Contents
Preface xiii
Acknowledgments xv
CHAPTER 1
Introduction to Operational Risk Management and Modeling 1
What is Operational Risk? 1
The Regulatory Environment 3
Why a Statistical Approach to Operational Risk Management? 5
Summary 6
Review Questions 6
Further Reading 6
CHAPTER 2
Random Variables, Risk indicators, and Probability 7
Random Variables and Operational Risk Indicators 7
Types of Random Variable 8
Probability 9
Frequency and Subjective Probability 11
Probability Functions 13
Case Studies 16
Case Study 2.1: Downtown Investment Bank 17
Case Study 2.2: Mr. Mondey’s OPVaR 20
Case Study 2.3: Risk in Software Development 20
Useful Excel Functions 24
Summary 24
Review Questions 25
Further Reading 26
CHAPTER 3
Expectation, Covariance, Variance, and Correlation 27
Expected Value of a RandomVariable 27
Variance and Standard Deviation 31
Covariance and Correlation 32
Some Rules for Correlation, Variance, and Covariance 34
Case Studies 35
Case Study 3.1: Expected Time to Complete
35
a Complex Transaction
Case Study 3.2: Operational Cost of System Down Time 37
Summary 38
Review Questions 38
Further Reading 39
CHAPTER 4
Modeling Central Tendency and Variability of Operational Risk Indicators 41
Empirical Measures of Central Tendency 41
Measures of Variability 43
Case Studies 44
Case Study 4.1: Approximating Business Risk 44
Excel Functions 47
Summary 47
Review Questions 48
Further Reading 49
CHAPTER 5
Measuring Skew and Fat Tails of Operational Risk Indicators 51
Measuring Skew 51
Measuring Fat Tails 54
Review of Excel and VBA Functions for Skew and Fat Tails 57
Summary 58
Review Questions 58
Further Reading 58
CHAPTER 6
Statistical Testing of Operational Risk Parameters 59
Objective and Language of Statistical Hypothesis Testing 59
Steps Involved In Conducting a Hypothesis Test 61
Confidence Intervals 64
Case Study 6.1: Stephan’s Mistake 65
Excel Functions for Hypothesis Testing 67
Summary 67
Review Questions 68
Further Reading 68
CHAPTER 7
Severity of Loss Probability Models 69
Normal Distribution 69
Estimation of Parameters 72
Beta Distribution 72
Erlang Distribution 77
Exponential Distribution 77
Gamma Distribution 78
Lognormal Distribution 80
Pareto Distribution 81
Weibull Distribution 81
Other Probability Distributions 83
What Distribution Best Fits My Severity of Loss Data? 84
Case Study 7.1: Modeling Severity of Loss Legal
86
Liability Losses
Summary 91
Review Questions 91
Further Reading 92
CHAPTER 8
Frequency of Loss Probability Models 93
Popular Frequency of Loss Probability Models 93
Other Frequency of Loss Distributions 98
Chi-Squared Goodness of Fit Test 100
Case Study 8.1: Key Personnel Risk 102
Summary 103
Review Questions 103
Further Reading 103
CHAPTER 9
Modeling Aggregate Loss Distributions 105
Aggregating Severity of Loss and Frequency
105
of Loss Distributions
Calculating OpVaR 108
Coherent Risk Measures 110
Summary 112
Review Questions 112
Further Reading 112
CHAPTER 10
The Law of Significant Digits and Fraud Risk Identification 113
The Law of Significant Digits 113
Benford’s Law in Finance 116
Case Study 10.1: Analysis of Trader’s Profit and Loss
116
Using Benford’s Law
A Step Towards Better Statistical Methods of Fraud Detection 118
Summary 120
Review Questions 120
Further Reading 120
CHAPTER 11
Correlation and Dependence 121
Measuring Correlation 121
Dependence 132
Stochastic Dependence 134
Summary 136
Review Questions 136
Further Reading 136
CHAPTER 12
Linear Regression in Operational Risk Management 137
The Simple Linear Regression Model 137
Multiple Regression 148
Prediction 153
Polynomial and Other Types of Regression 155
Multivariate Multiple Regression 155
Regime-Switching Regression 157
The Difference Between Correlation and Regression 158
A Strategy for Regression Model Building
159
in Operational Risk Management
Summary 159
Review Questions 159
Further Reading 160
CHAPTER 13
Logistic Regression in Operational Risk Management 161
Binary Logistic Regression 161
Bivariate Logistic Regression 165
Case Study 13.1: Nostro Breaks and Volume
172
in a Bivariate Logistic Regression
Other Approaches for Modeling Bivariate Binary Endpoints 173
Summary 176
Review Questions 177
Further Reading 177
CHAPTER 14
Mixed Dependent Variable Modeling 179
A Model for Mixed Dependent Variables 179
Working Assumption of Independence 181
Understanding the Benefits of Using a WAI 184
Case Study 14.1: Modeling Failure in Compliance 184
Summary 185
Review Questions 186
Further Reading 186
CHAPTER 15
Validating Operational Risk Proxies Using Surrogate Endpoints 187
The Need for Surrogate Endpoints in OR Modeling 187
The Prentice Criterion 188
Limitations of the Prentice Criterion 191
The Real Value Added of Using Surrogate Variables 193
Validation Via the Proportion Explained 196
Limitations of Surrogate Modelling in Operational
200
Risk Management
Case Study 15.1: Legal Experience as a Surrogate Endpoint
201
for Legal Costs for a Business Unit
Summary 202
Review Questions 202
Further Reading 202
CHAPTER 16
Introduction to Extreme Value Theory 203
Fisher-Tippet–Gnedenko Theorem 203
Method of Block Maxima 205
Peaks over Threshold Modeling 206
Summary 207
Review Questions 207
Further Reading 207
CHAPTER 17
Managing Operational Risk with Bayesian Belief Networks 209
What is a Bayesian Belief Network? 209
Case Study 17.1: A BBN Model for Software Product Risk 212
Creating a BBN-Based Simulation 215
Assessing the Impact of Different Managerial Strategies 216
Perceived Benefits of Bayesian Belief Network Modeling 218
Common Myths About BBNs—
222
The Truth for Operational Risk Management
Summary 224
Review Questions 224
Further Reading 224
CHAPTER 18
Epilogue 225
Winning the Operational Risk Argument 225
Final Tips on Applied Operational Risk Modeling 226
Further Reading 226
Appendix
227
Statistical Tables
Cumulative Distribution Function of the Standard
227
Normal Distribution
Chi-Squared Distribution 230
Student’s t Distribution 232
F Distribution 233
237
Notes
245
Bibliography
255
About the CD-ROM
259
Index
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