Measuring Market Risk, 2nd 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