Credit risk : modeling, valuation, and hedging /

Credit risk : modeling, valuation, and hedging /

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Bibliographic Details
Author / Creator:Bielecki, Tomasz R., 1955-
Imprint:Berlin ; New York : Springer, c2002.
Description:xviii, 500 p. ; 24 cm.
Language:English
Series:Springer finance
Subject:
Credit -- Mathematical models.
Risk management -- Mathematical models.
Credit -- Mathematical models.
Risk management -- Mathematical models.
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/4596351
Hidden Bibliographic Details
Other authors / contributors:Rutkowski, Marek, 1952-
ISBN:3540675930 (alk. paper)
Notes:Includes bibliographical references (p. [477]-494) and index.
Table of Contents:
  • 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 ¿
  • 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 Toft 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. Cathart and El-Jahel Approach
  • 3.4.4. Briys and de Varenne Approach
  • 3.4.5. Saá-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 ¿
  • 5.1.1. Conditional Expectations
  • 5.1.2. Semimartingale Representation of the Stopped Process
  • 5.1.3. Martingales Associated with the Hazard Process ¿
  • 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 ¿
  • 6.1.1. Martingale Invariance Property
  • 6.1.2. Evaluation of ¿: Special Case
  • 6.1.3. Evaluation of ¿: General Case
  • 6.1.4. Uniqueness of a Martingale Hazard Process ¿
  • 6.2. Relationships Between Hazard Processes ¿ and ¿
  • 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 Construction 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. Duffie 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 i 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 i th -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 Rate
  • 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 1 st Kind
  • 14.4.2. Settlement of the 2 nd Kind
  • 14.4.3. Settlement of the 3 rd 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 Schlögl Approach
  • 15.2.2. Schönbucher's Approach
  • A Guide to References
  • References
  • Basic Notation
  • Subject Index
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