Preface Part I. Structural Approach 1. Introduction to Credit Risk 1.1 Corporate Bonds 1.1.1 Recovery Rules 1.1.2 Safety Covenants 1.1.3 Credit Spreads 1.1.4 Credit Ratings 1.1.5 Corporate Coupon Bonds 1.1.6 Fixed and Floating Rate Notes 1.1.7 Bank Loans and Sovereign Debt 1.1.8 Cross Default 1.1.9 Default Correlations 1.2 Vulnerable Claims 1.2.1 Vulnerable Claims with Unilateral Default Risk 1.2.2 Vulnerable Claims with Bilateral Default Risk 1.2.3 Defaultable Interest Rate Contracts 1.3 Credit Derivatives 1.3.1 Default Swaps and Options 1.3.2 Total Rate of Return Swaps 1.3.3 Credit Linked Notes 1.3.4 Asset Swaps 1.3.5 First-to-Default Contracts 1.3.6 Credit Spread Swaps and Options 1.4 Quantitative Models of Credit Risk 1.4.1 Structural Models 1.4.2 Reduced-Form Models 1.4.3 Credit Risk Management 1.4.4 Liquidity Risk 1.4.5 Econometric Studies 2. Corporate Debt 2.1 Defaultable Claims 2.1.1 Risk-Neutral Valuation Formula 2.1.2 Self-Financing Trading Strategies 2.1.3 Martingale Measures 2.2 PDE Approach 2.2.1 PDE for the Value Function 2.2.2 Corporate Zero-Coupon Bonds 2.2.3 Corporate Coupon Bond 2.3 Merton's Approach to Corporate Debt 2.3.1 Merton's Model with Deterministic Interest Rates 2.3.2 Distance-to-Default 2.4 Extensions of Merton's Approach 2.4.1 Models with Stochastic Interest Rates 2.4.2 Discontinuous Value Process 2.4.3 Buffet's Approach 3. First-Passage-Time Models 3.1 Properties of First Passage Times 3.1.1 Probability Law of the First Passage Time 3.1.2 Joint Probability Law of Y and T
3.2 Black and Cox Model 3.2.1 Corporate Zero-Coupon Bond 3.2.2 Corporate Coupon Bond 3.2.3 Corporate Consol Bond 3.3 Optimal Capital Structure 3.3.1 Black and Cox Approach 3.3.2 Leland's Approach 3.3.3 Leland and Tort Approach 3.3.4 Further Developments 3.4 Models with Stochastic Interest Rates 3.4.1 Kim, Ramaswamy and Sundaresan Approach 3.4.2 Longstaff and Schwartz Approach 3.4.3 Cathcart and E1-Jahel Approach 3.4.4 Briys and de Varenne Approach 3.4.5 Saa-Requejo and Santa-Clara Approach 3.5 Further Developments 3.5.1 Convertible Bonds 3.5.2 Jump-Diffusion. Models 3.5.3 Incomplete Accounting Data 3.6 Dependent Defaults: Structural Approach 3.6.1 Default Correlations: J.P. Morgan's Approach 3.6.2 Default Correlations: Zhou's Approach Part II. Hazard Processes 4. Hazard Function of a Random Time 4.1 Conditional Expectations w.r.t. Natural Filtrations 4.2 Martingales Associated with a Continuous Hazard Function 4.3 Martingale Representation Theorem 4.4 Change of a Probability Measure 4.5 Martingale Characterization of the Hazard Function 4.6 Compensator of a Random Time 5. Hazard Process of a Random Time 5.1 Hazard Process Γ 5.1.1 Conditional Expectations 5.1.2 Semimartingale Representation of the Stopped Process 5.1.3 Martingales Associated with the Hazard Process Γ 5.1.4 Stochastic Intensity of a Random Time 5.2 Martingale Representation Theorems 5.2.1 General Case 5.2.2 Case of a Brownian Filtration 5.3 Change of a Probability Measure 6. Martingale Hazard Process 6.1 Martingale Hazard Process Λ 6.1.1 Martingale Invariance Property 6.1.2 Evaluation of Λ: Special Case 6.1.3 Evaluation of Λ: General Case 6.1.4 Uniqueness of a Martingale Hazard Process Λ 6.2 Relationships Between Hazard Processes Γ and Λ 6.3 Martingale Representation Theorem 6.4 Case of the Martingale Invariance Property 6.4.1 Valuation of Defaultable Claims
6.4.2 Case of a Stopping Time 6.5 Random Time with a Given Hazard Process 6.6 Poisson Process and Conditional Poisson Process 7. Case of Several Random Times 7.1 Minimum of Several Random Times 7.1.1 Hazard Function 7.1.2 Martingale Hazard Process 7.1.3 Martingale Representation Theorem 7.2 Change of a Probability Measure 7.3 Kusuoka's Counter-Example 7.3.1 Validity of Condition (F.2) 7.3.2 Validity of Condition (M.1) Part III. Reduced-Form Modeling 8. Intensity-Based Valuation of Defaultable Claims 8.1 Defaultable Claims 8.1.1 Risk-Neutral Valuation Formula 8.2 Valuation via the Hazard Process 8.2.1 Canonical Gonstruction of a Default