Credit Securitisations and Derivatives

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 rho12 78 5.3.4 Method of Images for Time-Varying Coefficients at Certain Values of rho12 79 5.3.5 Alternative Methodologies for General Values of rho12 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