Peter F. Christoffersen 2003

CONTENTS
PREFACE XI
ACKNOWLEDGMENTS XIII
1 Risk Management and Financial Returns
1.1. Chapter Outline 1
1.2. Learning Objectives 1
1.3. Risk Management and the Firm 2
1.4. A Brief Taxonomy of Risks 4
1.5. Stylized Facts of Asset Returns 6
1.6. Overview of the Book 9
1.7. Further Resources 9
1.8. Empirical Exercises on CD-ROM 10
References 18


2 Volatility Modeling
2.1. Chapter Overview 19
2.2. Simple Variance Forecasting 20
2.3. The GARCH Variance Model 23
2.4. Extensions to the GARCH Model 26
2.5. Maximum Likelihood Estimation 28
2.6. Variance Model Evaluation 30
2.7. Using Intraday Information 32
2.8. Summary 38
2.9. Further Resources 38
2.10. Empirical Exercises on CD-ROM 39
References 46
3 Correlation Modeling
3.1. Chapter Overview 47
3.2. Value at Risk for Simple Portfolios 48
3.3. Portfolio Variance 51
3.4. Modeling Conditional Covariances 52
3.5. Modeling Conditional Correlations 54
3.6. Quasi-Maximum Likelihood Estimation 58
3.7. Realized and Range-Based Covariance 59
3.8. Summary 61
3.9. Further Resources 61
3.10. Appendix: VaR from Logarithmic versus Arithmetic Returns 62
3.11. Empirical Exercises on CD-ROM 63
References 70
4 Modeling the Conditional Distribution
4.1. Chapter Overview 71
4.2. Visualizing Non-Normality 73
4.3. The Standardized t (d) Distribution 74
4.4. The Cornish-Fisher Approximation to VaR 79
4.5. Extreme Value Theory (EVT) 80
4.6. The Expected Shortfall Risk Measure 85
4.7. Summary 87
4.8. Further Resources 88
4.9. Empirical Exercises on CD-ROM 89
References 97

5 Simulation-Based Methods
5.1. Chapter Overview 99
5.2. Historical Simulation (HS) 100
5.3. Weighted Historical Simulation (WHS) 103
5.4. Multi-Period Risk Calculations 105
5.5. Monte Carlo Simulation (MCS) 108
5.6. Filtered Historical Simulation (FHS) 110
5.7. Summary 112
5.8. Further Resources 113
5.9. Empirical Exercises on CD-ROM 113
References 119
6 Option Pricing
6.1. Chapter Overview 121
6.2. Basic Definitions 122
6.3. Option Pricing Under the Normal Distribution 123
6.4. Allowing for Skewness and Kurtosis 129
6.5. Garch Option Pricing Models 133
6.6. Implied Volatility Function (IVF) Models 138
6.7. Summary 139
6.8. Further Resources 140
6.9. Appendix: The CFG Option Pricing Formula 141
6.10. Empirical Exercises on CD-ROM 142
References 151
7 Modeling Option Risk
7.1. Chapter Overview 153
7.2. The Option Delta 154
7.3. Portfolio Risk Using Delta 159
7.4. The Option Gamma 161
7.5. Portfolio Risk Using Gamma 163
7.6. Portfolio Risk Using Full Valuation 166
7.7. A Simple Example 168
7.8. Pitfall in the Delta and Gamma Approaches 171
7.9. Summary 173
7.10. Further Resources 174
7.11. Empirical Exercises on CD-ROM 175
References 180

x CONTENTS
8 Backtesting and Stress Testing
8.1. Chapter Overview 181
8.2. Backtesting VaRs 184
8.3. Increasing the Information Set 189
8.4. Backtesting Expected Shortfall 190
8.5. Backtesting the Entire Distribution 191
8.6. Stress Testing 194
8.7. Summary 197
8.8. Further Resources 198
8.9. Empirical Exercises on CD-ROM 198
References 208
Index 209