a Pseudo-sample from the Copula
• 7.5.3 Maximum Likelihood Estimation
• 8 Aggregate Risk
• 8.1 Coherent and Convex Risk Measures
• 8.1.1 Risk Measures and Acceptance Sets
• 8.1.2 Dual Representation of Convex Measures of Risk
• 8.1.3 Examples of Dual Representations
• 8.2 Law-Invariant Coherent Risk Measures
• 8.2.1 Distortion Risk Measures
• 8.2.2 The Expectile Risk Measure
• 8.3 Risk Measures for Linear Portfolios
• 8.3.1 Coherent Risk Measures as Stress Tests
• 8.3.2 Elliptically Distributed Risk Factors
• 8.3.3 Other Risk Factor Distributions
• 8.4 Risk Aggregation
• 8.4.1 Aggregation Based on Loss Distributions
• 8.4.2 Aggregation Based on Stressing Risk Factors
• 8.4.3 Modular versus Fully Integrated Aggregation Approaches
• 8.4.4 Risk Aggregation and Fréchet Problems
• 8.5 Capital Allocation
• 8.5.1 The Allocation Problem
• 8.5.2 The Euler Principle and Examples
• 8.5.3 Economic Properties of the Euler Principle
• III Applications
• 9 Market Risk
• 9.1 Risk Factors and Mapping
• 9.1.1 The Loss Operator
• 9.1.2 Delta and Delta–Gamma Approximations
• 9.1.3 Mapping Bond Portfolios
• 9.1.4 Factor Models for Bond Portfolios
• 9.2 Market Risk Measurement
• 9.2.1 Conditional and Unconditional Loss Distributions
• 9.2.2 Variance–Covariance Method
• 9.2.3 Historical Simulation
• 9.2.4 Dynamic Historical Simulation
• 9.2.5 Monte Carlo
• 9.2.6 Estimating Risk Measures
• 9.2.7 Losses over Several Periods and Scaling
• 9.3 Backtesting
• 9.3.1 Violation-Based Tests for VaR
• 9.3.2 Violation-Based Tests for Expected Shortfall
• 9.3.3 Elicitability and Comparison of Risk Measure Estimates
• 9.3.4 Empirical Comparison of Methods Using Backtesting Concepts
• 9.3.5 Backtesting the Predictive Distribution
• 10 Credit Risk
• 10.1 Credit-Risky Instruments
• 10.1.1 Loans
• 10.1.2 Bonds
• 10.1.3 Derivative Contracts Subject to Counterparty Risk
• 10.1.4 Credit Default Swaps and Related Credit Derivatives
• 10.1.5 PD, LGD and EAD
• 10.2 Measuring Credit Quality
• 10.2.1 Credit Rating Migration
• 10.2.2 Rating Transitions as a Markov Chain
• 10.3 Structural Models of Default
• 10.3.1 The Merton Model
• 10.3.2 Pricing in Merton’s Model
• 10.3.3 Structural Models in Practice: EDF and DD
• 10.3.4 Credit-Migration Models Revisited
• 10.4 Bond and CDS Pricing in Hazard Rate Models
• 10.4.1 Hazard Rate Models
• 10.4.2 Risk-Neutral Pricing Revisited
• 10.4.3 Bond Pricing
• 10.4.4 CDS Pricing
• 10.4.5 P versus Q: Empirical Results
• 10.5 Pricing with Stochastic Hazard Rates
• 10.5.1 Doubly Stochastic Random Times
• 10.5.2 Pricing Formulas
• 10.5.3 Applications
• 10.6 Affine Models
• 10.6.1 Basic Results
• 10.6.2 The CIR Square-Root Diffusion
• 10.6.3 Extensions
• 11 Portfolio Credit Risk Management
• 11.1 Threshold Models
• 11.1.1 Notation for One-Period Portfolio Models
• 11.1.2 Threshold Models and Copulas
• 11.1.3 Gaussian Threshold Models
• 11.1.4 Models Based on Alternative Copulas
• 11.1.5 Model Risk Issues
• 11.2 Mixture Models
• 11.2.1 Bernoulli Mixture Models
• 11.2.2 One-Factor Bernoulli Mixture Models
• 11.2.3 Recovery Risk in Mixture Models
• 11.2.4 Threshold Models as Mixture Models
• 11.2.5 Poisson Mixture Models and CreditRisk^+
• 11.3 Asymptotics for Large Portfolios
• 11.3.1 Exchangeable Models
• 11.3.2 General Results
• 11.3.3 The Basel IRB Formula
• 11.4 Monte Carlo Methods
• 11.4.1 Basics of Importance Sampling
• 11.4.2 Application to Bernoulli Mixture Models
• 11.5 Statistical Inference in Portfolio Credit Models
• 11.5.1 Factor Modelling in Industry Threshold Models
• 11.5.2 Estimation of Bernoulli Mixture Models
• 11.5.3 Mixture Models as GLMMs
• 11.5.4 A One-Factor Model with Rating Effect
• 12 Portfolio Credit Derivatives
• 12.1 Credit Portfolio Products
• 12.1.1 Collateralized Debt Obligations
• 12.1.2 Credit Indices and Index Derivatives
• 12.1.3 Basic Pricing Relationships for Index Swaps and CDOs
