Quantitative Risk Management: Concepts, Techniques, and Tools / Edition 1 available in Hardcover, eBook
Quantitative Risk Management: Concepts, Techniques, and Tools / Edition 1
- ISBN-10:
- 0691122555
- ISBN-13:
- 9780691122557
- Pub. Date:
- 10/16/2005
- Publisher:
- Princeton University Press
- ISBN-10:
- 0691122555
- ISBN-13:
- 9780691122557
- Pub. Date:
- 10/16/2005
- Publisher:
- Princeton University Press
Quantitative Risk Management: Concepts, Techniques, and Tools / Edition 1
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Overview
The book's methodology draws on diverse quantitative disciplines, from mathematical finance through statistics and econometrics to actuarial mathematics. Main concepts discussed include loss distributions, risk measures, and risk aggregation and allocation principles. A main theme is the need to satisfactorily address extreme outcomes and the dependence of key risk drivers. The techniques required derive from multivariate statistical analysis, financial time series modelling, copulas, and extreme value theory. A more technical chapter addresses credit derivatives. Based on courses taught to masters students and professionals, this book is a unique and fundamental reference that is set to become a standard in the field.
Product Details
ISBN-13: | 9780691122557 |
---|---|
Publisher: | Princeton University Press |
Publication date: | 10/16/2005 |
Series: | Princeton Series in Finance |
Edition description: | Older Edition |
Pages: | 544 |
Product dimensions: | 6.00(w) x 9.25(h) x (d) |
About the Author
Table of Contents
Preface xiii
CHAPTER 1: Risk in Perspective 11.1 Risk 11.1.1 Risk and Randomness 11.1.2 Financial Risk 21.1.3 Measurement and Management 31.2 A Brief History of Risk Management 51.2.1 From Babylon to Wall Street 51.2.2 The Road to Regulation 81.3 The New Regulatory Framework 101.3.1 Basel II 101.3.2 Solvency 2 131.4 Why Manage Financial Risk? 151.4.1 A Societal View 151.4.2 The Shareholder's View 161.4.3 Economic Capital 181.5 Quantitative Risk Management 191.5.1 The Nature of the Challenge 191.5.2 QRM for the Future 22
CHAPTER 2: Basic Concepts in Risk Management 252.1 Risk Factors and Loss Distributions 252.1.1 General Definitions 252.1.2 Conditional and Unconditional Loss Distribution 282.1.3 Mapping of Risks:Some Examples 292.2 Risk Measurement 342.2.1 Approaches to Risk Measurement 342.2.2 Value-at-Risk 372.2.3 Further Comments on VaR 402.2.4 Other Risk Measures Based on Loss Distributions 432.3 Standard Methods for Market Risks 482.3.1 Variance -Covariance Method 482.3.2 Historical Simulation 502.3.3 Monte Carlo 522.3.4 Losses over Several Periods and Scaling 532.3.5 Backtesting 552.3.6 An Illustrative Example 55
CHAPTER 3: Multivariate Models 613.1 Basics of Multivariate Modelling 613.1.1 Random Vectors and Their Distributions 623.1.2 Standard Estimators of Covariance and Correlation 643.1.3 The Multivariate Normal Distribution 663.1.4 Testing Normality and Multivariate Normality 683.2 Normal Mixture Distributions 733.2.1 Normal Variance Mixtures 733.2.2 Normal Mean-Variance Mixtures 773.2.3 Generalized Hyperbolic Distributions 783.2.4 Fitting Generalized Hyperbolic Distributions to Data 813.2.5 Empirical Examples 843.3 Spherical and Elliptical Distributions 893.3.1 Spherical Distributions 893.3.2 Elliptical Distributions 933.3.3 Properties of Elliptical Distributions 953.3.4 Estimating Dispersion and Correlation 963.3.5 Testing for Elliptical Symmetry 993.4 Dimension Reduction Techniques 1033.4.1 Factor Models 1033.4.2 Statistical Calibration Strategies 1053.4.3 Regression Analysis of Factor Models 1063.4.4 Principal Component Analysis 109
