Financial Risk Forecasting: The Theory and Practice of Forecasting Market Risk with Implementation in R and Matlab

Acknowledgments.

Abbreviations.

Notation.

1 Financial markets, prices and risk.

1.2 S&P 500 returns.

1.3 The stylized facts of financial returns.

1.4 Volatility.

1.5 Nonnormality and fat tails.

1.6 Identification of fat tails.

1.7 Nonlinear dependence.

1.8 Copulas.

1.9 Summary.

2 Univariate volatility modeling.

2.1 Modeling volatility.

2.2 Simple volatility models.

2.3 GARCH and conditional volatility.

2.4 Maximum likelihood estimation of volatility models.

2.5 Diagnosing volatility models.

2.6 Application of ARCH and GARCH.

2.7 Other GARCH-type models.

2.8 Alternative volatility models.

2.9 Summary.

3 Multivariate volatility models.

3.1 Multivariate volatility forecasting.

3.2 EWMA.

3.3 Orthogonal GARCH.

3.4 CCC and DCC models.

3.5 Estimation comparison.

3.6 Multivariate extensions of GARCH.

3.7 Summary.

4 Risk measures.

4.1 Defining and measuring risk.

4.2 Volatility.

4.3 Value-at-risk.

4.4 Issues in applying VaR.

4.5 Expected shortfall.

4.6 Holding periods, scaling and the square root of time.

4.7 Summary.

5 Implementing risk forecasts.

5.1 Application.

5.2 Historical simulation.

5.3 Risk measures and parametric methods.

5.4 What about expected returns?

5.5 VaR with time-dependent volatility.

5.6 Summary.

6 Analytical value-at-risk for options and bonds.

6.1 Bonds.

6.2 Options.

6.3 Summary.

7 Simulation methods for VaR for options and bonds.

7.1 Pseudo random number generators.

7.2 Simulation pricing.

7.3 Simulation of VaR for one asset.

7.4 Simulation of portfolio VaR.

7.5 Issues in simulation estimation.

7.6 Summary.

8 Backtesting and stress testing.

8.1 Backtesting.

8.2 Backtesting the S&P 500.

8.3 Significance of backtests.

8.4 Expected shortfall backtesting.

8.5 Problems with backtesting.

8.6 Stress testing.

8.7 Summary.

9 Extreme value theory.

9.1 Extreme value theory.

9.2 Asset returns and fat tails.

9.3 Applying EVT.

9.4 Aggregation and convolution.

9.5 Time dependence.

9.6 Summary.

10 Endogenous risk.

10.1 The Millennium Bridge.

10.2 Implications for financial risk management.

10.3 Endogenous market prices.

10.4 Dual role of prices.

10.5 Summary.

APPENDICES.

A Financial time series.

A.1 Random variables and probability density functions.

A.2 Expectations and variance.

A.3 Higher order moments.

A.4 Examples of distributions.

A.5 Basic time series concepts.

A.6 Simple time series models.

A.7 Statistical hypothesis testing.

B An introduction to R.

B.1 Inputting data.

B.2 Simple operations.

B.3 Distributions.

B.4 Time series.

B.5 Writing functions in R.

B.6 Maximum likelihood estimation.

B.7 Graphics.

C An introduction to Matlab.

C.1 Inputting data.

C.2 Simple operations.

C.3 Distributions.

C.3.1 Normality tests.

C.4 Time series.

C.5 Basic programming and M-files.

C.6 Maximum likelihood.

C.7 Graphics.

D Maximum likelihood.

D.1 Likelihood functions.

D.2 Optimizers.

D.3 Issues in ML estimation.

D.4 Information matrix.

D.5 Properties of maximum likelihood estimators.

D.6 Optimal testing procedures.

Bibliography.

Index.