Foreword xiii
PART I INTRODUCTION
1 Credit Securitizations and Derivatives 3
1.1 Economic Cycles and Credit Portfolio Risk 3
1.2 Credit Portfolio Risk Measurement 6
1.3 Credit Portfolio Risk Tranching 7
1.4 Credit Ratings 7
1.5 Actuarial vs. Market Credit Risk Pricing 7
1.6 Regulation 8
1.7 Thank You 9
References 9
2 Developments in Structured Finance Markets 11
2.1 Impairments of Asset-Backed Securities and Outstanding Ratings 11
2.2 Issuance of Asset-backed Securities and Outstanding Volume 17
2.3 Global CDO Issuance and Outstanding Volume 19
Concluding Remarks 29
Notes 29
References 31
PART II CREDIT PORTFOLIO RISK MEASUREMENT
3 Mortgage Credit Risk 35
3.1 Introduction 35
3.2 Five “C”s of Credit and Mortgage Credit Risk 38
3.3 Determinants of Mortgage Default, Loss Given Default and Exposure at Default 41
3.3.1 Determinants of Mortgage Default 41
3.3.2 Determinants of Mortgage LGD 43
3.3.3 Determinants of Mortgage EAD 48
3.4 Modeling Methods for Default, LGD and EAD 48
3.5 Model Risk Management 48
3.6 Conclusions 51
References 51
4 Credit Portfolio Correlations and Uncertainty 53
4.1 Introduction 53
4.2 Gaussian and Semi-Gaussian Single Risk Factor Model 54
4.3 Individual and Simultaneous Confidence Bounds and Intervals 55
4.4 Confidence Intervals for Asset Correlations 57
4.5 Confidence Intervals for Default and Survival Time Correlations 59
4.5.1 Confidence Intervals for Default Correlations 60
4.5.2 Confidence Intervals for Survival Time Correlations 61
4.6 Example 63
4.7 Conclusion 65
Appendix 66
Notes 69
References 69
5 Credit Portfolio Correlations with Dynamic Leverage Ratios 71
5.1 Introduction 71
5.2 The Hui et al. (2007) Model 72
5.2.1 The Method of Images for Constant Coefficients 73
5.2.2 The Method of Images for Time-Varying Coefficients 74
5.3 Modelling Default Correlations in a Two-Firm Model 75
5.3.1 Default Correlations 75
5.3.2 A Two-Firm Model with Dynamic Leverage Ratios 75
5.3.3 Method of Images for Constant Coefficients at Certain Values of ρ12 78
5.3.4 Method of Images for Time-Varying Coefficients at Certain Values of ρ12 79
5.3.5 Alternative Methodologies for General Values of ρ12 81
5.4 Numerical Results 81
5.4.1 Accuracy 83
5.4.2 The Impact of Correlation between Two Firms 84
5.4.3 The Impact of Dfferent Credit Quality Paired Firms 86
5.4.4 The Impact of Volatilities 87
5.4.5 The Impact of Drift Levels 88
5.4.6 The Impact of Initial Value of Leverage Ratio Levels 89
5.4.7 Impact of Correlation between Firms and Interest Rates 89
5.4.8 The Price of Credit-Linked Notes 91
5.5 Conclusion 92
Notes 93
References 94
6 A Hierarchical Model of Tail-Dependent Asset Returns 95
6.1 Introduction 95
6.2 The Variance Compound Gamma Model 97
6.2.1 Multivariate Process for Logarithmic Asset Returns 97
6.2.2 Dependence Structure 101
6.2.3 Sampling 105
6.2.4 Copula Properties 105
6.3 An Application Example 110
6.3.1 Portfolio Setup 110
6.3.2 Test Portfolios 113
6.3.3 Parameter Setup 113
6.3.4 Simulation Results 114
6.4 Importance Sampling Algorithm 116
6.5 Conclusions 120
Appendix A: The VCG Probability Distribution Function 121
Appendix B: HAC Representation for the VCG Framework 123
Notes 124
References 124
7 Monte Carlo Methods for Portfolio Credit Risk 127
7.1 Introduction 127
7.2 Modeling Credit Portfolio Losses 128
7.2.1 Risk Measures 128
7.2.2 Modeling Dependency 129
7.3 Estimating Risk Measures via Monte Carlo 129
7.3.1 Crude Monte Carlo Estimators 130
7.3.2 Importance Sampling 131
7.4 Specific Models 133
7.4.1 The Bernoulli Mixture Model 133
7.4.2 Factor Models 135
7.4.3 Copula Models 139
7.4.4 Intensity Models 143
7.4.5 An Example Point Process Model 145
Appendix A: A Primer on Rare-event Simulation 146
7.A.1 Efficiency 147
7.A.2 Importance Sampling 147
7.A.3 The Choice of g 148