CHAPTER 4: Financial Time Series 1164.1 Empirical Analyses of Financial Time Series 1174.1.1 Stylized Facts 1174.1.2 Multivariate Stylized Facts 1234.2 Fundamentals of Time Series Analysis 1254.2.1 Basic Definitions 1254.2.2 ARMA Processes 1284.2.3 Analysis in the Time Domain 1324.2.4 Statistical Analysis of Time Series 1344.2.5 Prediction 1364.3 GARCH Models for Changing Volatility 1394.3.1 ARCH Processes 1394.3.2 GARCH Processes 1454.3.3 Simple Extensions of the GARCH Model 1484.3.4 Fitting GARCH Models to Data 1504.4 Volatility Models and Risk Estimation 1584.4.1 Volatility Forecasting 1584.4.2 Conditional Risk Measurement 1604.4.3 Backtesting 1624.5 Fundamentals of Multivariate Time Series 1644.5.1 Basic Definitions 1644.5.2 Analysis in the Time Domain 1664.5.3 Multivariate ARMA Processes 1684.6 Multivariate GARCH Processes 1704.6.1 General Structure of Models 1704.6.2 Models for Conditional Correlation 1724.6.3 Models for Conditional Covariance 1754.6.4 Fitting Multivariate GARCH Models 1784.6.5 Dimension Reduction in MGARCH 1794.6.6 MGARCH and Conditional Risk Measurement 182
CHAPTER 5: Copulas and Dependence 1845.1 Copulas 1845.1.1 Basic Properties 1855.1.2 Examples of Copulas 1895.1.3 Meta Distributions 1925.1.4 Simulation of Copulas and Meta Distributions 1935.1.5 Further Properties of Copulas 1955.1.6 Perfect Dependence 1995.2 Dependence Measures 2015.2.1 Linear Correlation 2015.2.2 Rank Correlation 2065.2.3 Coefficients of Tail Dependence 2085.3 Normal Mixture Copulas 2105.3.1 Tail Dependence 2105.3.2 Rank Correlations 2155.3.3 Skewed Normal Mixture Copulas 2175.3.4 Grouped Normal Mixture Copulas 2185.4 Archimedean Copulas 2205.4.1 Bivariate Archimedean Copulas 2205.4.2 Multivariate Archimedean Copulas 2225.4.3 Non-exchangeable Archimedean Copulas 2245.5 Fitting Copulas to Data 2285.5.1 Method-of-Moments using Rank Correlation 2295.5.2 Forming a Pseudo-Sample from the Copula 2325.5.3 Maximum Likelihood Estimation 234
CHAPTER 6: Aggregate Risk 2386.1 Coherent Measures of Risk 2386.1.1 The Axioms of Coherence 2386.1.2 Value-at-Risk 2416.1.3 Coherent Risk Measures Based on Loss Distributions 2436.1.4 Coherent Risk Measures as Generalized Scenarios 2446.1.5 Mean-VaR Portfolio Optimization 2466.2 Bounds for Aggregate Risks 2486.2.1 The General Fr chet Problem 2486.2.2 The Case of VaR 2506.3 Capital Allocation 2566.3.1 The Allocation Problem 2566.3.2 The Euler Principle and Examples 2576.3.3 Economic Justification of the Euler Principle 261
CHAPTER 7: Extreme Value Theory 2647.1 Maxima 2647.1.1 Generalized Extreme Value Distribution 2657.1.2 Maximum Domains of Attraction 2677.1.3 Maxima of Strictly Stationary Time Series 2707.1.4 The Block Maxima Method 2717.2 Threshold Exceedances 2757.2.1 Generalized Pareto Distribution 2757.2.2 Modelling Excess Losses 2787.2.3 Modelling Tails and Measures of Tail Risk 2827.2.4 The Hill Method 2867.2.5 Simulation Study of EVT Quantile Estimators 2897.2.6 Conditional EVT for Financial Time Series 2917.3 Tails of Specific Models 2937.3.1 Domain of Attraction of Fr chet Distribution 2937.3.2 Domain of Attraction of Gumbel Distribution 2947.3.3 Mixture Models 2957.4 Point Process Models 2987.4.1 Threshold Exceedances for Strict White Noise 2997.4.2 The POT Model 3017.4.3 Self-Exciting Processes 3067.4.4 A Self-Exciting POT Model 3077.5 Multivariate Maxima 3117.5.1 Multivariate Extreme Value Copulas 3117.5.2 Copulas for Multivariate Minima 3147.5.3 Copula Domains of Attraction 3147.5.4 Modelling Multivariate Block Maxima 3177.6 Multivariate Threshold Exceedances 3197.6.1 Threshold Models Using EV Copulas 3197.6.2 Fitting a Multivariate Tail Model 3207.6.3 Threshold Copulas and Their Limits 322
