Risk management

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
CONTENTS......Page 7
Contributors......Page 9
Introduction......Page 11
1 Introduction......Page 17
2.1 Discounted cash flow formula......Page 20
2.2 Types of revaluation models......Page 21
2.3 Revaluation systems and valuation error......Page 22
2.4 Sources of valuation differences and valuation error......Page 23
3.1 General and specific market risk factors......Page 27
4 Introduction to market risk measurement......Page 28
4.1 Types of market risk......Page 29
4.3 Scenario measurements of market risk......Page 30
4.4 Statistical measurements of market risk......Page 32
4.5 Holding period and assumption of static portfolio......Page 33
4.6 Limitations on VAR......Page 34
4.7 The two basic components of VAR calculation......Page 35
5.1 Historical simulation......Page 36
5.2 Parametric statistical simulation......Page 37
5.3 Technical issues in simulating changes in market factors......Page 38
5.5 Positive definiteness......Page 39
5.6 Completeness of market factors......Page 40
5.7 Simulation of market risk with specific risk......Page 41
6.1 Full valuation......Page 42
6.3 Grids of factor sensitivities and the terms of a Tay-lor series expansion......Page 43
6.4 Parametric portfolio revaluation and the represen-tation of yield curve......Page 46
7.1 Forms of credit risk......Page 47
7.2 Defining pre-settlement exposure......Page 48
7.3 Credit exposure and credit risk......Page 51
7.4 Contrasting the exposure of Lending Risk, Issuer Risk and Pre-Settlement Risk......Page 53
7.5 Pre-settlement exposure to options......Page 54
7.6 Pre-settlement exposure of multiple contracts and netting......Page 55
7.7 Pre-settlement exposure and potential future re-placement cost......Page 56
7.8 Simple transaction exposure method of measuring pre-settlement exposure......Page 57
7.9 BIS requirements for pre-settlement credit risk......Page 62
7.10 Limitations of simple transaction method......Page 64
7.11 Counterparty portfolio simulation method and counterparty exposure profile......Page 66
7.12 Effects of a margin agreement on exposure and risk......Page 67
7.13 Economic capital for pre-settlement risk–general principles......Page 71
7.14 Economic capital for pre-settlement risk–simple example......Page 72
8 Comparing and contrasting market risk and pre-settlement risk......Page 73
1 Introduction......Page 76
The Original Contract......Page 78
The Swap and the Embedded Option......Page 79
3 The Nature of the Bet......Page 80
The Ex Post Behavior of Interest Rates and the Spread......Page 83
4 Value at Risk......Page 85
Notes on the Implementation and Choice of Model......Page 86
The Volatility Estimation......Page 87
The Spread and Future Contract Values......Page 88
5 Conclusion......Page 89
References......Page 91
Introduction......Page 92
1 A Review of the VaR Framework......Page 94
2 Stress Testing in the Context of VaR......Page 96
3 Stress Tests Scenarios based upon Historical Covariances......Page 97
Identifying Stress Events......Page 98
Stress Test Scenarios......Page 99
Results......Page 100
Anomalies......Page 106
5 Stress Testing with Volatility and Correlation Shocks......Page 108
Stressing Volatilities......Page 109
Shocking Volatilities and Correlations......Page 110
6 Issues Regarding Full Repricing......Page 112
7 Practical Issues Related to Scenario Specification......Page 113
References......Page 114
1 Introduction......Page 116
2 The dynamic stochastic programming approach......Page 118
Tracking problems......Page 121
Scenario trees......Page 123
The optimization problem......Page 124
The transaction cost model......Page 125
Turning the solution into a trading strategy......Page 126
4 The options problem......Page 127
The tradable instruments......Page 128
The scenario tree......Page 129
5 Numerical Experiments......Page 130
Portfolio compression......Page 131
Dynamic portfolio replication......Page 134
Benchmark results......Page 137
Experiments varying tree size......Page 138
Experiments varying initial branching......Page 139
6 Conclusions......Page 141
References......Page 143
1.1 VaRs for Market and Credit Risk......Page 145
1.2 Interest Rate and Credit Risk Correlation......Page 146
1.3 Decomposing Credit Risk......Page 147
2.2 Long-Horizon Correlations......Page 148
2.3 Non-Parametric Estimates on International Bond Spreads......Page 149
2.4 Non-Parametric Estimates on Bloomberg Spreads......Page 150
3.1 Transition Data......Page 152
3.2 Transition Matrices......Page 153
3.3 VaR Calculations......Page 156
References......Page 158
1 Introduction......Page 161
2.1 Risk as the random variable: future net worth......Page 163
2.2 Axioms on Acceptance Sets (Sets of Acceptable Future Net Worths)......Page 164
2.3 Correspondence between Acceptance Sets and Measures of Risk......Page 166
2.4 Correspondence between the Axioms on Acceptance Sets and the Axioms on Measures of Risks......Page 169
3.1 An Organized Exchange’s Rules: The SPAN Computations......Page 171
3.2 Some Model-Free Measures of Risks: the SEC rules on Final Net Worth......Page 173
3.3 Some Model-Dependent Rules based on Quantiles......Page 176
4.1 Representation of Coherent Risk Measures by Scenarios......Page 179
4.2 Construction of Coherent Risk Measures by Extension of Certain Risk Measurements......Page 181
5.1 A Proposal: the ‘Worst Conditional Expectation’ Measure of Risk......Page 184
5.2 Construction of a Measure Out of Measures on Separate Classes of Risks......Page 188
Acknowledgments......Page 189
References......Page 190
1.1 Correlation in finance and insurance......Page 192
1.2 Correlation as a source of confusion......Page 193
2 Copulas......Page 195
2.1 What is a copula?......Page 196
2.2 Examples of copulas......Page 197
2.3 Invariance......Page 198
3.1 What is correlation?......Page 199
3.2 Shortcomings of correlation......Page 200
3.3 Spherical and elliptical distributions......Page 201
3.4 Covariance and elliptical distributions in risk management......Page 205
4.1 Comonotonicity......Page 208
4.2 Desired properties of dependence measures......Page 209
4.3 Rank correlation......Page 211
4.4 Tail Dependence......Page 213
4.5 Concordance......Page 216
5 Fallacies......Page 218
6.1 Given marginals and linear correlations......Page 228
6.2 Given marginals and Spearman’s rank correlations......Page 232
6.3 Given marginals and copula......Page 234
7 Conclusions......Page 235
References......Page 236
1 Introduction......Page 240
2 Outline of Extreme Value Theory......Page 242
3 Bayesian Statistics for Risk Assessment......Page 248
4 Multivariate Extremes......Page 252
5 A Changepoint Model for Stochastic Volatility......Page 254
6 Conclusions......Page 259
References......Page 260
1 Introduction......Page 263
2 Firm-wide operational risk management......Page 265
3 Stable random variables and extreme value theory......Page 268
4 Stochastic model for measuring of operational risk......Page 273
5 Simulation of peaks over threshold model parameters by MCMC......Page 276
6 Example: bank trading losses analysis through the Russian crisis......Page 279
Prediction of actual losses by the economic loss capital provision at firm level......Page 282
Economic capital for operational risk at business unit level......Page 285
Economic capital for operational risk at firm level......Page 287
Conclusions and future directions......Page 288
References......Page 289