Fully revised and restructured, Measuring Market Risk, Second Edition includes a new chapter on options risk management, as well as substantial new information on parametric risk, non-parametric measurements and liquidity risks, more practical information to help with specific calculations, and new examples including Q&A's and case studies.
Autorentext
Kevin Dowd is Professor of Financial Risk Management at Nottingham University. Kevin is an Adjunct Scholar at the Cato Institute in Washington, D.C., and a Fellow of the Pensions Institute at Birkbeck College.
Klappentext
The second edition of Measuring Market Risk provides an extensive treatment of the state of the art in market risk measurement. The book covers all aspects of modern market risk measurement, and in doing so emphasises new developments in the subject such as coherent and spectral risk measures, the uses of copulas, new applications of stochastic methods, and new developments in backtesting.
The topics covered include: the rise of VaR as a risk measure; different measures of financial risk (including coherent and distortion risk measures); non-parametric approaches (including the bootstrap, order statistics, non-parametric density estimation, and principal components and factor analysis); parametric approaches (including copulas and extreme-value approaches); the theory and applications of stochastic methods; the forecasting of volatilities and correlations; liquidity risk; options risk measurement; risk decomposition; mapping; stress-testing; backtesting; and model risk.
Measuring Market Risk is written in a clear and accessible style, and includes many worked examples of market risk measurement problems.
Inhalt
Preface to the Second Edition xiii
Acknowledgements xix
1 The Rise of Value at Risk 1
1.1 The emergence of financial risk management 2
1.2 Market risk measurement 4
1.3 Risk measurement before VaR 5
1.3.1 Gap analysis 5
1.3.2 Duration analysis 5
1.3.3 Scenario analysis 6
1.3.4 Portfolio theory 7
1.3.5 Derivatives risk measures 8
1.4 Value at risk 9
1.4.1 The origin and development of VaR 9
1.4.2 Attractions of VaR 11
1.4.3 Criticisms of VaR 13
Appendix: Types of Market Risk 15
2 Measures of Financial Risk 19
2.1 The mean-variance framework for measuring financial risk 20
2.2 Value at risk 27
2.2.1 Basics of VaR 27
2.2.2 Determination of the VaR parameters 29
2.2.3 Limitations of VaR as a risk measure 31
2.3 Coherent risk measures 32
2.3.1 The coherence axioms and their implications 32
2.3.2 The expected shortfall 35
2.3.3 Spectral risk measures 37
2.3.4 Scenarios as coherent risk measures 42
2.4 Conclusions 44
Appendix 1: Probability Functions 45
Appendix 2: Regulatory Uses of VaR 52
3 Estimating Market Risk Measures: An Introduction and Overview 53
3.1 Data 53
3.1.1 Profit/loss data 53
3.1.2 Loss/profit data 54
3.1.3 Arithmetic return data 54
3.1.4 Geometric return data 54
3.2 Estimating historical simulation VaR 56
3.3 Estimating parametric VaR 57
3.3.1 Estimating VaR with normally distributed profits/losses 57
3.3.2 Estimating VaR with normally distributed arithmetic returns 59
3.3.3 Estimating lognormal VaR 61
3.4 Estimating coherent risk measures 64
3.4.1 Estimating expected shortfall 64
3.4.2 Estimating coherent risk measures 64
3.5 Estimating the standard errors of risk measure estimators 69
3.5.1 Standard errors of quantile estimators 69
3.5.2 Standard errors in estimators of coherent risk measures 72
3.6 The core issues: an overview 73
Appendix 1: Preliminary Data Analysis 75
Appendix 2: Numerical Integration Methods 80
4 Non-parametric Approaches 83
4.1 Compiling historical simulation data 84
4.2 Estimation of historical simulation VaR and ES 84
4.2.1 Basic historical simulation 84
4.2.2 Bootstrapped historical simulation 85
4.2.3 Historical simulation using non-parametric density estimation 86
4.2.4 Estimating curves and surfaces for VAR and ES 88
4.3 Estimating confidence intervals for historical simulation VaR and ES 89
4.3.1 An order-statistics approach to the estimation of confidence intervals for HS VaR and ES 89
4.3.2 A bootstrap approach to the estimation of confidence intervals for HS VaR and ES 90
4.4 Weighted historical simulation 92
4.4.1 Age-weighted historical simulation 93
4.4.2 Volatility-weighted historical simulation 94
4.4.3 Correlation-weighted historical simulation 95
4.4.4 Filtered historical simulation 96
4.5 Advantages and disadvantages of non-parametric methods 99
4.5.1 Advantages 99
4.5.2 Disadvantages 100
4.6 Conclusions 101
Appendix 1: Estimating Risk Measures with Order Statistics 102
Appendix 2: The Bootstrap 105
Appendix 3: Non-parametric Density Estimation 111
Appendix 4: Principal Components Analysis and Factor Analysis 118
5 Forecasting Volatilities, Covariances and Correlations 127
5.1 Forecasting volatilities 127
5.1.1 Defining volatility 127
5.1.2 Historical volatility forecasts 128
5.1.3 Exponentially weighted moving average volatility 129
5.1.4 GARCH models 131
5.1.5 Implied volatilities 136
5.2 Forecasting covariances and correlations 137
5.2.1 Defining covariances and correlations 137
5.2.2 Historical covariances and correlations 138
5.2.3 Exponentially weighted moving average covariances 140
5.2.4 GARCH covariances 140
5.2.5 Implied covariances and correlations 141
5.2.6 Some pitfalls with correlation estimation 141
5.3 Forecasting covariance matrices 142
5.3.1 Positive definiteness and positive semi-definiteness 142
5.3.2 Historical variance-covariance estimation 142
5.3.3 Multivariate EWMA 142
5.3.4 Multivariate GARCH 142
5.3.5 Computational problems with covariance and correlation matrices 143
Appendix: Modelling Dependence: Correlations and Copulas 145
6 Parametric Approaches (I) 151
6.1 Conditional vs unconditional distributions 152
6.2 Normal VaR and ES 154
6.3 The t-distribution 159
6.4 The lognormal distribution 161
6.5 Miscellaneous parametric approaches 165
6.5.1 Lévy approaches 165
6.5.2 Elliptical and hyperbolic approaches 167
6.5.3 Normal mixture approaches 167
6.5.4 Jump diffusion 168
6.5.5 Stochastic volatility approaches 169
6.5.6 The Cornish-Fisher approximation 171
6.6 The multivariate normal variance-covariance approach 173
6.7 Non-normal variance-covariance approaches 176
6.7.1 Multivariate t-distributions 176
6.7.2 Multivariate elliptical distributions 177
6.7.3 The Hull-White transformation-into-normality approach 177
6.8 Handling multivariate return distributions with copulas 178
6.8.1 Motivation 178
6.8.2 Estimating VaR with copulas 179
6.9 Conclusions 182
Appendix: Forecasting Longer-term Risk Measures 184
7 Parametric Approaches (II): Extreme Value 189
7.1 Generalised extreme-value theory 190
7.1.1 Theory 190
7.1.2 A short-cut EV method 194
7.1.3 Estimation of EV parameters 195
7.2 The peaks-over-threshold approach: the generalised Pareto distribution 201
7.2.1 Theory 201
7.2.2 Estimation 203
7.2.3 GEV vs POT 204
7.3 Refinements to EV approaches 204
7.3…