An introduction to market risk measurement

An Introduction to Market Risk Measurement......Page 4
Contents......Page 8
Preface......Page 14
Acknowledgements......Page 22
1.1.1 A Volatile Environment......Page 24
1.1.3 Advances in Information Technology......Page 25
1.2.1 Gap Analysis......Page 26
1.2.3 Scenario Analysis......Page 27
1.2.4 Portfolio Theory......Page 28
1.2.5 Derivatives Risk Measures......Page 29
1.3.1 The Origin and Development of VaR......Page 30
1.3.2 Attractions of VaR......Page 33
1.3.3 Criticisms of VaR......Page 34
1.4 Recommended Reading......Page 35
2.1.1 The Normality Assumption......Page 36
2.1.2 Limitations of the Normality Assumption......Page 38
2.1.3.2 Duration Approaches to Fixed-income Risk Measurement......Page 41
2.2.1 VaR Basics......Page 42
2.2.2 Choice of VaR Parameters......Page 47
2.2.3.1 VaR Uninformative of Tail Losses......Page 48
2.2.3.2 VaR Can Create Perverse Incentive Structures......Page 49
2.2.3.4 VaR Not Sub-additive......Page 50
2.3.1 Coherent Risk Measures......Page 51
2.3.2 The Expected Tail Loss......Page 52
2.5 Recommended Reading......Page 56
3.1.2 Loss/Profit Data......Page 58
3.2 Estimating Historical Simulation VaR......Page 59
3.3 Estimating Parametric VaR......Page 60
3.3.1 Estimating VaR with Normally Distributed Profits/Losses......Page 61
3.3.2 Estimating VaR with Normally Distributed Arithmetic Returns......Page 62
3.3.3 Estimating Lognormal VaR......Page 63
3.4 Estimating Expected Tail Loss......Page 65
3.5 Summary......Page 67
Appendix: Mapping Positions to Risk Factors......Page 68
A3.1.1 Selecting Core Instruments......Page 69
A3.2.1.1 Basic FX Positions......Page 70
A3.2.1.2 Basic Equity Positions......Page 71
A3.2.1.3 Zero-coupon Bonds......Page 73
A3.2.1.4 Basic Forward/Futures......Page 74
A3.2.2 More Complex Positions......Page 75
A3.3 Recommended Reading......Page 76
4.1 Compiling Historical Simulation Data......Page 78
4.2.1 Basic Historical Simulation......Page 79
4.2.2 Estimating Curves and Surfaces for VaR and ETL......Page 80
4.3.2 An Order Statistics Approach to the Estimation of Confidence Intervals for HS VaR and ETL......Page 81
4.3.3 A Bootstrap Approach to the Estimation of Confidence Intervals for HS VaR and ETL......Page 82
4.4 Weighted Historical Simulation......Page 84
4.4.1 Age-weighted Historical Simulation......Page 85
4.4.2 Volatility-weighted Historical Simulation......Page 86
4.4.3 Filtered Historical Simulation......Page 87
4.5.1 Advantages......Page 89
4.5.2.1 Total Dependence on the Data Set......Page 90
4.6 Principal Components Approaches to VaR and ETL Estimation......Page 91
4.7 Conclusions......Page 92
4.8 Recommended Reading......Page 93
5 Parametric VaR and ETL......Page 94
5.1.1 General Features......Page 95
5.1.2 Disadvantages of Normality......Page 99
5.2 The Student t-distribution......Page 100
5.3 The Lognormal Distribution......Page 101
5.4.1 The Generalised Extreme Value Distribution......Page 104
5.4.2 The Peaks Over Threshold (Generalised Pareto) Approach......Page 105
5.5 The Multivariate Normal Variance–Covariance Approach......Page 107
5.6 Conclusions......Page 109
5.7 Recommended Reading......Page 110
A5.1 Delta–normal Approaches......Page 111
A5.2.2 The Delta–Gamma Normal Approach......Page 113
A5.2.3 Wilson’s Delta–Gamma Approach......Page 114
A5.2.4 Other Delta–Gamma Approaches......Page 116
A5.3 Conclusions......Page 117
A5.4 Recommended Reading......Page 118