Time 8.2.2 Integral Representation of the Value Process 8.2.3 Case of a Deterministic Intensity 8.2.4 Implied Probabilities of Default 8.2.5 Exogenous Recovery Rules 8.3 Valuation via the Martingale Approach 8.3.1 Martingale Hypotheses 8.3.2 Endogenous Recovery Rules 8.4 Hedging of Defaultable Claims 8.5 General Reduced-Form Approach 8.6 Reduced-Form Models with State Variables 8.6.1 Lando's Approach 8.6.2 Duffle and Singleton Approach 8.6.3 Hybrid Methodologies 8.6.4 Credit Spread Models 9. Conditionally Independent Defaults 9.1 Basket Credit Derivatives 9.1.1 Mutually Independent Default Times 9.1.2 Conditionally Independent Default Times 9.1.3 Valuation of the/th-to-Default Contract 9.1.4 Vanilla Default Swaps of Basket Type 9.2 Default Correlations and Conditional Probabilities 9.2.1 Default Correlations 9.2.2 Conditional Probabilities 10. Dependent Defaults 10.1 Dependent Intensities 10.1.1 Kusuoka's Approach 10.1.2 Jarrow and Yu Approach 10.2 Martingale Approach to Basket Credit Derivatives 10.2.1 Valuation of the ith-to-Default Claims 11. Markov Chains 11.1 Discrete-Time Markov Chains 11.1.1 Change of a Probability Measure
11.1.2 The Law of the Absorption Time 11.1.3 Discrete-Time Conditionally Markov Chains 11.2 Continuous-Time Markov Chains 11.2.1 Embedded Discrete-Time Markov Chain 11.2.2 Conditional Expectations 11.2.3 Probability Distribution of the Absorption Time 11.2.4 Martingales Associated with Transitions 11.2.5 Change of a Probability Measure 11.2.6 Identification of the Intensity Matrix 11.3 Continuous-Time Conditionally Markov Chains 11.3.1 Construction of a Conditionally Markov Chain 11.3.2 Conditional Markov Property 11.3.3 Associated Local Martingales 11.3.4 Forward Kolmogorov Equation 12. Markovian Models of Credit Migrations 12.1 JLT Markovian Model and its Extensions 12.1.1 JLT Model: Discrete-Time Case 12.1.2 JLT Model: Continuous-Time Case 12.1.3 Kijima and Komoribayashi Model 12.1.4 Das and Tufano Model 12.1.5 Thomas, Allen and Morkel-Kingsbury Model 12.2 Conditionally Markov Models 12.2.1 Lando's Approach 12.3 Correlated Migrations 12.3.1 Huge and Lando Approach 13. Heath-Jarrow-Morton Type Models 13.1 HJM Model with Default 13.1.1 Model's Assumptions 13.1.2 Default-Free Term Structure 13.1.3 Pre-Default Value of a Corporate Bond 13.1.4 Dynamics of Forward Credit Spreads 13.1.5 Default Time of a Corporate Bond 13.1.6 Case of Zero Recovery 13.1.7 Default-Free and Defaultable LIBOR Rates 13.1.8 Case of a Non-Zero Recovery Rate 13.1.9 Alternative Recovery Rules 13.2 HJM Model with Credit Migrations 13.2.1 Model's Assumption 13.2.2 Migration Process 13.2.3 Special Case 13.2.4 General Case 13.2.5 Alternative Recovery Schemes 13.2.6 Defaultable Coupon Bonds 13.2.7 Default Correlations 13.2.8 Market Prices of Interest Rate and Credit Risk 13.3 Applications to Credit Derivatives 13.3.1 Valuation of Credit Derivatives 13.3.2 Hedging of Credit Derivatives 14. Defaultable Market Rates 14.1 Interest Rate Contracts with Default Risk
14.1.1 Default-Free LIBOR and Swap Rates 14.1.2 Defaultable Spot LIBOR Rates 14.1.3 Defaultable Spot Swap Rates 14.1.4 FRAs with Unilateral Default Risk 14.1.5 Forward Swaps with Unilateral Default Risk 14.2 Multi-Period IRAs with Unilateral Default Risk 14.3 Multi-Period Defaultable Forward Nominal Rates 14.4 Defaultable Swaps with Unilateral Default Risk 14.4.1 Settlement of the 1st Kind 14.4.2 Settlement of the 2ad Kind 14.4.3 Settlement of the 3rd Kind 14.4.4 Market Conventions 14.5 Defaultable Swaps with Bilateral Default Risk 14.6 Defaultable Forward Swap Rates 14.6.1 Forward Swaps with Unilateral Default Risk 14.6.2 Forward Swaps with Bilateral Default Risk 15. Modeling of Market Rates 15.1 Models of Default-Free Market Rates 15.1.1 Modeling of Forward LIBOR Rates 15.1.2 Modeling of Forward Swap Rates 15.2 Modeling of Defaultable Forward LIBOR Rates 15.2.1 Lotz and Schlogl Approach 15.2.2 Sch6nbucher's Approach References Basic Notation Subject Index
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