Quantitative Risk Management: Concepts, Techniques And Tools

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Quantitative Risk Management: Concepts, Techniques And Tools

Format:  Hardcover,

538 pages

Publisher: Princeton Univ Pr

Publish Date: Sep 2005

ISBN-13: 9780691122557

ISBN-10: 0691122555

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The implementation of sound quantitative risk models is a vital concern for all financial institutions, and this trend has accelerated in recent years with regulatory processes such as Basel II. This book provides a comprehensive treatment of the theoretical concepts and modelling techniques of quantitative risk management and equips readers--whether financial risk analysts, actuaries, regulators, or students of quantitative finance--with practical tools to solve real-world problems. The authors cover methods for market, credit, and operational risk modelling; place standard industry approaches on a more formal footing; and describe recent developments that go beyond, and address main deficiencies of, current practice.

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.

Specifications

Publisher: Princeton Univ Pr
Publish Date: Sep 2005
ISBN-13: 9780691122557
ISBN-10: 0691122555
Format: Hardcover
Number of Pages: 538
Shipping Weight (in pounds): 2.0
Product in Inches (L x W x H): 6.25 x 9.25 x 1.25
Walmart No.: 0691122555

Chapter outline

Prefacep. xiii
Risk in Perspectivep. 1
Riskp. 1
Risk and Randomnessp. 1
Financial Riskp. 2
Measurement and Managementp. 3
A Brief History of Risk Managementp. 5
From Babylon to Wall Streetp. 5
The Road to Regulationp. 8
The New Regulatory Frameworkp. 10
Basel IIp. 10
Solvency 2p. 13
Why Manage Financial Risk?p. 15
A Societal Viewp. 15
The Shareholder's Viewp. 16
Economic Capitalp. 18
Quantitative Risk Managementp. 19
The Nature of the Challengep. 19
QRM for the Futurep. 22
Basic Concepts in Risk Managementp. 25
Risk Factors and Loss Distributionsp. 25
General Definitionsp. 25
Conditional and Unconditional Loss Distributionp. 28
Mapping of Risks: Some Examplesp. 29
Risk Measurementp. 34
Approaches to Risk Measurementp. 34
Value-at-Riskp. 37
Further Comments on VaRp. 40
Other Risk Measures Based on Loss Distributionsp. 43
Standard Methods for Market Risksp. 48
Variance-Covariance Methodp. 48
Historical Simulationp. 50
Monte Carlop. 52
Losses over Several Periods and Scalingp. 53
Backtestingp. 55
An Illustrative Examplep. 55
Multivariate Modelsp. 61
Basics of Multivariate Modellingp. 61
Random Vectors and Their Distributionsp. 62
Standard Estimators of Covariance and Correlationp. 64
The Multivariate Normal Distributionp. 66
Testing Normality and Multivariate Normalityp. 68
Normal Mixture Distributionsp. 73
Normal Variance Mixturesp. 73
Normal Mean-Variance Mixturesp. 77
Generalized Hyperbolic Distributionsp. 78
Fitting Generalized Hyperbolic Distributions to Datap. 81
Empirical Examplesp. 84
Spherical and Elliptical Distributionsp. 89
Spherical Distributionsp. 89
Elliptical Distributionsp. 93
Properties of Elliptical Distributionsp. 95
Estimating Dispersion and Correlationp. 96
Testing for Elliptical Symmetryp. 99
Dimension Reduction Techniquesp. 103
Factor Modelsp. 103
Statistical Calibration Strategiesp. 105
Regression Analysis of Factor Modelsp. 106
Principal Component Analysisp. 109
Financial Time Seriesp. 116
Empirical Analyses of Financial Time Seriesp. 117
Stylized Factsp. 117
Multivariate Stylized Factsp. 123
Fundamentals of Time Series Analysisp. 125
Basic Definitionsp. 125
ARMA Processesp. 128
Analysis in the Time Domainp. 132
Statistical Analysis of Time Seriesp. 134
Predictionp. 136
