Credit risk is today one of the most intensely studied topics in quantitative finance. This book provides an introduction and overview for readers who seek an up-to-date reference to the central problems of the field and to the tools currently used to analyze them. The book is aimed at researchers and students in finance, at quantitative analysts in banks and other financial institutions, and at regulators interested in the modeling aspects of credit risk. David Lando considers the two broad approaches to credit risk analysis: that based on classical option pricing models on the one hand, and on a direct modeling of the default probability of issuers on the other. He offers insights that can be drawn from each approach and demonstrates that the distinction between the two approaches is not at all clear-cut. The book strikes a fruitful balance between quickly presenting the basic ideas of the models and offering enough detail so readers can derive and implement the models themselves. The discussion of the models and their limitations and five technical appendixes help readers expand and generalize the models themselves or to understand existing generalizations. The book emphasizes models for pricing as well as statistical techniques for estimating their parameters. Applications include rating-based modeling, modeling of dependent defaults, swap- and corporate-yield curve dynamics, credit default swaps, and collateralized debt obligations.
"Credit Risk Modeling provides the broadest coverage of topics I have seen in a book on credit risk. Lando successfully guides the reader through the maze of a very active field of research by clearly identifying the leading problems and the attempts that have been made to solve these problems. At the same time, never does he neglect the statistical estimation of the models he presents. This is a very valuable book to any practitioner, student, or researcher in credit risk, written by one of the leading experts in the field."
- Philipp Schönbucher, Swiss Federal Institute of Technology Zurich (ETH), author of Credit Derivatives Pricing Models
"This very well written book represents a superb presentation of both credit risk theory and its empirical evidence. It is a complete introduction to the topic, enabling the reader to access and understand current research."
- Robert Jarrow, Cornell University
"This is an excellent book for researchers, financial engineers, and advanced practitioners in the field of credit risk. It is a remarkable contribution to our field."
- Didier Cossin, Ecole des Hautes Etudes Commerciales, University of Lausanne
2. Corporate Liabilities as Contingent Claims
2.1 Introduction
2.2 The Merton Model
2.3 The Merton Model with Stochastic Interest Rates
2.4 The Merton Model with Jumps in Asset Value
2.5 Discrete Coupons in a Merton Model
2.6 Default Barriers: the Black-Cox Setup
2.7 Continuous Coupons and Perpetual Debt
2.8 Stochastic Interest Rates and Jumps with Barriers
2.9 A Numerical Scheme when Transition Densities are Known
2.10 Towards Dynamic Capital Structure: Stationary Leverage Ratios
2.11 Estimating Asset Value and Volatility
2.12 On the KMV Approach
2.13 The Trouble with the Credit Curve
2.14 Bibliographical Notes
3. Endogenous Default Boundaries and Optimal Capital Structure
3.1 Leland's Model
3.2 A Model with a Maturity Structure
3.3 EBIT-Based Models
3.4 A Model with Strategic Debt Service
3.5 Bibliographical Notes
4. Statistical Techniques for Analyzing Defaults
4.1 Credit Scoring Using Logistic Regression
4.2 Credit Scoring Using Discriminant Analysis
4.3 Hazard Regressions: Discrete Case
4.4 Continuous-Time Survival Analysis Methods
4.5 Markov Chains and Transition-Probability Estimation
4.6 The Difference between Discrete and Continuous
4.7 A Word of Warning on the Markov Assumption
4.8 Ordered Probits and Ratings
4.9 Cumulative Accuracy Profiles
4.10 Bibliographical Notes
5. Intensity Modeling
5.1 What Is an Intensity Model?
5.2 The Cox Process Construction of a Single Jump Time
5.3 A Few Useful Technical Results
5.4 The Martingale Property
5.5 Extending the Scope of the Cox Specification
5.6 Recovery of Market Value
5.7 Notes on Recovery Assumptions
5.8 Correlation in Affine Specifications
5.9 Interacting Intensities
5.10 The Role of Incomplete Information
5.11 Risk Premiums in Intensity-Based Models
5.12 The Estimation of Intensity Models
5.13 The Trouble with the Term Structure of Credit Spreads
5.14 Bibliographical Notes
6. Rating-Based Term-Structure Models
6.1 Introduction
6.2 A Markovian Model for Rating-Based Term Structures
6.3 An Example of Calibration
6.4 Class-Dependent Recovery
6.5 Fractional Recovery of Market Value in the Markov Model
6.6 A Generalized Markovian Model
6.7 A System of PDEs for the General Specification
6.8 Using Thresholds Instead of a Markov Chain
6.9 The Trouble with Pricing Based on Ratings
6.10 Bibliographical Notes
7. Credit Risk and Interest-Rate Swaps
7.1 LIBOR
7.2 A Useful Starting Point
7.3 Fixed-Floating Spreads and the "Comparative-Advantage Story"
7.4 Why LIBOR and Counterparty Credit Risk Complicate Things
7.5 Valuation with Counterparty Risk
7.6 Netting and the Nonlinearity of Actual Cash Flows: a Simple Example
7.7 Back to Linearity: Using Different Discount Factors
7.8 The Swap Spread versus the Corporate-Bond Spread
7.9 On the Swap Rate, Repo Rates, and the Riskless Rate
7.10 Bibliographical Notes
8. Credit Default Swaps, CDOs, and Related Products
8.1 Some Basic Terminology
8.2 Decomposing the Credit Default Swap
8.3 Asset Swaps
8.4 Pricing the Default Swap
8.5 Some Differences between CDS Spreads and Bond Spreads
8.6 A First-to-Default Calculation
8.7 A Decomposition of m-of-n-to-Default Swaps
8.8 Bibliographical Notes
9. Modeling Dependent Defaults
9.1 Some Preliminary Remarks on Correlation and Dependence
9.2 Homogeneous Loan Portfolios
9.3 Asset-Value Correlation and Intensity Correlation
9.4 The Copula Approach
9.5 Network Dependence
9.6 Bibliographical Notes
Appendix A: Discrete-Time Implementation
A.1 The Discrete-Time, Finite-State-Space Model
A.2 Equivalent Martingale Measures
A.3 The Binomial Implementation of Option-Based Models
A.4 Term-Structure Modeling Using Trees
A.5 Bibliographical Notes
Appendix B: Some Results Related to Brownian Motion
B.1 Boundary Hitting Times
B.2 Valuing a Boundary Payment when the Contract Has Finite Maturity
B.3 Present Values Associated with Brownian Motion
B.4 Bibliographical Notes
Appendix D: Stochastic Calculus for Jump-Diffusions
D.1 The Poisson Process
D.2 A Fundamental Martingale
D.3 The Stochastic Integral and Itô's Formula for a Jump Process
D.4 The General Itô Formula for Semimartingales
D.5 The Semimartingale Exponential
D.6 Special Semimartingales
D.7 Local Characteristics and Equivalent Martingale Measures
D.8 Asset Pricing and Risk Premiums for Special Semimartingales
D.9 Two Examples
D.10 Bibliographical Notes
Appendix E: A Term-Structure Workhorse
References
Index
About David Lando
David Lando is Professor of Finance at the Copenhagen Business School. He is an associate editor of three finance journals and a member of Moody's Academic Advisory and Research Committee.
Shopping basket