7.A.4 Adaptive Importance Sampling 149
7.A.5 Importance Sampling for Stochastic Processes 150
References 151
8 Credit Portfolio Risk and Diversification 153
8.1 Introduction 153
8.2 Model Setup 154
8.3 Independent Asset Values 155
8.4 Correlated Asset Values 159
8.5 Large Portfolio Limit 161
8.5.1 Correlated Diffusion 161
8.5.2 Correlated GARCH Process 166
8.6 Applications of the Structural Recovery Rate 168
8.7 Conclusions 169
References 169
PART III CREDIT PORTFOLIO RISK SECURITIZATION AND TRANCHING
9 Differences in Tranching Methods: Some Results and Implications 173
9.1 Introduction 173
9.2 Defining a Tranche 174
9.3 The Mathematics of Tranching 175
9.3.1 PD-based Tranching 175
9.3.2 EL-based Tranching 176
9.4 The EL of a Tranche Necessarily Increases When Either the Attachment Point or the Detachment Point is Decreased 177
9.5 Upper Bound on Tranche Expected LGD (LGDt) Assumption Given EL-based Tranches 180
9.6 “Skipping” of Some Tranches in the EL-based Approach 182
9.7 Conclusion 183
Notes 184
References 185
10 Global Structured Finance Rating 187
10.1 Introduction 187
10.2 Asset-Backed Securities 188
10.2.1 The ABS Structure for the Experiment 188
10.2.2 Cash Flow Modeling 189
10.2.3 Modeling and Simulating Defaults 192
10.2.4 Expected Loss Rating 193
10.3 Global Sensitivity Analysis 194
10.3.1 Elementary Effects 195
10.3.2 Variance-based Method 196
10.4 Global Sensitivity Analysis Results 197
10.4.1 Uncertainty Analysis 197
10.4.2 Sensitivity Analysis 198
10.5 Global Rating 202
10.5.1 Methodology 203
10.6 Conclusion 204
Acknowledgment 205
Notes 205
References 205
PART IV CREDIT DERIVATIVES
11 Analytic Dynamic Factor Copula Model 209
11.1 Introduction 209
11.2 Pricing Equations 210
11.3 One-factor Copula Model 211
11.4 Multi-period Factor Copula Models 212
11.5 Calibration 218
11.6 Numerical Examples 219
11.7 Conclusions 222
Notes 223
References 223
12 Dynamic Modeling of Credit Derivatives 225
12.1 Introduction 225
12.1.1 General Model Choice 225
12.1.2 Modeling Option Prices 226
12.1.3 Modeling Credit Risk 227
12.2 Portfolio Credit Derivatives 229
12.3 Modeling Asset Dynamics 230
12.3.1 The Market Model 230
12.3.2 The Asset-value Model 234
12.4 Empirical Analysis 236
12.4.1 Elementary Data 236
12.4.2 Implied Dividends 236
12.4.3 Market Dynamics 237
12.4.4 Asset Value Model 239
12.4.5 Tranche Pricing 240
12.4.6 Out-of-time Application 240
12.5 Conclusion 242
Notes 243
References 243
13 Pricing and Calibration in Market Models 245
13.1 Introduction 245
13.2 Basic notions 246
13.3 The model 248
13.3.1 Modeling Assumptions 248
13.3.2 Absence of Arbitrage 249
13.4 An affine specification 252
13.5 Pricing 254
13.6 Calibration 258
13.6.1 Calibration Procedure 261
13.6.2 Calibration Results 263
Appendix A: Computations 265
References 270
14 Counterparty Credit Risk and Clearing of Derivatives – From the Perspective of an Industrial Corporate with a Focus on Commodity Markets 271
14.1 Introduction 271
14.2 Credit exposures in commodity business 272
14.2.1 Settlement Exposure 272
14.2.2 Performance Exposure 273
14.2.3 Example of Fixed Price Deal with Performance Exposure 274
14.2.4 Example of a Floating Price Deal with Performance Exposure 275
14.2.5 General Remarks on Credit Exposure Concepts 276
14.3 Ex Ante exposure-reducing techniques 277
14.3.1 Payment Terms 277
14.3.2 Material Adverse Change Clauses 277
14.3.3 Master Agreements 278
14.3.4 Netting 278
14.3.5 Margining 279
14.3.6 Close Out Exposure and Threshold 280
14.4 Ex Ante risk-reducing techniques 281
14.4.1 Credit Enhancements in General 281
14.4.2 Parent Company Guarantees 281
14.4.3 Letters of Credit 282
14.4.4 Credit Insurance 283
14.4.5 Clearing via a Central Counterparty 283
14.5 Ex Post risk-reducing techniques 287
14.5.1 Factoring 287