GARCH Models for Changing Volatilityp. 139
ARCH Processesp. 139
GARCH Processesp. 145
Simple Extensions of the GARCH Modelp. 148
Fitting GARCH Models to Datap. 150
Volatility Models and Risk Estimationp. 158
Volatility Forecastingp. 158
Conditional Risk Measurementp. 160
Backtestingp. 162
Fundamentals of Multivariate Time Seriesp. 164
Basic Definitionsp. 164
Analysis in the Time Domainp. 166
Multivariate ARMA Processesp. 168
Multivariate GARCH Processesp. 170
General Structure of Modelsp. 170
Models for Conditional Correlationp. 172
Models for Conditional Covariancep. 175
Fitting Multivariate GARCH Modelsp. 178
Dimension Reduction in MGARCHp. 179
MGARCH and Conditional Risk Measurementp. 182
Copulas and Dependencep. 184
Copulasp. 184
Basic Propertiesp. 185
Examples of Copulasp. 189
Meta Distributionsp. 192
Simulation of Copulas and Meta Distributionsp. 193
Further Properties of Copulasp. 195
Perfect Dependencep. 199
Dependence Measuresp. 201
Linear Correlationp. 201
Rank Correlationp. 206
Coefficients of Tail Dependencep. 208
Normal Mixture Copulasp. 210
Tail Dependencep. 210
Rank Correlationsp. 215
Skewed Normal Mixture Copulasp. 217
Grouped Normal Mixture Copulasp. 218
Archimedean Copulasp. 220
Bivariate Archimedean Copulasp. 220
Multivariate Archimedean Copulasp. 222
Non-exchangeable Archimedean Copulasp. 224
Fitting Copulas to Datap. 228
Method-of-Moments using Rank Correlationp. 229
Forming a Pseudo-Sample from the Copulap. 232
Maximum Likelihood Estimationp. 234
Aggregate Riskp. 238
Coherent Measures of Riskp. 238
The Axioms of Coherencep. 238
Value-at-Riskp. 241
Coherent Risk Measures Based on Loss Distributionsp. 243
Coherent Risk Measures as Generalized Scenariosp. 244
Mean-VaR Portfolio Optimizationp. 246
Bounds for Aggregate Risksp. 248
The General Frechet Problemp. 248
The Case of VaRp. 250
Capital Allocationp. 256
The Allocation Problemp. 256
The Euler Principle and Examplesp. 257
Economic Justification of the Euler Principlep. 261
Extreme Value Theoryp. 264
Maximap. 264
Generalized Extreme Value Distributionp. 265
Maximum Domains of Attractionp. 267
Maxima of Strictly Stationary Time Seriesp. 270
The Block Maxima Methodp. 271
Threshold Exceedancesp. 275
Generalized Pareto Distributionp. 275
Modelling Excess Lossesp. 278
Modelling Tails and Measures of Tail Riskp. 282
The Hill Methodp. 286
Simulation Study of EVT Quantile Estimatorsp. 289
Conditional EVT for Financial Time Seriesp. 291
Tails of Specific Modelsp. 293
Domain of Attraction of Frechet Distributionp. 293
Domain of Attraction of Gumbel Distributionp. 294
Mixture Modelsp. 295
Point Process Modelsp. 298
Threshold Exceedances for Strict White Noisep. 299
The POT Modelp. 301
Self-Exciting Processesp. 306
A Self-Exciting POT Modelp. 307
Multivariate Maximap. 311
Multivariate Extreme Value Copulasp. 311
Copulas for Multivariate Minimap. 314
Copula Domains of Attractionp. 314
Modelling Multivariate Block Maximap. 317
Multivariate Threshold Exceedancesp. 319
Threshold Models Using EV Copulasp. 319
Fitting a Multivariate Tail Modelp. 320
Threshold Copulas and Their Limitsp. 322
Credit Risk Managementp. 327
Introduction to Credit Risk Modellingp. 327
Credit Risk Modelsp. 327
The Nature of the Challengep. 329
Structural Models of Defaultp. 331
The Merton Modelp. 331
Pricing in Merton's Modelp. 332
The KMV Modelp. 336
Models Based on Credit Migrationp. 338
Multivariate Firm-Value Modelsp. 342
Threshold Modelsp. 343
Notation for One-Period Portfolio Modelsp. 344
Threshold Models and Copulasp. 345
Industry Examplesp. 347
Models Based on Alternative Copulasp. 348
Model Risk Issuesp. 350
The Mixture Model Approachp. 352
One-Factor Bernoulli Mixture Modelsp. 353