CHAPTER 8: Credit Risk Management 3278.1 Introduction to Credit Risk Modelling 3278.1.1 Credit Risk Models 3278.1.2 The Nature of the Challenge 3298.2 Structural Models of Default 3318.2.1 The Merton Model 3318.2.2 Pricing in Merton's Model 3328.2.3 The KMV Model 3368.2.4 Models Based on Credit Migration 3388.2.5 Multivariate Firm-Value Models 3428.3 Threshold Models 3438.3.1 Notation for One-Period Portfolio Models 3448.3.2 Threshold Models and Copulas 3458.3.3 Industry Examples 3478.3.4 Models Based on Alternative Copulas 3488.3.5 Model Risk Issues 3508.4 The Mixture Model Approach 3528.4.1 One-Factor Bernoulli Mixture Models 3538.4.2 CreditRisk +3568.4.3 Asymptotics for Large Portfolios 3578.4.4 Threshold Models as Mixture Models 3598.4.5 Model-Theoretic Aspects of Basel II 3628.4.6 Model Risk Issues 3648.5 Monte Carlo Methods 3678.5.1 Basics of Importance Sampling 3678.5.2 Application to Bernoulli-Mixture Models 3708.6 Statistical Inference for Mixture Models 3748.6.1 Motivation 3748.6.2 Exchangeable Bernoulli-Mixture Models 3758.6.3 Mixture Models as GLMMs 3778.6.4 One-Factor Model with Rating Effect 381
CHAPTER 9: Dynamic Credit Risk Models 3859.1 Credit Derivatives 3869.1.1 Overview 3869.1.2 Single-Name Credit Derivatives 3879.1.3 Portfolio Credit Derivatives 3899.2 Mathematical Tools 3929.2.1 Random Times and Hazard Rates 3939.2.2 Modelling Additional Information 3959.2.3 Doubly Stochastic Random Times 3979.3 Financial and Actuarial Pricing of Credit Risk 4009.3.1 Physical and Risk-Neutral Probability Measure 4019.3.2 Risk-Neutral Pricing and Market Completeness 4059.3.3 Martingale Modelling 4089.3.4 The Actuarial Approach to Credit Risk Pricing 4119.4 Pricing with Doubly Stochastic Default Times 4149.4.1 Recovery Payments of Corporate Bonds 4149.4.2 The Model 4159.4.3 Pricing Formulas 4169.4.4 Applications 4189.5 Affine Models 4219.5.1 Basic Results 4229.5.2 The CIR Square-Root Diffusion 4239.5.3 Extensions 4259.6 Conditionally Independent Defaults 4299.6.1 Reduced-Form Models for Portfolio Credit Risk 4299.6.2 Conditionally Independent Default Times 4319.6.3 Examples and Applications 4359.7 Copula Models 4409.7.1 Definition and General Properties 4409.7.2 Factor Copula Models 4449.8 Default Contagion in Reduced-Form Models 4489.8.1 Default Contagion and Default Dependence 4489.8.2 Information-Based Default Contagion 4539.8.3 Interacting Intensities 456
CHAPTER 10: Operational Risk and Insurance Analytics 46310.1 Operational Risk in Perspective 46310.1.1 A New Risk Class 46310.1.2 The Elementary Approaches 46510.1.3 Advanced Measurement Approaches 46610.1.4 Operational Loss Data 46810.2 Elements of Insurance Analytics 47110.2.1 The Case for Actuarial Methodology 47110.2.2 The Total Loss Amount 47210.2.3 Approximations and Panjer Recursion 47610.2.4 Poisson Mixtures 48210.2.5 Tails of Aggregate Loss Distributions 48410.2.6 The Homogeneous Poisson Process 48410.2.7 Processes Related to the Poisson Process 487
Appendix 494A.1 Miscellaneous Definitions and Results 494A.1.1 Type of Distribution 494A.1.2 Generalized Inverses and Quantiles 494A.1.3 Karamata's Theorem 495A.2 Probability Distributions 496A.2.1 Beta 496A.2.2 Exponential 496A.2.3 F 496A.2.4 Gamma 496A.2.5 Generalized Inverse Gaussian 497A.2.6 Inverse Gamma 497A.2.7 Negative Binomial 498A.2.8 Pareto 498A.2.9 Stable 498A.3 Likelihood Inference 499A.3.1 Maximum Likelihood Estimators 499A.3.2 Asymptotic Results:Scalar Parameter 499A.3.3 Asymptotic Results:Vector of Parameters 500A.3.4 Wald Test and Confidence Intervals 501A.3.5 Likelihood Ratio Test and Confidence Intervals 501A.3.6 Akaike Information Criterion 502
References 503Index 529
What People are Saying About This