14.5.2 Novation 287
14.5.3 Risk-reducing Trades 288
14.5.4 Hedging with CDS 288
14.5.5 Hedging with Contingent-CDS 290
14.5.6 Hedging with Puts on Equity 290
14.6 Ex Post work out considerations 290
14.7 Practical credit risk management and pricing 291
14.8 Peculiarities of commodity markets 292
14.9 Peculiarities of commodity related credit portfolios 294
14.10 Credit Risk Capital for a commodity related portfolio – measured with an extension of CreditMetrics 295
14.11 Case study: CreditRisk+ applied to a commodity related credit portfolio 300
14.12 Outlook 302
Notes 303
References 304
15 CDS Industrial Sector Indices, Credit and Liquidity Risk 307
15.1 Introduction 307
15.2 The Data 308
15.3 Methodology and Results 312
15.3.1 Preliminary Analysis 312
15.3.2 Common Factor Analysis 316
15.4 Stability of Relations 321
15.5 Conclusions 322
References 323
16 Risk Transfer and Pricing of Illiquid Assets with Loan CDS 325
16.1 Introduction 325
16.2 Shipping Market 326
16.3 Loan Credit Default Swaps 327
16.3.1 LCDS Pricing 327
16.3.2 Modeling LCDS Under the Intensity-based Model 329
16.4 Valuation Framework for LCDS 331
16.4.1 The Structural Approach 331
16.4.2 Credit Risk in Shipping Loans 332
16.4.3 Valuation of LCDS on Shipping Loans 334
16.4.4 Simulation Model 335
16.5 Numerical Results 336
16.6 Conclusion 338
Appendix A: Monte Carlo Parameterization 339
References 339
PART V REGULATION
17 Regulatory Capital Requirements for Securitizations 343
17.1 Regulatory Approaches for Securitizations 343
17.1.1 Ratings Based Approach (RBA) 343
17.1.2 Supervisory Formula Approach (SFA) 346
17.1.3 Standardized Approach (SA) 353
17.2 Post-crisis Revisions to the Basel Framework 353
17.3 Outlook 354
Notes 355
References 355
18 Regulating OTC Derivatives 357
18.1 Overview 357
18.2 The Wall Street Transparency and Accountability Part of the Dodd–Frank Act of 2010 358
18.2.1 Which Derivatives Will Be Affected? 359
18.2.2 Clearing 359
18.2.3 Transparency and Reporting Requirements 361
18.2.4 Bankruptcy-Related Issues 361
18.2.5 Trading and Risk Mitigation 362
18.2.6 Extraterritorial Enforcement and International Coordination 363
18.3 Evaluation of Proposed Reforms 364
18.4 Clearing, Margins, Transparency, and Systemic Risk of Clearinghouses 369
18.4.1 Migration to Centralized Clearing Should Start with Credit Derivatives 369
18.4.2 Margin Requirements versus Transparency 370
18.4.3 Toward a Transparency Standard 374
18.4.4 Deal with the Dealers First 375
18.4.5 Proposed Reforms Will Help End Users 377
18.4.6 Centralized Clearinghouses: Too Systemic to Fail? 380
18.5 Conclusion: How Will the Derivatives Reforms Affect Global Finance in Future? 383
Appendix A: Items Concerning OTC Derivatives Left by the Dodd–Frank Act for Future Study 385
Appendix B: Current OTC Disclosure Provided by Dealer Banks 387
Appendix C: Sovereign Credit Default Swaps Markets 392
Notes 398
References 401
19 Governing Derivatives after the Financial Crisis: The Devil is in the Details 403
19.1 Introduction 403
19.2 Securitization and Risk Management 404
19.2.1 Securitization and Interest Rate Risk 405
19.2.2 Securitization and Credit Risk 405
19.2.3 Securitization and Credit Risk Transfer 406
19.2.4 Skin in the Game 407
19.3 The Regulation of Derivative Contracts 407
19.3.1 Regulation Prior to 2000 407
19.3.2 The Commodity Futures Modernization Act (CFMA) of 2000 408
19.3.3 The Dodd–Frank Wall Street Reform and Consumer Protection Act of 2010 408
19.4 Regulatory Challenges and Responses 409
19.4.1 Fostering an Exchange-traded Credit Derivatives Market 409
19.4.2 Counterparty Risk 410
19.4.3 Disclosure and Transparency 411
19.4.4 Accounting, Valuation and Stability Issues 412
19.5 Conclusions 412
Notes 413
References 415
About the Authors 417
Index 429
