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
9 Applications of Stochastic Risk Measurement Methods
10 Estimating Options Risk Measures
11 Incremental and Component Risks
12 Mapping Positions to Risk Factors
14 Estimating Liquidity Risks
15 Backtesting Market Risk Models
16 Model Risk
Bibliography
Author Index
Subject Index