• 12.2 Copula Models
• 12.2.1 Definition and Properties
• 12.2.2 Examples
• 12.3 Pricing of Index Derivatives in Factor Copula Models
• 12.3.1 Analytics
• 12.3.2 Correlation Skews
• 12.3.3 The Implied Copula Approach
• 13 Operational Risk and Insurance Analytics
• 13.1 Operational Risk in Perspective
• 13.1.1 An Important Risk Class
• 13.1.2 The Elementary Approaches
• 13.1.3 Advanced Measurement Approaches
• 13.1.4 Operational Loss Data
• 13.2 Elements of Insurance Analytics
• 13.2.1 The Case for Actuarial Methodology
• 13.2.2 The Total Loss Amount
• 13.2.3 Approximations and Panjer Recursion
• 13.2.4 Poisson Mixtures
• 13.2.5 Tails of Aggregate Loss Distributions
• 13.2.6 The Homogeneous Poisson Process
• 13.2.7 Processes Related to the Poisson Process
• IV Special Topics
• 14 Multivariate Time Series
• 14.1 Fundamentals of Multivariate Time Series
• 14.1.1 Basic Definitions
• 14.1.2 Analysis in the Time Domain
• 14.1.3 Multivariate ARMA Processes
• 14.2 Multivariate GARCH Processes
• 14.2.1 General Structure of Models
• 14.2.2 Models for Conditional Correlation
• 14.2.3 Models for Conditional Covariance
• 14.2.4 Fitting Multivariate GARCH Models
• 14.2.5 Dimension Reduction in MGARCH
• 14.2.6 MGARCH and Conditional Risk Measurement
• 15 Advanced Topics in Multivariate Modelling
• 15.1 Normal Mixture and Elliptical Distributions
• 15.1.1 Estimation of Generalized Hyperbolic Distributions
• 15.1.2 Testing for Elliptical Symmetry
• 15.2 Advanced Archimedean Copula Models
• 15.2.1 Characterization of Archimedean Copulas
• 15.2.2 Non-exchangeable Archimedean Copulas
• 16 Advanced Topics in Extreme Value Theory
• 16.1 Tails of Specific Models
• 16.1.1 Domain of Attraction of the Fréchet Distribution
• 16.1.2 Domain of Attraction of the Gumbel Distribution
• 16.1.3 Mixture Models
• 16.2 Self-exciting Models for Extremes
• 16.2.1 Self-exciting Processes
• 16.2.2 A Self-exciting POT Model
• 16.3 Multivariate Maxima
• 16.3.1 Multivariate Extreme Value Copulas
• 16.3.2 Copulas for Multivariate Minima
• 16.3.3 Copula Domains of Attraction
• 16.3.4 Modelling Multivariate Block Maxima
• 16.4 Multivariate Threshold Exceedances
• 16.4.1 Threshold Models Using EV Copulas
• 16.4.2 Fitting a Multivariate Tail Model
• 16.4.3 Threshold Copulas and Their Limits
• 17 Dynamic Portfolio Credit Risk Models and Counterparty Risk
• 17.1 Dynamic Portfolio Credit Risk Models
• 17.1.1 Why Dynamic Models of Portfolio Credit Risk?
• 17.1.2 Classes of Reduced-Form Models of Portfolio Credit Risk
• 17.2 Counterparty Credit Risk Management
• 17.2.1 Uncollateralized Value Adjustments for a CDS
• 17.2.2 Collateralized Value Adjustments for a CDS
• 17.3 Conditionally Independent Default Times
• 17.3.1 Definition and Mathematical Properties
• 17.3.2 Examples and Applications
• 17.3.3 Credit Value Adjustments
• 17.4 Credit Risk Models with Incomplete Information
• 17.4.1 Credit Risk and Incomplete Information
• 17.4.2 Pure Default Information
• 17.4.3 Additional Information
• 17.4.4 Collateralized Credit Value Adjustments and Contagion Effects
• Appendix
• A.1 Miscellaneous Definitions and Results
• A.1.1 Type of Distribution
• A.1.2 Generalized Inverses and Quantiles
• A.1.3 Distributional Transform
• A.1.4 Karamata’s Theorem
• A.1.5 Supporting and Separating Hyperplane Theorems
• A.2 Probability Distributions
• A.2.1 Beta
• A.2.2 Exponential
• A.2.3 F
• A.2.4 Gamma
• A.2.5 Generalized Inverse Gaussian
• A.2.6 Inverse Gamma
• A.2.7 Negative Binomial
• A.2.8 Pareto
• A.2.9 Stable
• A.3 Likelihood Inference
• A.3.1 Maximum Likelihood Estimators
• A.3.2 Asymptotic Results: Scalar Parameter
• A.3.3 Asymptotic Results: Vector of Parameters
• A.3.4 Wald Test and Confidence Intervals
• A.3.5 Likelihood Ratio Test and Confidence Intervals
• A.3.6 Akaike Information Criterion
• References
• Index