Credit Risk : Modeling, Valuation and Hedging

Modeling, Valuation and Hedging

By: Tomasz R. Bielecki, Marek Rutkowski

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Hardcover | 1 January 2002

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524 Pages

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22.86 x 15.88 x 3.18

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The main objective of Credit Risk: Modeling, Valuation and Hedging is to present a comprehensive survey of the past developments in the area of credit risk research, as well as to put forth the most recent advancements in this field. An important aspect of this text is that it attempts to bridge the gap between the mathematical theory of credit risk and the financial practice, which serves as the motivation for the mathematical modeling studied in the book. Mathematical developments are presented in a thorough manner and cover the structural (value-of-the-firm) and the reduced (intensity-based) approaches to credit risk modeling, applied both to single and to multiple defaults. In particular, the book offers a detailed study of various arbitrage-free models of defaultable term structures with several rating grades.

Industry Reviews

From the reviews:

T.R. Bielecki and M. Rutkowski

Credit Risk

Modeling, Valuation and Hedging

"A fairly complete overview of the most important recent developments of credit risk modelling from the viewpoint of mathematical finance . . . It provides an excellent treatment of mathematical aspects of credit risk and will also be useful as a reference for technical details to traders and analysts dealing with credit-risky assets. It is a worthwhile addition to the literature and will serve as highly recommended reading for students and researchers in the subject area for some years to come."

-MATHEMATICAL REVIEWS

"The main purpose of this outstanding monograph is to present a comprehensive survey of the existing developments in the area of credit risk research, as well as to put forth the most recent advancements in this field. An important feature of this book is its attempt to bridge the gap between the mathematical theory of credit risk and the financial practice. ... The content of this book provides an indispensable guide to graduate students, researchers, and also to advanced practitioners in the fields ... ." (Neculai Curteanu, Zentralblatt MATH, Vol. 979, 2002)

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You Can Find This Book In

Non-Fiction Accounting & Finance Accounting Economics Econometrics Economic Statistics Business & Management Sales & Marketing Mathematics Applied Mathematics Mathematical Modelling Macroeconomics

Monetary Economics Probability & Statistics Stochastics Finance Public Accounting in Finance Tax & Taxation

