Coherent Stress Testing: A Bayesian Approach to the Analysis of Financial Risk / Edition 1

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“Rebonato’s refreshingly original book is the most significant advance in financial risk management in many years. It is rigorous yet thoroughly practical, proposing an operational Bayesian framework that complements purely statistical approaches with the causal/economic structure needed for coherent stress testing. Prominently displayed and mixed beautifully throughout are both the expansive wisdom of a serious scholar, and the pragmatic applied sense of a seasoned industry veteran. Rebonato has defined the new frontier of best-practice financial risk management. I am open-mouthed with admiration.”
Francis X. Diebold, Paul F. and Warren S. Miller Professor of Economics, Co-Director, Wharton Financial Institutions Center, Professor of Finance and Statistics, University of Pennsylvania

“Risk management is at a crossroads. The ‘certainty’ provided by statistical analysis of historical data has been shown to be an illusion. The challenge is how to inject a dose of judgment but not revert to pure subjectivity. There is no clear answer, and a reliable guide is required to navigate what can be a minefield. Fortunately Dr. Rebonato has used his unique combination of technical skills and experience to explain what can cannot be done using stress testing. Anyone who is interested in combining the best aspects of statistical analysis and disciplined subjective judgment should read this book.”
Ian Cooper, Professor Finance, London Business School

“Wall Street goes Bayesian! Theses methods have long been used as a standard technique in reliability engineering and operations research, now this book introduces Bayesian nets as a stress testing tool for the financial industry. Every quantitative risk manager ought to be aware of their potential: this is an excellent start.”
Paul Embrechts, Department of Mathematics and RiskLab, ETH Zurich

“Stress tests are essential complements to VaR models, which are inadequate for very rare events. In practice, however, scenarios can be difficult to handle because they are typically not associated with a probability. This book shows how to build subjective, yet consistent probabilities for scenarios. Highly recommended.”
Philippe Jorion, Professor, University of California at Irvine

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Product Details

  • ISBN-13: 9780470666012
  • Publisher: Wiley
  • Publication date: 7/21/2010
  • Series: Wiley Finance Series
  • Edition number: 1
  • Pages: 240
  • Sales rank: 1,302,162
  • Product dimensions: 6.60 (w) x 9.70 (h) x 1.00 (d)

Meet the Author

DR. RICCARDO REBONATO (London, UK) is Head of Front Office Risk Management and Head of the Clients Analytics team at BGM RBS. He is visiting lecturer at Oxford University (Mathematical Finance) and adjunct professor at Imperial College (Tanaka Business School). He sits on the Board of Directors of ISDA and on the Board of Trustees for GARP. He is an editor for the International Journal of Theoretical and Applied Finance, Applied Mathematical Finance, Journal of Risk, and the Journal of Risk Management in Financial Institutions. He holds doctorates in Nuclear Engineering and in Science of Material/Solid State Phsyics. He was a research fellow in Physics at Corpus Christi College, Oxford, UK.

