Measuring Market Risk

Abstract

Preface to the Second EditionAcknowledgements1 The Rise of Value at Risk1.1 The emergence of financial risk management1.2 Market risk management1.3 Risk management before VaR1.4 Value at riskAppendix 1: Types of Market Risk2 Measures of Financial Risk2.1 The Mean-Variance framework for measuring financial risk2.2 Value at risk2.3 Coherent risk measures2.4 ConclusionsAppendix 1: Probability FunctionsAppendix 2: Regulatory Uses of VaR3 Estimating Market Risk Measures: An Introduction and Overview3.1 Data3.2 Estimating historical simulation VaR3.3 Estimating parametric VaR3.4 Estimating coherent risk measures3.5 Estimating the standard errors of risk measure estimators3.6 OverviewAppendix 1: Preliminary Data AnalysisAppendix 2: Numerical Integration Methods4 Non-parametric Approaches4.1 Compiling historical simulation data4.2 Estimation of historical simulation VaR and ES4.3 Estimating confidence intervals for historical simulation VaR and ES4.4 Weighted historical simulation4.5 Advantages and disadvantages of non-parametric methods4.6 ConclusionsAppendix 1: Estimating Risk Measures with Order StatisticsAppendix 2: The BootstrapAppendix 3: Non-parametric Density EstimationAppendix 4: Principal Components Analysis and Factor Analysis5 Forecasting Volatilities, Covariances and Correlations5.1 Forecasting volatilities5.2 Forecasting covariances and correlations5.3 Forecasting covariance matricesAppendix 1: Modelling Dependence: Correlations and Copulas6 Parametric Approaches (I)6.1 Conditional vs unconditional distributions6.2 Normal VaR and ES6.3 The t-distribution6.4 The lognormal distribution6.5 Miscellaneous parametric approaches6.6 The multivariate normal variance-covariance approach6.7 Non-normal variance-covariance approaches6.8 Handling multivariate return distributions with copulas6.9 ConclusionsAppendix 1: Forecasting longer-term Risk Measures7 Parametric Approaches (II): Extreme Value7.1 Generalised extreme-value theory7.2 The peaks-over-threshold approach: the generalised pareto distribution7.3 Refinements to EV approaches7.4 Conclusions8 Monte Carlo Simulation Methods8.1 Uses of monte carlo simulation8.2 Monte carlo simulation with a single risk factor8.3 Monte carlo simulation with multiple risk factors8.4 Variance-reduction methods8.5 Advantages and disadvantages of monte carlo simulation8.6 Conclusions9 Applications of Stochastic Risk Measurement Methods9.1 Selecting stochastic processes9.2 Dealing with multivariate stochastic processes9.3 Dynamic risks9.4 Fixed-income risks9.5 Credit-related risks9.6 Insurance risks9.7 Measuring pensions risks9.8 Conclusions10 Estimating Options Risk Measures10.1 Analytical and algorithmic solutions m for options VaR10.2 Simulation approaches10.3 Delta-gamma and related approaches10.4 Conclusions11 Incremental and Component Risks11.1 Incremental VaR11.2 Component VaR11.3 Decomposition of coherent risk measures12 Mapping Positions to Risk Factors12.1 Selecting core instruments12.2 Mapping positions and VaR estimation13 Stress Testing13.1 Benefits and difficulties of stress testing13.2 Scenario analysis13.3 Mechanical stress testing13.4 Conclusions14 Estimating Liquidity Risks14.1 Liquidity and liquidity risks14.2 Estimating liquidity-adjusted VaR14.3 Estimating liquidity at risk (LaR)14.4 Estimating liquidity in crises15 Backtesting Market Risk Models15.1 Preliminary data issues15.2 Backtests based on frequency tests15.3 Backtests based on tests of distribution equality15.4 Comparing alternative models15.5 Backtesting with alternative positions and data15.6 Assessing the precision of backtest results15.7 Summary and conclusionsAppendix 1: Testing Whether Two Distributions are Different16 Model Risk16.1 Models and model risk16.2 Sources of model risk16.3 Quantifying model risk16.4 Managing model risk16.5 ConclusionsBibliographyAuthor IndexSubject Index