Measuring Market Risk

Preface to the Second Edition Acknowledgements 1 The Rise of Value at Risk 1.1 The emergence of financial risk management 1.2 Market risk management 1.3 Risk management before VaR 1.4 Value at risk Appendix 1: Types of Market Risk 2 Measures of Financial Risk 2.1 The Mean-Variance framework for measuring financial risk 2.2 Value at risk 2.3 Coherent risk measures 2.4 Conclusions Appendix 1: Probability Functions Appendix 2: Regulatory Uses of VaR 3 Estimating Market Risk Measures: An Introduction and Overview 3.1 Data 3.2 Estimating historical simulation VaR 3.3 Estimating parametric VaR 3.4 Estimating coherent risk measures 3.5 Estimating the standard errors of risk measure estimators 3.6 Overview Appendix 1: Preliminary Data Analysis Appendix 2: Numerical Integration Methods 4 Non-parametric Approaches 4.1 Compiling historical simulation data 4.2 Estimation of historical simulation VaR and ES 4.3 Estimating confidence intervals for historical simulation VaR and ES 4.4 Weighted historical simulation 4.5 Advantages and disadvantages of non-parametric methods 4.6 Conclusions Appendix 1: Estimating Risk Measures with Order Statistics Appendix 2: The Bootstrap Appendix 3: Non-parametric Density Estimation Appendix 4: Principal Components Analysis and Factor Analysis 5 Forecasting Volatilities, Covariances and Correlations 5.1 Forecasting volatilities 5.2 Forecasting covariances and correlations 5.3 Forecasting covariance matrices Appendix 1: Modelling Dependence: Correlations and Copulas 6 Parametric Approaches (I) 6.1 Conditional vs unconditional distributions 6.2 Normal VaR and ES 6.3 The t-distribution 6.4 The lognormal distribution 6.5 Miscellaneous parametric approaches 6.6 The multivariate normal variance-covariance approach 6.7 Non-normal variance-covariance approaches 6.8 Handling multivariate return distributions with copulas 6.9 Conclusions Appendix 1: Forecasting longer-term Risk Measures 7 Parametric Approaches (II): Extreme Value 7.1 Generalised extreme-value theory 7.2 The peaks-over-threshold approach: the generalised pareto distribution 7.3 Refinements to EV approaches 7.4 Conclusions 8 Monte Carlo Simulation Methods 8.1 Uses of monte carlo simulation 8.2 Monte carlo simulation with a single risk factor 8.3 Monte carlo simulation with multiple risk factors 8.4 Variance-reduction methods 8.5 Advantages and disadvantages of monte carlo simulation 8.6 Conclusions 9 Applications of Stochastic Risk Measurement Methods 9.1 Selecting stochastic processes 9.2 Dealing with multivariate stochastic processes 9.3 Dynamic risks 9.4 Fixed-income risks 9.5 Credit-related risks 9.6 Insurance risks 9.7 Measuring pensions risks 9.8 Conclusions 10 Estimating Options Risk Measures 10.1 Analytical and algorithmic solutions m for options VaR 10.2 Simulation approaches 10.3 Delta-gamma and related approaches 10.4 Conclusions 11 Incremental and Component Risks 11.1 Incremental VaR 11.2 Component VaR 11.3 Decomposition of coherent risk measures 12 Mapping Positions to Risk Factors 12.1 Selecting core instruments 12.2 Mapping positions and VaR estimation 13 Stress Testing 13.1 Benefits and difficulties of stress testing 13.2 Scenario analysis 13.3 Mechanical stress testing 13.4 Conclusions 14 Estimating Liquidity Risks 14.1 Liquidity and liquidity risks 14.2 Estimating liquidity-adjusted VaR 14.3 Estimating liquidity at risk (LaR) 14.4 Estimating liquidity in crises 15 Backtesting Market Risk Models 15.1 Preliminary data issues 15.2 Backtests based on frequency tests 15.3 Backtests based on tests of distribution equality 15.4 Comparing alternative models 15.5 Backtesting with alternative positions and data 15.6 Assessing the precision of backtest results 15.7 Summary and conclusions Appendix 1: Testing Whether Two Distributions are Different 16 Model Risk 16.1 Models and model risk 16.2 Sources of model risk 16.3 Quantifying model risk 16.4 Managing model risk 16.5 Conclusions Bibliography Author Index Subject Index