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Table of Contents

Acknowledgements xi

1 Introduction 1

1.1 Why We Need Stress Testing 1

1.2 Plan of the Book 5

1.3 Suggestions for Further Reading 6

I Data, Models and Reality 7

2 Risk and Uncertainty - or, Why Stress Testing is Not Enough 9

2.1 The Limits of Quantitative Risk Analysis 9

2.2 Risk or Uncertainty? 10

2.3 Suggested Reading 13

3 The Role of Models in Risk Management and Stress Testing 15

3.1 How Did We Get Here? 16

3.2 Statement of the Two Theses of this Chapter 17

3.3 Defence of the First Thesis (Centrality of Models) 18

3.3.1 Models as Indispensable Interpretative Tools 18

3.3.2 The Plurality-of-Models View 21

3.4 Defence of the Second Thesis (Coordination) 23

3.4.1 Traders as Agents 23

3.4.2 Agency Brings About Coordination 25

3.4.3 From Coordination to Positive Feedback 26

3.5 The Role of Stress and Scenario Analysis 27

3.6 Suggestions for Further Reading 29

4 What Kind of Probability Do We Need in Risk Management? 31

4.1 Frequentist versus Subjective Probability 31

4.2 Tail Co-dependence 36

4.3 From Structural Models to Co-dependence 38

4.4 Association or Causation? 39

4.5 Suggestions for Further Reading 42

II The Probabilistic Tools and Concepts 45

5 Probability with Boolean Variables I: Marginal and Conditional Probabilities 47

5.1 The Set-up and What We are Trying to Achieve 47

5.2 (Marginal) Probabilities 50

5.3 Deterministic Causal Relationship 53

5.4 Conditional Probabilities 55

5.5 Time Ordering and Causation 56

5.6 An Important Consequence: Bayes' Theorem 57

5.7 Independence 58

5.8 Two Worked-Out Examples 59

5.8.1 Dangerous Running 59

5.8.2 Rare and Even More Dangerous Diseases 61

5.9 Marginal and Conditional Probabilities: A Very Important Link 62

5.10 Interpreting and Generalizing the Factors xik 65

5.11 Conditional Probability Maps 67

6 Probability with Boolean Variables II: Joint Probabilities 71

6.1 Conditioning on More Than One Event 71

6.2 Joint Probabilities 73

6.3 A Remark on Notation 75

6.4 From the Joint to the Marginal and the Conditional Probabilities 76

6.5 From the Joint Distribution to Event Correlation 77

6.6 From the Conditional and Marginal to the Joint Probabilities? 83

6.7 Putting Independence to Work 84

6.8 Conditional Independence 86

6.9 Obtaining Joint Probabilities with Conditional Independence 88

6.10 At a Glance 89

6.11 Summary 90

6.12 Suggestions for Further Reading 90

7 Creating Probability Bounds 93

7.1 The Lay of the Land 93

7.2 Bounds on Joint Probabilities 93

7.3 How Tight are these Bounds in Practice? 96

8 Bayesian Nets I: An Introduction 99

8.1 Bayesian Nets: An Informal Definition 99

8.2 Defining the Structure of Bayesian Nets 101

8.3 More About Conditional Independence 104

8.4 What Goes in the Conditional Probability Tables? 106

8.5 Useful Relationships 107

8.6 A Worked-Out Example 109

8.7 A Systematic Approach 111

8.8 What Can We Do with Bayesian Nets? 113

8.8.1 Unravelling the Causal Structure 113

8.8.2 Estimating the Joint Probabilities 114

8.9 Suggestions for Further Reading 115

9 Bayesian Nets II: Constructing Probability Tables 117

9.1 Statement of the Problem 117

9.2 Marginal Probabilities - First Approach 118

9.2.1 Starting from a Fixed Probability 119

9.2.2 Starting from a Fixed Magnitude of the Move 120

9.3 Marginal Probabilities - Second Approach 120

9.4 Handling Events of Different Probability 122

9.5 Conditional Probabilities: A Reasonable Starting Point 123

9.6 Conditional Probabilities: Checks and Constraints 125

9.6.1 Necessary Conditions 125

9.6.2 Triplet Conditions 126

9.6.3 Independence 127

9.6.4 Deterministic Causation 127

9.6.5 Incompatibility of Events 128

9.7 Internal Compatibility of Conditional Probabilities: The Need for a Systematic Approach 129

III Applications 131

10 Obtaining a Coherent Solution I: Linear Programming 133

10.1 Plan of the Work Ahead 133

10.2 Coherent Solution with Conditional Probabilities Only 135

10.3 The Methodology in Practice: First Pass 141

10.4 The CPU Cost of the Approach 144

10.5 Illustration of the Linear Programming Technique 144

10.6 What Can We Do with this Information? 149

10.6.1 Extracting Information with Conditional Probabilities Only 149

10.6.2 Extracting Information with Conditional and Marginal Probabilities 151

11 Obtaining a Coherent Solution II: Bayesian Nets 155

11.1 Solution with Marginal and n-conditioned Probabilities 156

11.1.1 Generalizing the Results 164

11.2 An 'Automatic' Prescription to Build Joint Probabilities 165

11.3 What Can We Do with this Information? 167

11.3.1 Risk-Adjusting Returns 168

IV Making It Work In Practice 171

12 Overcoming Our Cognitive Biases 173

12.1 Cognitive Shortcoming and Bounded Rationality 174

12.1.1 How Pervasive are Cognitive Shortcomings? 175

12.1.2 The Social Context 175

12.1.3 Adaptiveness 176

12.2 Representativeness 178

12.3 Quantification of the Representativeness Bias 181

12.4 Causal/Diagnostic and Positive/Negative Biases 182

12.5 Conclusions 184

12.6 Suggestions for Further Reading 185

13 Selecting and Combining Stress Scenarios 187

13.1 Bottom Up or Top Down? 187

13.2 Relative Strengths and Weaknesses of the Two Approaches 187

13.3 Possible Approaches to a Top-Down Analysis 190

13.4 Sanity Checks 191

13.5 How to Combine Stresses - Handling the Dimensionality Curse 192

13.6 Combining the Macro and Bottom-Up Approaches 194

14 Governance 197

14.1 The Institutional Aspects of Stress Testing 197

14.1.1 Transparency and Ease of Use 197

14.1.2 Challenge by Non-specialists 198

14.1.3 Checks for Completeness 198

14.1.4 Interactions among Different Specialists 199

14.1.5 Auditability of the Process and of the Results 201

14.2 Lines of Criticism 201

14.2.1 The Role of Subjective Inputs 202

14.2.2 The Complexity of the Stress-testing Process 203

Appendix: A Simple Introduction to Linear Programming 205

A.1 Plan of the Appendix 205

A.2 Linear Programming - A Refresher 205

A.3 The Simplex Method 208

References 213

Index 217

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