Credit Risk Modeling: Theory and Applications by David LandoPublisher: Princeton University Press (June 1, 2004)Language: EnglishISBN-10: 0691089299ISBN-13: 978-0691089294Book DescriptionCredit 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 xi1. An Overview 12. Corporate Liabilities as Contingent Claims 72.1 Introduction 72.2 The Merton Model 82.3 The Merton Model with Stochastic Interest Rates 172.4 The Merton Model with Jumps in Asset Value 202.5 Discrete Coupons in a Merton Model 272.6 Default Barriers: the Black-Cox Setup 292.7 Continuous Coupons and Perpetual Debt 342.8 Stochastic Interest Rates and Jumps with Barriers 362.9 A Numerical Scheme when Transition Densities are Known 402.10 Towards Dynamic Capital Structure: Stationary Leverage Ratios 412.11 Estimating Asset Value and Volatility 422.12 On the KMV Approach 482.13 The Trouble with the Credit Curve 512.14 Bibliographical Notes 543. Endogenous Default Boundaries and Optimal Capital Structure 593.1 Leland's Model 603.2 A Model with a Maturity Structure 643.3 EBIT-Based Models 663.4 A Model with Strategic Debt Service 703.5 Bibliographical Notes 724. Statistical Techniques for Analyzing Defaults 754.1 Credit Scoring Using Logistic Regression 754.2 Credit Scoring Using Discriminant Analysis 774.3 Hazard Regressions: Discrete Case 814.4 Continuous-Time Survival Analysis Methods 834.5 Markov Chains and Transition-Probability Estimation 874.6 The Difference between Discrete and Continuous 934.7 A Word of Warning on the Markov Assumption 974.8 Ordered Probits and Ratings 1024.9 Cumulative Accuracy Profiles 1044.10 Bibliographical Notes 1065. Intensity Modeling 1095.1 What Is an Intensity Model? 1115.2 The Cox Process Construction of a Single Jump Time 1125.3 A Few Useful Technical Results 1145.4 The Martingale Property 1155.5 Extending the Scope of the Cox Specification 1165.6 Recovery of Market Value 1175.7 Notes on Recovery Assumptions 1205.8 Correlation in Affine Specifications 1225.9 Interacting Intensities 1265.10 The Role of Incomplete Information 1285.11 Risk Premiums in Intensity-Based Models 1335.12 The Estimation of Intensity Models 1395.13 The Trouble with the Term Structure of Credit Spreads 1425.14 Bibliographical Notes 1436. Rating-Based Term-Structure Models 1456.1 Introduction 1456.2 A Markovian Model for Rating-Based Term Structures 1456.3 An Example of Calibration 1526.4 Class-Dependent Recovery 1556.5 Fractional Recovery of Market Value in the Markov Model 1576.6 A Generalized Markovian Model 1596.7 A System of PDEs for the General Specification 1626.8 Using Thresholds Instead of a Markov Chain 1646.9 The Trouble with Pricing Based on Ratings 1666.10 Bibliographical Notes 1667. Credit Risk and Interest-Rate Swaps 1697.1 LIBOR 1707.2 A Useful Starting Point 1707.3 Fixed-Floating Spreads and the "Comparative-Advantage Story" 1717.4 Why LIBOR and Counterparty Credit Risk Complicate Things 1767.5 Valuation with Counterparty Risk 1787.6 Netting and the Nonlinearity of Actual Cash Flows: a Simple Example 1827.7 Back to Linearity: Using Different Discount Factors 1837.8 The Swap Spread versus the Corporate-Bond Spread 1897.9 On the Swap Rate, Repo Rates, and the Riskless Rate 1927.10 Bibliographical Notes 1948. Credit Default Swaps, CDOs, and Related Products 1978.1 Some Basic Terminology 1978.2 Decomposing the Credit Default Swap 2018.3 Asset Swaps 2048.4 Pricing the Default Swap 2068.5 Some Differences between CDS Spreads and Bond Spreads 2088.6 A First-to-Default Calculation 2098.7 A Decomposition of m-of-n-to-Default Swaps 2118.8 Bibliographical Notes 2129. Modeling Dependent Defaults 2139.1 Some Preliminary Remarks on Correlation and Dependence 2149.2 Homogeneous Loan Portfolios 2169.3 Asset-Value Correlation and Intensity Correlation 2339.4 The Copula Approach 2429.5 Network Dependence 2459.6 Bibliographical Notes 249Appendix A: Discrete-Time Implementation 251A.1 The Discrete-Time, Finite-State-Space Model 251A.2 Equivalent Martingale Measures 252A.3 The Binomial Implementation of Option-Based Models 255A.4 Term-Structure Modeling Using Trees 256A.5 Bibliographical Notes 257Appendix B: Some Results Related to Brownian Motion 259B.1 Boundary Hitting Times 259B.2 Valuing a Boundary Payment when the Contract Has Finite Maturity 260B.3 Present Values Associated with Brownian Motion 261B.4 Bibliographical Notes 265Appendix C: Markov Chains 267C.1 Discrete-Time Markov Chains 267C.2 Continuous-Time Markov Chains 268C.3 Bibliographical Notes 273Appendix D: Stochastic Calculus for Jump-Diffusions 275D.1 The Poisson Process 275D.2 A Fundamental Martingale 276D.3 The Stochastic Integral and Itô's Formula for a Jump Process 276D.4 The General Itô Formula for Semimartingales 278D.5 The Semimartingale Exponential 278D.6 Special Semimartingales 279D.7 Local Characteristics and Equivalent Martingale Measures 282D.8 Asset Pricing and Risk Premiums for Special Semimartingales 286D.9 Two Examples 288D.10 Bibliographical Notes 290Appendix E: A Term-Structure Workhorse 291References 297Index 307
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