McNeil, Frey, and Embrechts present a wide-ranging yet remarkably clear and coherent introduction to the modelling of financial risk. Unlike most finance texts, where the focus is on pricing individual instruments, the primary focus in this book is the statistical behavior of portfolios of risky instruments, which is, after all, the primary concern of risk management. This ought to be a core text in every risk manager's training, and a useful reference for experienced professionals.
This book provides a framework and a useful toolkit for analysis a wide variety of risk management problems. Common pitfalls are pointed out, and mathematical sophistication is used in pursuit of useful and usable solutions. Every financial institution has a risk management department that looks at aggregated portfolio-wide risks on longer time scales, and at risk exposure to large, or extreme, market movements. Risk managers are always on the lookout for good techniques to help them do their jobs. This very good book provides these techniques and addresses an important, and under-developed, area of practical research.
Martin Baxter, Nomura International
There is no book that provides the type of rigorous and detailed coverage of risk management topics that this book does. This could become the book on quantitative risk management.
Riccardo Rebonato, Royal Bank of Scotland, author of "Modern Pricing of Interest-Rate Derivatives"
This book is a compendium of the statistical arrows that should be in any quantitative risk manager's quiver. It includes extensive discussion of dynamic volatility models, extreme value theory, copulas, and credit risk. Academics, Ph.D. students, and quantitative practitioners will find many new and useful results in this important volume.
Robert F. Engle III, 2003 Nobel Laureate in Economic Sciences, Michael Armellino Professor in the Management of Financial Services at New York University's Stern School of Business
"This book is a compendium of the statistical arrows that should be in any quantitative risk manager's quiver. It includes extensive discussion of dynamic volatility models, extreme value theory, copulas, and credit risk. Academics, Ph.D. students, and quantitative practitioners will find many new and useful results in this important volume."—Robert F. Engle III, 2003 Nobel Laureate in Economic Sciences, Michael Armellino Professor in the Management of Financial Services at New York University's Stern School of Business"This book provides a framework and a useful toolkit for analysis a wide variety of risk management problems. Common pitfalls are pointed out, and mathematical sophistication is used in pursuit of useful and usable solutions. Every financial institution has a risk management department that looks at aggregated portfolio-wide risks on longer time scales, and at risk exposure to large, or extreme, market movements. Risk managers are always on the lookout for good techniques to help them do their jobs. This very good book provides these techniques and addresses an important, and under-developed, area of practical research."—Martin Baxter, Nomura International"McNeil, Frey, and Embrechts present a wide-ranging yet remarkably clear and coherent introduction to the modelling of financial risk. Unlike most finance texts, where the focus is on pricing individual instruments, the primary focus in this book is the statistical behavior of portfolios of risky instruments, which is, after all, the primary concern of risk management. This ought to be a core text in every risk manager's training, and a useful reference for experienced professionals."—Michael Gordy"There is no book that provides the type of rigorous and detailed coverage of risk management topics that this book does. This could become the book on quantitative risk management."—Riccardo Rebonato, Royal Bank of Scotland, author of Modern Pricing of Interest-Rate Derivatives