Preface	p. V
Structural Approach
Introduction to Credit Risk	p. 3
Corporate Bonds	p. 4
Recovery Rules	p. 5
Safety Covenants	p. 6
Credit Spreads	p. 7
Credit Ratings	p. 7
Corporate Coupon Bonds	p. 8
Fixed and Floating Rate Notes	p. 9
Bank Loans and Sovereign Debt	p. 11
Cross Default	p. 11
Default Correlations	p. 11
Vulnerable Claims	p. 12
Vulnerable Claims with Unilateral Default Risk	p. 12
Vulnerable Claims with Bilateral Default Risk	p. 13
Defaultable Interest Rate Contracts	p. 14
Credit Derivatives	p. 16
Default Swaps and Options	p. 18
Total Rate of Return Swaps	p. 21
Credit Linked Notes	p. 22
Asset Swaps	p. 24
First-to-Default Contracts	p. 24
Credit Spread Swaps and Options	p. 25
Quantitative Models of Credit Risk	p. 26
Structural Models	p. 26
Reduced-Form Models	p. 27
Credit Risk Management	p. 29
Liquidity Risk	p. 30
Econometric Studies	p. 30
Corporate Debt	p. 31
Defaultable Claims	p. 33
Risk-Neutral Valuation Formula	p. 34
Self-Financing Trading Strategies	p. 37
Martingale Measures	p. 38
PDE Approach	p. 40
PDE for the Value Function	p. 44
Corporate Zero-Coupon Bonds	p. 47
Corporate Coupon Bond	p. 50
Merton's Approach to Corporate Debt	p. 51
Merton's Model with Deterministic Interest Rates	p. 51
Distance-to-Default	p. 57
Extensions of Merton's Approach	p. 58
Models with Stochastic Interest Rates	p. 59
Discontinuous Value Process	p. 60
Buffet's Approach	p. 64
First-Passage-Time Models	p. 65
Properties of First Passage Times	p. 66
Probability Law of the First Passage Time	p. 67
Joint Probability Law of Y and	p. 69
Black and Cox Model	p. 71
Corporate Zero-Coupon Bond	p. 71
Corporate Coupon Bond	p. 79
Corporate Consol Bond	p. 81
Optimal Capital Structure	p. 82
Black and Cox Approach	p. 82
Leland's Approach	p. 84
Leland and Toft Approach	p. 86
Further Developments	p. 88
Models with Stochastic Interest Rates	p. 90
Kim, Ramaswamy and Sundaresan Approach	p. 96
Longstaff and Schwartz Approach	p. 98
Cathart and El-Jahel Approach	p. 103
Briys and de Varenne Approach	p. 104
Saá-Requejo and Santa-Clara Approach	p. 107
Further Developments	p. 113
Convertible Bonds	p. 113
Jump-Diffusion Models	p. 113
Incomplete Accounting Data	p. 113
Dependent Defaults: Structural Approach	p. 114
Default Correlations: J.P. Morgan's Approach	p. 116
Default Correlations: Zhou's Approach	p. 117
Hazard Processes
Hazard Function of a Random Time	p. 123
Conditional Expectations w.r.t. Natural Filtrations	p. 123
Martingales Associated with a Continuous Hazard Function	p. 127
Martingale Representation Theorem	p. 131
Change of a Probability Measure	p. 133
Martingale Characterization of the Hazard Function	p. 137
Compensator of a Random Time	p. 140
Hazard Process of a Random Time	p. 141
Hazard Process	p. 141
Conditional Expectations	p. 143
Semimartingale Representation of the Stopped Process	p. 150
Martingales Associated with the Hazard Process	p. 152
Stochastic Intensity of a Random Time	p. 155
Martingale Representation Theorems	p. 156
General Case	p. 156
Case of a Brownian Filtration	p. 159
Change of a Probability Measure	p. 162
Martingale Hazard Process	p. 165
Martingale Hazard Process	p. 165
Martingale Invariance Property	p. 166
Evaluation of : Special Case	p. 167
Evaluation of : General Case	p. 169
Uniqueness of a Martingale Hazard Process	p. 172
Relationships Between Hazard Processes and	p. 173
Martingale Representation Theorem	p. 177
Case of the Martingale Invariance Property	p. 179
Valuation of Defaultable Claims	p. 180
Case of a Stopping Time	p. 182
Random Time with a Given Hazard Process	p. 183
Poisson Process and Conditional Poisson Process	p. 186
Case of Several Random Times	p. 197
Minimum of Several Random Times	p. 197
Hazard Function	p. 198
Martingale Hazard Process	p. 198
Martingale Representation Theorem	p. 200
Change of a Probability Measure	p. 203
Kusuoka's Counter-Example	p. 209
Validity of Condition (F.2)	p. 216
Validity of Condition (M.1)	p. 218
Reduced-Form Modeling
Intensity-Based Valuation of Defaultable Claims	p. 221
Defaultable Claims	p. 222
Risk-Neutral Valuation Formula	p. 223
Valuation via the Hazard Process	p. 225
