Understanding and Managing Model Risk

Massimo Morini is Head of Credit Models and Coordinator of Model Research at IMI Bank of Intesa San Paolo. He has spent the last ten years inventing new models, implementing them, and helping practitioners in using them for buying, selling, and hedging derivatives. This has exposed him to the most practical side of model risk, and has led him to investigate model uncertainty, model robustness, and the management of the risk of model losses. Massimo is also Professor of Fixed Income at Bocconi University and was a Research Fellow at Cass Business School, City University London. He regularly delivers advanced training in London New York and worldwide on model risk management, credit modelling, interest rate models and correlation modelling, where he teaches cutting edge innovations in quantitative finance and discusses their implications with practitioners from the major institutions. He has led workshops on financial modelling and the financial crisis at major international conferences, including Global Derivatives, the Quant Congress, and the Fixed Income Conference. He has published papers in journals including Risk Magazine, Mathematical Finance, and the Journal of Derivatives. Massimo holds a PhD in Mathematics and an MSc in Economics.

Preface xi Acknowledgements xix Part I Theory and Practice of Model Risk Management 1 Understanding Model Risk 3 1.1 What Is Model Risk? 3 1.1.1 The Value Approach 4 1.1.2 The Price Approach 6 1.1.3 A Quant Story of the Crisis 9 1.1.4 A Synthetic View on Model Risk 17 1.2 Foundations of Modelling and the Reality of Markets 22 1.2.1 The Classic Framework 22 1.2.2 Uncertainty and Illiquidity 30 1.3 Accounting for Modellers 38 1.3.1 Fair Value 38 1.3.2 The Liquidity Bubble and the Accountancy Boards 40 1.3.3 Level 1, 2, 3 .go? 41 1.3.4 The Hidden Model Assumptions in vanilla Derivatives 42 1.4 What Regulators Said After the Crisis 48 1.4.1 Basel New Principles: The Management Process 49 1.4.2 Basel New Principles: The Model, The Market and The Product 51 1.4.3 Basel New Principles: Operative Recommendations 52 1.5 Model Validation and Risk Management: Practical Steps 53 1.5.1 A Scheme for Model Validation 54 1.5.2 Special Points in Model Risk Management 59 1.5.3 The Importance of Understanding Models 60 2 Model Validation and Model Comparison: Case Studies 63 2.1 The Practical Steps of Model Comparison 63 2.2 First Example: The Models 65 2.2.1 The Credit Default Swap 66 2.2.2 Structural First-Passage Models 67 2.2.3 Reduced-Form Intensity Models 69 2.2.4 Structural vs Intensity: Information 72 2.3 First Example: The Payoff. Gap Risk in a Leveraged Note 74 2.4 The Initial Assessment 77 2.4.1 First Test: Calibration to Liquid Relevant Products 77 2.4.2 Second Test: a Minimum Level of Realism 78 2.5 The Core Risk in the Product 81 2.5.1 Structural Models: Negligible Gap Risk 82 2.5.2 Reduced-Form Models: Maximum Gap Risk 82 2.6 A Deeper Analysis: Market Consensus and Historical Evidence 85 2.6.1 What to Add to the Calibration Set 85 2.6.2 Performing Market Intelligence 86 2.6.3 The Lion and the Turtle. Incompleteness in Practice 86 2.6.4 Reality Check: Historical Evidence and Lack of it 87 2.7 Building a Parametric Family of Models 88 2.7.1 Understanding Model Implications 93 2.8 Managing Model Uncertainty: Reserves, Limits, Revisions 95 2.9 Model Comparison: Examples from Equity and Rates 99 2.9.1 Comparing Local and Stochastic Volatility Models in Pricing Equity Compound and Barrier Options 99 2.9.2 Comparing Short Rate and Market Models in Pricing Interest Rate Bermudan Options 105 3 Stress Testing and the Mistakes of the Crisis 111 3.1 Learning Stress Test from the Crisis 111 3.1.1 The Meaning of Stress Testing 112 3.1.2 Portfolio Stress Testing 113 3.1.3 Model Stress Testing 116 3.2 The Credit Market and the Formula that Killed Wall Street 118 3.2.1 The CDO Payoff 118 3.2.2 The Copula 119 3.2.3 Applying the Copula to CDOs 122 3.2.4 The Market Quotation Standard 124 3.3 Portfolio Stress Testing and the Correlation Mistake 125 3.3.1 From Flat Correlation Towards a Realistic Approach 126 3.3.2 A Correlation Parameterization to Stress the Market Skew 131 3.4 Payoff Stress and the Liquidity Mistake 136 3.4.1 Detecting the Problem: Losses Concentrated in Time 137 3.4.2 The Problem in Practice 139 3.4.3 A Solution. From Copulas to Real Models 145 3.4.4 Conclusions 150 3.5 Testing with Historical Scenarios and the Concentration Mistake 151 3.5.1 The Mapping Methods for Bespoke Portfolios 152 3.5.2 The Lehman Test 156 3.5.3 Historical Scenarios to Test Mapping Methods 157 3.5.4 The Limits of Mapping and the Management of Model Risk 164 3.5.5 Conclusions 168 4 Preparing for Model Change. Rates and Funding in the New Era 171 4.1 Explaining the Puzzle in the Interest Rates Market and Models 171 4.1.1 The Death of a Market Model: 9 August 2007 173 4.1.2 Finding the New Market Model 174 4.1.3 The Classic Risk-free Market Model 178 4.1.4 A Market Model with Stable Default Risk 182 4.1.5 A Market with Volatile Credit Risk 192 4.1.6 Conclusions 200 4.2 Rethinking the Valu