别莱茨基所著的《信用风险的建模评估和对冲》旨在研究信用风险定价发展中的数学模型，这一研究提供了信用风险数学研究理论和金融实践之间过渡的桥梁。书中的数学知识全面，给出了信用风险模型的结构化和约化形式，具有等级违约术语结构的一些套利自由模型做了详细地研究。

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