6.1.1 Preliminary Considerations......Page 120
6.1.2 An Example: Estimating the VaR and ETL of an American Put......Page 121
6.2.1 Basic Principal Components Simulation......Page 122
6.2.2 Scenario Simulation......Page 123
6.3.1.1 Stochastic Processes for Interest Rates......Page 125
6.3.2 A General Approach to Fixed-income VaR and ETL......Page 126
6.4 Estimating VaR and ETL under a Dynamic Portfolio Strategy......Page 128
6.5 Estimating Credit-related Risks with Simulation Methods......Page 130
6.6 Estimating Insurance Risks with Simulation Methods......Page 132
6.7 Estimating Pensions Risks with Simulation Methods......Page 133
6.7.1 Estimating Risks of Defined-benefit Pension Plans......Page 134
6.7.2 Estimating Risks of Defined-contribution Pension Plans......Page 136
6.9 Recommended Reading......Page 138
7.1.1 Interpreting Incremental VaR......Page 140
7.1.2 Estimating IVaR by Brute Force: The ‘Before and After’ Approach......Page 141
7.1.3.1 Garman’s ‘delVaR’ Approach......Page 142
7.2.1 Properties of Component VaR......Page 145
7.2.2.1 ‘Drill-down’ Capability......Page 147
7.2.2.2 Reporting Component VaRs......Page 148
7.4 Recommended Reading......Page 149
8.1 Liquidity and Liquidity Risks......Page 150
8.2.1 A Transactions Cost Approach......Page 151
8.2.2 The Exogenous Spread Approach......Page 154
8.2.4 Derivatives Pricing Approaches......Page 155
8.2.5 The Liquidity Discount Approach......Page 156
8.2.6 A Summary and Comparison of Alternative Approaches......Page 157
8.3 Estimating Liquidity at Risk (LaR)......Page 158
8.4 Estimating Liquidity in Crises......Page 160
8.5 Recommended Reading......Page 162
9.1.1 Obtaining Data......Page 164
9.2.1 The Basic Frequency-of-tail-losses (or Kupiec) Test......Page 166
9.2.2 The Time-to-first-tail-loss Test......Page 168
9.2.3 A Tail-loss Confidence-interval Test......Page 169
9.3.1 The Basic Sizes-of-tail-losses Test......Page 170
9.3.2 The Crnkovic–Drachman Backtest Procedure......Page 172
9.3.3 The Berkowitz Approach......Page 174
9.4.1 Basic Ideas......Page 176
9.4.3 The Size-adjusted Frequency (Lopez II) Approach......Page 177
9.4.5 An Alternative Sizes-of-tail-losses Approach......Page 178
9.6 Assessing the Accuracy of Backtest Results......Page 179
9.7 Backtesting with Alternative Confidence Levels, Positions and Data......Page 180
9.7.1 Backtesting with Alternative Confidence Levels......Page 181
9.8 Summary......Page 182
9.9 Recommended Reading......Page 183
10 Stress Testing......Page 184
10.1.1 Benefits of Stress Testing......Page 186
10.1.2 Difficulties with Stress Tests......Page 188
10.2.1.1 Stylised Scenarios......Page 190
10.2.1.2 Actual Historical Events......Page 191
10.2.2 Evaluating the Effects of Scenarios......Page 193
10.3.1 Factor Push Analysis......Page 195
10.3.2 Maximum Loss Optimisation......Page 197
10.5 Recommended Reading......Page 198
11.1.1 Models......Page 200
11.1.2 Model Risk......Page 201
11.2.1 Incorrect Model Specification......Page 202
11.2.3 Implementation Risk......Page 204
11.2.4.2 Programming Problems......Page 205
11.3 Combating Model Risk......Page 206
11.3.2 Combating Model Risk: Some Guidelines for Managers......Page 207
11.3.3.1 Procedures to Vet, Check and Review Models......Page 209
11.3.3.2 Independent Risk Oversight......Page 210
11.5 Recommended Reading......Page 211
Toolkit......Page 212
Bibliography......Page 284
Author Index......Page 294
Subject Index......Page 298
Software Index......Page 306