1.1 VAR, ETL, Expected Loss and Unexpected Loss 5
1.2 Classification of Risk 7
1.3 Classification of Uncertainties 11
1.4 The FSA’s Classification of Risk Faced by
Insurance Companies 12
1.5 Risks Facing a Bank 12
1.6 Overlapping of Risk Types 14
1.7 Probability Distributions with Similar Best and
Worst Cases 16
1.8 Risk Analysis of Carry Trade 18
1.9 A Schematic Representation of the
Simulation Exercise (1) 19
1.10 A Schematic Representation of the
Simulation Exercise (2) 20
1.11 Factors Leading to Rising Exposure to
Operational Risk 23
1.12 Components of Tier 1 and Tier 2 Capital 34
1.13 An Illustration of Regulatory Capital Arbitrage 36
1.14 The Effect of Securitisation 37
2.1 The Basel Committee’s Structure (up to October 2006) 41
2.2 The Basel Committee’s Present Structure 41
2.3 Risk-Based Weights under Basel I 47
2.4 The Three Pillars and Objectives of Basel II 56
2.5 Components of Credit Risk 57
2.6 The Betas Assigned to Business Lines 60
2.7 The BCBS Business Lines with Examples 60
2.8 Alternative Measures of Exposure to Operational
Risk by Business Line 62
2A1.1 Difference between Capital Charges under the
BIA and STA Case (1) 80
Figures
x FIGURES
2A1.2 The Weighted Average of Business Line Betas (Case 1) 80
2A1.3 Difference between Capital Charges under the
BIA and STA (Case 2) 81
2A1.4 The Weighted Average of Business Line Betas (Case 2) 81
3.1 Decomposition of the BCBS Definition of
Operational Risk 86
3.2 Operational Risk: Causes, Events and
Forms of Loss 96
3.3 Operational Risk by Cause 97
3.4 The Credit Suisse Classification of
Operational Risk by Cause 99
3.5 The BCBS Classification of Operational
Losses by Event Type 100
3.6 Classification of Loss Events by Frequency
and Severity 103
3.7 Classification of Loss Events by Frequency,
Severity and Business Line 104
3.8 Frequency of Loss Events by Business Line 105
3.9 Severity of Loss Events by Business Line 106
3.10 A Modified US Air Force Risk Classification System 107
3.11 Nominal, Ordinary and Exceptional Operational Risk 108
3.12 The Distributions of Inherent and Residual Risk 110
3.13 Loss Events by Type and Business Line (BCBS Data) 111
3.14 Severity by Business Line and Event Type
(BCBS Data) 112
3.15 A Risk Map of the BCBS Loss
Events (by Event Type/Business Line) 113
3.16 Loss Events by Type and Business Line
(US LDCE Data) 113
3.17 A Risk Map of the US Loss Events
(by Event Type/Business Line) 114
3.18 Loss Events by Type and Business
Line (Japanese LDCE Data) 115
3.19 A Risk Map of the Japanese Loss Events (by Event
Type/Business Line) 116
3.20 Direct and Indirect Reporting of
Operational Loss Data 126
3.21 Local and Central Databases 127
4.1 Risk Assessment/Measurement as a
Component of Risk Management 139
4.2 Classification of Operational Risk Models 144
4.3 Decomposition of a Foreign Exchange
Transaction Process 145
FIGURES xi
4.4 Steps Involved in the Loss Distribution Approach 148
4.5 Definitions of the Capital Charge 149
4.6 Steps Involved in the Scenario-Based Approach 152
4.7 Determination of Resource Allocation to
Reduce Operational Risk 155
4.8 A Fractured AMA Jigsaw 157
4.9 Capital Charge versus Complexity of the Approach (?) 166
5.1 A Typical Histogram of Operational Loss Data 178
5.2 The Time Setup for Event Studies 190
6.1 Monte Carlo Simulations of Frequency and Severity 199
6.2 Fitting Distributions to a Histogram of Historical Data 202
6.3 Q-Q Plots for the Body and Tail of the Distribution 204
6.4 The Firm-wide Capital Charge (Perfect Correlation) 206
6.5 The Firm-wide Capital Charge (Zero Correlation) 207
6.6 Hypothetical Loss Data 210
6.7 Q-Q Plots of the Frequency Distributions 211
6.8 Q-Q Plots of the Severity Distributions 213
6.9 Frequency, Severity and Total Loss Distributions
(Business Line A) 214
6.10 Frequency, Severity and Total Loss Distributions
(Business Line B) 215
6.11 Q-Q Plots of Total Loss Distributions 216
6.12 The Effect of Changing the Loss Distributions
(Business Line A) 217
6.13 The Effect of Correlation on the Firm-wide
Capital Charge 220
6.14 Value at Risk, Capital Charge and Correlation 224
xii
1.1 Selected Measures of Risk 3
2.1 Description of the Components of the
BCBS’s Present Structure 42
2.2 New Work Streams of the BCBS 44
3.1 Examples of Operational Risk by Cause 98
3.2 The Patterns of Numbers/Amounts 116
3.3 Elements of the Information Provided by a
Qualitative Database 119
6.1 Frequency and Severity of Hypothetical Loss Events 209
6.2 Severity Distributions 212
6.3 Capital Charges under Various Total Loss
Distributions (A) 219
6.4 The Effect of the Correlation Assumption on the
Firm-wide Capital Charge 224