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Friday, January 13, 2012

Operational Risk with Excel and VBA






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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