Quantitative risk management concepts techniques and tools 1st edition by Alexander McNeil, Rüdiger Frey, Paul Embrechts ISBN‎ 0691166277‎ 978-0691166278

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ISBN 10:‎ 0691166277
ISBN 13:‎ 978-0691166278
Author:  Alexander McNeil, Rüdiger Frey, Paul Embrechts 

This book provides the most comprehensive treatment of the theoretical concepts and modelling techniques of quantitative risk management. Whether you are a financial risk analyst, actuary, regulator or student of quantitative finance, Quantitative Risk Management gives you the practical tools you need to solve real-world problems.

Describing the latest advances in the field, Quantitative Risk Management covers the methods for market, credit and operational risk modelling. It places standard industry approaches on a more formal footing and explores key concepts such as loss distributions, risk measures and risk aggregation and allocation principles. The book’s methodology draws on diverse quantitative disciplines, from mathematical finance and statistics to econometrics and actuarial mathematics. A primary theme throughout is the need to satisfactorily address extreme outcomes and the dependence of key risk drivers. Proven in the classroom, the book also covers advanced topics like credit derivatives.

• Fully revised and expanded to reflect developments in the field since the financial crisis
• Features shorter chapters to facilitate teaching and learning
• Provides enhanced coverage of Solvency II and insurance risk management and extended treatment of credit risk, including counterparty credit risk and CDO pricing
• Includes a new chapter on market risk and new material on risk measures and risk aggregation

Quantitative risk management concepts techniques and tools 1st Table of contents:

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

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