Credit Risk Modeling

by Lando, David

• ISBN13: 9780691089294
• ISBN10: 0691089299
• eBook ISBN(s): 9781400829194
• Format: Hardcover
• Copyright: 2004-06-01
• Publisher: Princeton Univ Pr

Summary

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.

Table of Contents

Preface	xi
1 An Overview	1	(6)
2 Corporate Liabilities as Contingent Claims	7	(52)
2.1 Introduction	7	(1)
2.2 The Merton Model	8	(9)
2.3 The Merton Model with Stochastic Interest Rates	17	(3)
2.4 The Merton Model with Jumps in Asset Value	20	(7)
2.5 Discrete Coupons in a Merton Model	27	(2)
2.6 Default Barriers: the Black-Cox Setup	29	(5)
2.7 Continuous Coupons and Perpetual Debt	34	(2)
2.8 Stochastic Interest Rates and Jumps with Barriers	36	(4)
2.9 A Numerical Scheme when Transition Densities are Known	40	(1)
2.10 Towards Dynamic Capital Structure: Stationary Leverage Ratios	41	(1)
2.11 Estimating Asset Value and Volatility	42	(6)
2.12 On the KMV Approach	48	(3)
2.13 The Trouble with the Credit Curve	51	(3)
2.14 Bibliographical Notes	54	(5)
3 Endogenous Default Boundaries and Optimal Capital Structure	59	(16)
3.1 Leland's Model	60	(4)
3.2 A Model with a Maturity Structure	64	(2)
3.3 EBIT-Based Models	66	(4)
3.4 A Model with Strategic Debt Service	70	(2)
3.5 Bibliographical Notes	72	(3)
4 Statistical Techniques for Analyzing Defaults	75	(34)
4.1 Credit Scoring Using Logistic Regression	75	(2)
4.2 Credit Scoring Using Discriminant Analysis	77	(4)
4.3 Hazard Regressions: Discrete Case	81	(2)
4.4 Continuous-Time Survival Analysis Methods	83	(4)
4.5 Markov Chains and Transition-Probability Estimation	87	(6)
4.6 The Difference between Discrete and Continuous	93	(4)
4.7 A Word of Warning on the Markov Assumption	97	(5)
4.8 Ordered Probits and Ratings	102	(2)
4.9 Cumulative Accuracy Profiles	104	(2)
4.10 Bibliographical Notes	106	(3)
5 Intensity Modeling	109	(36)
5.1 What Is an Intensity Model?	111	(1)
5.2 The Cox Process Construction of a Single Jump Time	112	(2)
5.3 A Few Useful Technical Results	114	(1)
5.4 The Martingale Property	115	(1)
5.5 Extending the Scope of the Cox Specification	116	(1)
5.6 Recovery of Market Value	117	(3)
5.7 Notes on Recovery Assumptions	120	(2)
5.8 Correlation in Affine Specifications	122	(4)
5.9 Interacting Intensities	126	(2)
5.10 The Role of Incomplete Information	128	(5)
5.11 Risk Premiums in Intensity-Based Models	133	(6)
5.12 The Estimation of Intensity Models	139	(3)
5.13 The Trouble with the Term Structure of Credit Spreads	142	(1)
5.14 Bibliographical Notes	143	(2)
6 Rating-Based Term-Structure Models	145	(24)
6.1 Introduction	145	(1)
6.2 A Markovian Model for Rating-Based Term Structures	145	(7)
6.3 An Example of Calibration	152	(3)
6.4 Class-Dependent Recovery	155	(2)
6.5 Fractional Recovery of Market Value in the Markov Model	157	(2)
6.6 A Generalized Markovian Model	159	(3)
6.7 A System of PDEs for the General Specification	162	(2)
6.8 Using Thresholds Instead of a Markov Chain	164	(2)
6.9 The Trouble with Pricing Based on Ratings	166	(1)
6.10 Bibliographical Notes	166	(3)
7 Credit Risk and Interest-Rate Swaps	169	(28)
7.1 LIBOR	170	(1)
7.2 A Useful Starting Point	170	(1)
7.3 Fixed-Floating Spreads and the "Comparative-Advantage Story"	171	(5)
7.4 Why LIBOR and Counterparty Credit Risk Complicate Things	176	(2)
7.5 Valuation with Counterparty Risk	178	(4)
7.6 Netting and the Nonlinearity of Actual Cash Flows: a Simple Example	182	(1)
7.7 Back to Linearity: Using Different Discount Factors	183	(6)
7.8 The Swap Spread versus the Corporate-Bond Spread	189	(3)
7.9 On the Swap Rate, Repo Rates, and the Riskless Rate	192	(2)
7.10 Bibliographical Notes	194	(3)
8 Credit Default Swaps, CDOs, and Related Products	197	(16)
8.1 Some Basic Terminology	197	(4)
8.2 Decomposing the Credit Default Swap	201	(3)
8.3 Asset Swaps	204	(2)
8.4 Pricing the Default Swap	206	(2)
8.5 Some Differences between CDS Spreads and Bond Spreads	208	(1)
8.6 A First-to-Default Calculation	209	(2)
8.7 A Decomposition of m-of-n-to-Default Swaps	211	(1)
8.8 Bibliographical Notes	212	(1)
9 Modeling Dependent Defaults	213	(38)
9.1 Some Preliminary Remarks on Correlation and Dependence	214	(2)
9.2 Homogeneous Loan Portfolios	216	(17)
9.3 Asset-Value Correlation and Intensity Correlation	233	(9)
9.4 The Copula Approach	242	(3)
9.5 Network Dependence	245	(4)
9.6 Bibliographical Notes	249	(2)
Appendix A Discrete-Time Implementation	251	(8)
A.1 The Discrete-Time, Finite-State-Space Model	251	(1)
A.2 Equivalent Martingale Measures	252	(3)
A.3 The Binomial Implementation of Option-Based Models	255	(1)
A.4 Term-Structure Modeling Using Trees	256	(1)
A.5 Bibliographical Notes	257	(2)
Appendix B Some Results Related to Brownian Motion	259	(8)
B.1 Boundary Hitting Times	259	(1)
B.2 Valuing a Boundary Payment when the Contract Has Finite Maturity	260	(1)
B.3 Present Values Associated with Brownian Motion	261	(4)
B.4 Bibliographical Notes	265	(2)
Appendix C Markov Chains	267	(8)
C.1 Discrete-Time Markov Chains	267	(1)
C.2 Continuous-Time Markov Chains	268	(5)
C.3 Bibliographical Notes	273	(2)
Appendix D Stochastic Calculus for Jump-Diffusions	275	(16)
D.1 The Poisson Process	275	(1)
D.2 A Fundamental Martingale	276	(1)
D.3 The Stochastic Integral and Ito's Formula for a Jump Process	276	(2)
D.4 The General Ito Formula for Semimartingales	278	(1)
D.5 The Semimartingale Exponential	278	(1)
D.6 Special Semimartingales	279	(3)
D.7 Local Characteristics and Equivalent Martingale Measures	282	(4)
D.8 Asset Pricing and Risk Premiums for Special Semimartingales	286	(2)
D.9 Two Examples	288	(2)
D.10 Bibliographical Notes	290	(1)
Appendix E A Term-Structure Workhorse	291	(6)
References	297	(10)
Index	307