CreditRisk+p. 356
Asymptotics for Large Portfoliosp. 357
Threshold Models as Mixture Modelsp. 359
Model-Theoretic Aspects of Basel IIp. 362
Model Risk Issuesp. 364
Monte Carlo Methodsp. 367
Basics of Importance Samplingp. 367
Application to Bernoulli-Mixture Modelsp. 370
Statistical Inference for Mixture Modelsp. 374
Motivationp. 374
Exchangeable Bernoulli-Mixture Modelsp. 375
Mixture Models as GLMMsp. 377
One-Factor Model with Rating Effectp. 381
Dynamic Credit Risk Modelsp. 385
Credit Derivativesp. 386
Overviewp. 386
Single-Name Credit Derivativesp. 387
Portfolio Credit Derivativesp. 389
Mathematical Toolsp. 392
Random Times and Hazard Ratesp. 393
Modelling Additional Informationp. 395
Doubly Stochastic Random Timesp. 397
Financial and Actuarial Pricing of Credit Riskp. 400
Physical and Risk-Neutral Probability Measurep. 401
Risk-Neutral Pricing and Market Completenessp. 405
Martingale Modellingp. 408
The Actuarial Approach to Credit Risk Pricingp. 411
Pricing with Doubly Stochastic Default Timesp. 414
Recovery Payments of Corporate Bondsp. 414
The Modelp. 415
Pricing Formulasp. 416
Applicationsp. 418
Affine Modelsp. 421
Basic Resultsp. 422
The CIR Square-Root Diffusionp. 423
Extensionsp. 425
Conditionally Independent Defaultsp. 429
Reduced-Form Models for Portfolio Credit Riskp. 429
Conditionally Independent Default Timesp. 431
Examples and Applicationsp. 435
Copula Modelsp. 440
Definition and General Propertiesp. 440
Factor Copula Modelsp. 444
Default Contagion in Reduced-Form Modelsp. 448
Default Contagion and Default Dependencep. 448
Information-Based Default Contagionp. 453
Interacting Intensitiesp. 456
Operational Risk and Insurance Analyticsp. 463
Operational Risk in Perspectivep. 463
ANew Risk Classp. 463
The Elementary Approachesp. 465
Advanced Measurement Approachesp. 466
Operational Loss Datap. 468
Elements of Insurance Analyticsp. 471
The Case for Acturaial Methodologyp. 471
The Total Loss Amountp. 472
Approximations and Panjer Recursionp. 476
Poisson Mixturesp. 482
Tails of Aggregate Loss Distributionsp. 484
The Homogeneous Poisson Processp. 484
Processes Related to the Poisson Processp. 487
Appendixp. 494
Miscellaneous Definitions and Resultsp. 494
Type of Distributionp. 494
Generalized Inverses and Quantilesp. 494
Karamata's Theoremp. 495
Probability Distributionsp. 496
Betap. 496
Exponentialp. 496
Fp. 496
Gammap. 496
Generalized Inverse Gaussianp. 497
Inverse Gammap. 497
Negative Binomialp. 498
Paretop. 498
Stablep. 498
Likelihood Inferencep. 499
Maximum Likelihood Estimatorsp. 499
Asymptotic Results: Scalar Parameterp. 499
Asymptotic Results: Vector of Parametersp. 500
Wald Test and Confidence Intervalsp. 501
Likelihood Ratio Test and Confidence Intervalsp. 501
Akaike Information Criterionp. 502
Referencesp. 503
Indexp. 529

Book description

The implementation of sound quantitative risk models is a vital concern for all financial institutions, and this trend has accelerated in recent years with regulatory processes such as Basel II. This book provides a comprehensive treatment of the theoretical concepts and modelling techniques of quantitative risk management and equips readers--whether financial risk analysts, actuaries, regulators, or students of quantitative finance--with practical tools to solve real-world problems. The authors cover methods for market, credit, and operational risk modelling; place standard industry approaches on a more formal footing; and describe recent developments that go beyond, and address main deficiencies of, current practice.

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.

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