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1、QuantitativeRiskManagementConcepts, Techniques and ToolsContentsPrefacexiii1Risk in Perspective1 1.1Risk1 1.1.1Risk and Randomness1 1.1.2Financial Risk2 1.1.3Measurement and Management3 1.2A Brief History of Risk Management5 1.2.1From Babylon to Wall Street5 1.2.2The Road to Regulation8 1.3The New R
2、egulatory Framework10 1.3.1Basel II10 1.3.2Solvency 213 1.4Why Manage Financial Risk?15 1.4.1A SocietalView15 1.4.2The ShareholdersView16 1.4.3Economic Capital18 1.5Quantitative Risk Management19 1.5.1The Nature of the Challenge19 1.5.2QRM for the Future222Basic Concepts in Risk Management25 2.1Risk
3、 Factors and Loss Distributions25 2.1.1General Definitions25 2.1.2Conditional and Unconditional Loss Distribution28 2.1.3Mapping of Risks: Some Examples29 2.2Risk Measurement34 2.2.1Approaches to Risk Measurement34 2.2.2Value-at-Risk37 2.2.3Further Comments on VaR40 2.2.4Other Risk Measures Based on
4、 Loss Distributions43 2.3Standard Methods for Market Risks48 2.3.1VarianceCovariance Method48 2.3.2Historical Simulation50 2.3.3Monte Carlo52 2.3.4Losses over Several Periods and Scaling53 2.3.5Backtesting55 2.3.6An Illustrative Example55viiiContents3Multivariate Models61 3.1Basics of Multivariate M
5、odelling61 3.1.1Random Vectors and Their Distributions62 3.1.2Standard Estimators of Covariance and Correlation64 3.1.3The Multivariate Normal Distribution66 3.1.4Testing Normality and Multivariate Normality68 3.2Normal Mixture Distributions73 3.2.1NormalVariance Mixtures73 3.2.2Normal Mean-Variance
6、 Mixtures77 3.2.3Generalized Hyperbolic Distributions78 3.2.4Fitting Generalized Hyperbolic Distributions to Data81 3.2.5Empirical Examples84 3.3Spherical and Elliptical Distributions89 3.3.1Spherical Distributions89 3.3.2Elliptical Distributions93 3.3.3Properties of Elliptical Distributions95 3.3.4
7、Estimating Dispersion and Correlation96 3.3.5Testing for Elliptical Symmetry99 3.4Dimension Reduction Techniques103 3.4.1Factor Models103 3.4.2Statistical Calibration Strategies105 3.4.3RegressionAnalysis of Factor Models106 3.4.4Principal ComponentAnalysis1094Financial Time Series116 4.1EmpiricalAn
8、alyses of Financial Time Series117 4.1.1Stylized Facts117 4.1.2Multivariate Stylized Facts123 4.2Fundamentals of Time SeriesAnalysis125 4.2.1Basic Definitions125 4.2.2ARMA Processes128 4.2.3Analysis in the Time Domain132 4.2.4StatisticalAnalysis of Time Series134 4.2.5Prediction136 4.3GARCH Models f
9、or Changing Volatility139 4.3.1ARCH Processes139 4.3.2GARCH Processes145 4.3.3Simple Extensions of the GARCH Model148 4.3.4Fitting GARCH Models to Data150 4.4Volatility Models and Risk Estimation158 4.4.1Volatility Forecasting158 4.4.2Conditional Risk Measurement160 4.4.3Backtesting162 4.5Fundamenta
10、ls of Multivariate Time Series164 4.5.1Basic Definitions164 4.5.2Analysis in the Time Domain166 4.5.3MultivariateARMA Processes168 4.6Multivariate GARCH Processes170 4.6.1General Structure of Models170 4.6.2Models for Conditional Correlation172 4.6.3Models for Conditional Covariance175Contentsix4.6.
11、4Fitting Multivariate GARCH Models178 4.6.5Dimension Reduction in MGARCH179 4.6.6MGARCH and Conditional Risk Measurement1825Copulas and Dependence184 5.1Copulas184 5.1.1Basic Properties185 5.1.2Examples of Copulas189 5.1.3Meta Distributions192 5.1.4Simulation of Copulas and Meta Distributions193 5.1
12、.5Further Properties of Copulas195 5.1.6Perfect Dependence199 5.2Dependence Measures201 5.2.1Linear Correlation201 5.2.2Rank Correlation206 5.2.3Coefficients of Tail Dependence208 5.3Normal Mixture Copulas210 5.3.1Tail Dependence210 5.3.2Rank Correlations215 5.3.3Skewed Normal Mixture Copulas217 5.3
13、.4Grouped Normal Mixture Copulas218 5.4Archimedean Copulas220 5.4.1BivariateArchimedean Copulas220 5.4.2MultivariateArchimedean Copulas222 5.4.3Non-exchangeableArchimedean Copulas224 5.5Fitting Copulas to Data228 5.5.1Method-of-Moments using Rank Correlation229 5.5.2Forming a Pseudo-Sample from the
14、Copula232 5.5.3Maximum Likelihood Estimation2346Aggregate Risk238 6.1Coherent Measures of Risk238 6.1.1TheAxioms of Coherence238 6.1.2Value-at-Risk241 6.1.3Coherent Risk Measures Based on Loss Distributions243 6.1.4Coherent Risk Measures as Generalized Scenarios244 6.1.5Mean-VaR Portfolio Optimizati
15、on246 6.2Bounds forAggregate Risks248 6.2.1The General Fr echet Problem248 6.2.2The Case ofVaR250 6.3CapitalAllocation256 6.3.1TheAllocation Problem256 6.3.2The Euler Principle and Examples257 6.3.3Economic Justification of the Euler Principle2617Extreme Value Theory264 7.1Maxima264 7.1.1Generalized
16、 Extreme Value Distribution265 7.1.2Maximum Domains ofAttraction267 7.1.3Maxima of Strictly Stationary Time Series270 7.1.4The Block Maxima Method271xContents7.2Threshold Exceedances275 7.2.1Generalized Pareto Distribution275 7.2.2Modelling Excess Losses278 7.2.3Modelling Tails and Measures of Tail Risk282 7.2.4The Hill Method286 7.2.5Simulation Study of EVT Quantile Estimators289 7.2.6Conditional EVT for Financial Time Series291 7.3Tails of Specific Models293 7.3.1Domain ofAttraction of Fr
