Hands-On Value-at-Risk and Expected Shortfall (eBook)

Martin Auer is senior consultant in the areas of quantitative finance, market and credit risk, and IT, working for the likes of Raiffeisen Bank International, Kommunalkredit, and T-Systems in Vienna, and for Bank of America in New York. He holds degrees in computer science, mathematics, and mathematics of finance from Vienna University of Technology, University of Vienna, and Columbia University. 

Endorsements 6
Preface 8
Acknowledgments 10
Contents 11
List of Figures 14
1 Introduction 16
2 Motivation 18
Part I Measures 25
3 Basic Terms and Notation 26
4 Historical Value-at-Risk 33
5 Sensitivities 39
6 Stress Tests 44
7 Analytical Value-at-Risk 46
7.1 Approximate VaR 46
7.2 VaR-Sensitivity 48
7.3 VaR-Contribution 49
8 Expected Shortfall 50
9 Model Choices 52
10 A Monte Carlo Modification 60
11 Support Measures 64
Part II Operations 70
12 Properties of VaR 71
13 Properties of ES 75
14 VaR Noise 79
15 Backtesting 83
16 Distribution Tests 87
17 Nine to Five 93
17.1 Why Did My VaR Increase? 93
17.2 How Will the VaR Change? 96
17.3 How Good Is the VaR Model Anyway? 97
17.4 Hmm, How Did the Parameters Materialize? 98
17.5 Can You Validate Your Model? 100
17.6 What About the Kurtosis? 101
Part III Setup 107
18 Context 108
19 Scope and Workflow 111
19.1 VaR Flow 111
19.2 Backtesting Flow 113
19.3 Sensitivity Flow 114
19.4 Stress Test and Stressed VaR Flow 114
19.5 Partial VaR Flow 115
19.6 Naming 115
19.7 Encapsulation 116
20 Implementation 117
20.1 Generating Scenarios 117
20.2 Computing PnLs 119
20.3 Aggregating 120
20.4 Accessing the Database 121
20.5 Coding Guidelines 121
20.6 File Formats 122
20.7 Optimizations 126
20.8 Metal 128
Part IV Wrap-Up 129
21 Conclusion 130
A Statistics 101 131
A.1 Random Variables and Probabilities 131
A.2 Expected Value 134
A.3 Variance and Standard Deviation 136
A.4 Sample Estimates 137
A.5 Kurtosis 139
A.6 Multiple Random Variables and Covariance 140
A.7 Distribution, Inverse, and Quantiles 143
A.8 Conditional Expectation 145
A.9 The Normal Distribution 145
A.10 Sums of Randoms 147
A.11 Some Densities for the Road (to Independence) 151
B Pricing 156
B.1 Trades as Asset Exchanges 157
B.2 Prices as Ratios 159
B.3 Prices of Future Delivery 159
B.4 Prices as Expectations 161
B.5 The Call Option 163
B.6 Views on Probabilities 164
C Further Reading 168
References 170
Index 172