目次

Preface xi 1. An Overview 1 2. Corporate Liabilities as ContingentClaims 7 2.1 Introduction 7 2.2 The Merton Model 8 2.3 The Merton Modelwith Stochastic Interest Rates 17 2.4 The Merton Model with Jumps in AssetValue 20 2.5 Discrete Coupons in a Merton Model 27 2.6 Default Barriers:the Black-Cox Setup 29 2.7 Continuous Coupons and Perpetual Debt 34 2.8Stochastic Interest Rates and Jumps with Barriers 36 2.9 A Numerical Schemewhen Transition Densities are Known 40 2.10 Towards Dynamic CapitalStructure: Stationary Leverage Ratios 41 2.11 Estimating Asset Value andVolatility 42 2.12 On the KMV Approach 48 2.13 The Trouble with the CreditCurve 51 2.14 Bibliographical Notes 54 3. Endogenous Default Boundaries andOptimal Capital Structure 59 3.1 Leland's Model 60 3.2 A Model with aMaturity Structure 64 3.3 EBIT-Based Models 66 3.4 A Model with StrategicDebt Service 70 3.5 Bibliographical Notes 72 4. Statistical Techniques forAnalyzing Defaults 75 4.1 Credit Scoring Using Logistic Regression 75 4.2Credit Scoring Using Discriminant Analysis 77 4.3 Hazard Regressions:Discrete Case 81 4.4 Continuous-Time Survival Analysis Methods 83 4.5Markov Chains and Transition-Probability Estimation 87 4.6 The Differencebetween Discrete and Continuous 93 4.7 A Word of Warning on the MarkovAssumption 97 4.8 Ordered Probits and Ratings 102 4.9 Cumulative AccuracyProfiles 104 4.10 Bibliographical Notes 106 5. Intensity Modeling 109 5.1What Is an Intensity Model? 111 5.2 The Cox Process Construction of a SingleJump Time 112 5.3 A Few Useful Technical Results 114 5.4 The MartingaleProperty 115 5.5 Extending the Scope of the Cox Specification 116 5.6Recovery of Market Value 117 5.7 Notes on Recovery Assumptions 120 5.8Correlation in Affine Specifications 122 5.9 Interacting Intensities 1265.10 The Role of Incomplete Information 128 5.11 Risk Premiums inIntensity-Based Models 133 5.12 The Estimation of Intensity Models 139 5.13The Trouble with the Term Structure of Credit Spreads 142 5.14Bibliographical Notes 143 6. Rating-Based Term-Structure Models 145 6.1Introduction 145 6.2 A Markovian Model for Rating-Based Term Structures 1456.3 An Example of Calibration 152 6.4 Class-Dependent Recovery 155 6.5Fractional Recovery of Market Value in the Markov Model 157 6.6 AGeneralized Markovian Model 159 6.7 A System of PDEs for the GeneralSpecification 162 6.8 Using Thresholds Instead of a Markov Chain 164 6.9The Trouble with Pricing Based on Ratings 166 6.10 Bibliographical Notes 1667. Credit Risk and Interest-Rate Swaps 169 7.1 LIBOR 170 7.2 A UsefulStarting Point 170 7.3 Fixed-Floating Spreads and the "Comparative-AdvantageStory" 171 7.4 Why LIBOR and Counterparty Credit Risk Complicate Things 1767.5 Valuation with Counterparty Risk 178 7.6 Netting and the Nonlinearity ofActual Cash Flows: a Simple Example 182 7.7 Back to Linearity: UsingDifferent Discount Factors 183 7.8 The Swap Spread versus the Corporate-BondSpread 189 7.9 On the Swap Rate, Repo Rates, and the Riskless Rate 192 7.10Bibliographical Notes 194 8. Credit Default Swaps, CDOs, and RelatedProducts 197 8.1 Some Basic Terminology 197 8.2 Decomposing the CreditDefault Swap 201 8.3 Asset Swaps 204 8.4 Pricing the Default Swap 206 8.5Some Differences between CDS Spreads and Bond Spreads 208 8.6 AFirst-to-Default Calculation 209 8.7 A Decomposition of m-of-n-to-DefaultSwaps 211 8.8 Bibliographical Notes 212 9. Modeling Dependent Defaults 2139.1 Some Preliminary Remarks on Correlation and Dependence 214 9.2Homogeneous Loan Portfolios 216 9.3 Asset-Value Correlation and IntensityCorrelation 233 9.4 The Copula Approach 242 9.5 Network Dependence 245 9.6Bibliographical Notes 249 Appendix A: Discrete-Time Implementation 251 A.1The Discrete-Time, Finite-State-Space Model 251 A.2 Equivalent MartingaleMeasures 252 A.3 The Binomial Implementation of Option-Based Models 255 A.4Term-Structure Modeling Using Trees 256 A.5 Bibliographical Notes 257Appendix B: Some Results Related to Brownian Motion 259 B.1 Boundary HittingTimes 259 B.2 Valuing a Boundary Payment when the Contract Has FiniteMaturity 260 B.3 Present Values Associated with Brownian Motion 261 B.4Bibliographical Notes 265 Appendix C: Markov Chains 267 C.1 Discrete-TimeMarkov Chains 267 C.2 Continuous-Time Markov Chains 268 C.3 BibliographicalNotes 273 Appendix D: Stochastic Calculus for Jump-Diffusions 275 D.1 ThePoisson Process 275 D.2 A Fundamental Martingale 276 D.3 The StochasticIntegral and Ito's Formula for a Jump Process 276 D.4 The General ItoFormula for Semimartingales 278 D.5 The Semimartingale Exponential 278 D.6Special Semimartingales 279 D.7 Local Characteristics and EquivalentMartingale Measures 282 D.8 Asset Pricing and Risk Premiums for SpecialSemimartingales 286 D.9 Two Examples 288 D.10 Bibliographical Notes 290Appendix E: A Term-Structure Workhorse 291 References 297 Index 307