Canonical Construction of a Default Time	p. 227
Integral Representation of the Value Process	p. 230
Case of a Deterministic Intensity	p. 232
Implied Probabilities of Default	p. 234
Exogenous Recovery Rules	p. 236
Valuation via the Martingale Approach	p. 239
Martingale Hypotheses	p. 242
Endogenous Recovery Rules	p. 243
Hedging of Defaultable Claims	p. 246
General Reduced-Form Approach	p. 250
Reduced-Form Models with State Variables	p. 253
Lando's Approach	p. 253
Duffie and Singleton Approach	p. 255
Hybrid Methodologies	p. 259
Credit Spread Models	p. 264
Conditionally Independent Defaults	p. 265
Basket Credit Derivatives	p. 266
Mutually Independent Default Times	p. 267
Conditionally Independent Default Times	p. 268
Valuation of the i^th-to-Default Contract	p. 274
Vanilla Default Swaps of Basket Type	p. 281
Default Correlations and Conditional Probabilities	p. 284
Default Correlations	p. 284
Conditional Probabilities	p. 287
Dependent Defaults	p. 293
Dependent Intensities	p. 295
Kusuoka's Approach	p. 295
Jarrow and Yu Approach	p. 296
Martingale Approach to Basket Credit Derivatives	p. 306
Valuation of the i^th-to-Default Claims	p. 311
Markov Chains	p. 313
Discrete-Time Markov Chains	p. 314
Change of a Probability Measure	p. 316
The Law of the Absorption Time	p. 320
Discrete-Time Conditionally Markov Chains	p. 322
Continuous-Time Markov Chains	p. 324
Embedded Discrete-Time Markov Chain	p. 329
Conditional Expectations	p. 329
Probability Distribution of the Absorption Time	p. 332
Martingales Associated with Transitions	p. 333
Change of a Probability Measure	p. 334
Identification of the Intensity Matrix	p. 338
Continuous-Time Conditionally Markov Chains	p. 340
Construction of a Conditionally Markov Chain	p. 342
Conditional Markov Property	p. 346
Associated Local Martingales	p. 347
Forward Kolmogorov Equation	p. 350
Markovian Models of Credit Migrations	p. 351
JLT Markovian Model and its Extensions	p. 352
JLT Model: Discrete-Time Case	p. 354
JLT Model: Continuous-Time Case	p. 362
Kijima and Komoribayashi Model	p. 367
Das and Tufano Model	p. 369
Thomas, Allen and Morkel-Kingsbury Model	p. 371
Conditionally Markov Models	p. 373
Lando's Approach	p. 374
Correlated Migrations	p. 376
Huge and Lando Approach	p. 380
Heath-Jarrow-Morton Type Models	p. 385
HJM Model with Default	p. 386
Model's Assumptions	p. 386
Default-Free Term Structure	p. 388
Pre-Default Value of a Corporate Bond	p. 390
Dynamics of Forward Credit Spreads	p. 392
Default Time of a Corporate Bond	p. 394
Case of Zero Recovery Rate	p. 397
Default-Free and Defaultable LIBOR Rates	p. 398
Case of a Non-Zero Recovery Rate	p. 400
Alternative Recovery Rules	p. 403
HJM Model with Credit Migrations	p. 405
Model's Assumption	p. 405
Migration Process	p. 407
Special Case	p. 408
General Case	p. 410
Alternative Recovery Schemes	p. 413
Defaultable Coupon Bonds	p. 415
Default Correlations	p. 416
Market Prices of Interest Rate and Credit Risk	p. 417
Applications to Credit Derivatives	p. 421
Valuation of Credit Derivatives	p. 421
Hedging of Credit Derivatives	p. 422
Defaultable Market Rates	p. 423
Interest Rate Contracts with Default Risk	p. 424
Default-Free LIBOR and Swap Rates	p. 424
Defaultable Spot LIBOR Rates	p. 426
Defaultable Spot Swap Rates	p. 427
FRAs with Unilateral Default Risk	p. 428
Forward Swaps with Unilateral Default Risk	p. 432
Multi-Period IRAs with Unilateral Default Risk	p. 434
Multi-Period Defaultable Forward Nominal Rates	p. 438
Defaultable Swaps with Unilateral Default Risk	p. 441
Settlement of the 1^st Kind	p. 442
Settlement of the 2^nd Kind	p. 444
Settlement of the 3^rd Kind	p. 445
Market Conventions	p. 446
Defaultable Swaps with Bilateral Default Risk	p. 447
Defaultable Forward Swap Rates	p. 449
Forward Swaps with Unilateral Default Risk	p. 449
Forward Swaps with Bilateral Default Risk	p. 450
Modeling of Market Rates	p. 451
Models of Default-Free Market Rates	p. 452
Modeling of Forward LIBOR Rates	p. 452
Modeling of Forward Swap Rates	p. 458
Modeling of Defaultable Forward LIBOR Rates	p. 465
Lotz and Schlögl Approach	p. 465
Schönbucher's Approach	p. 469
A Guide to References	p. 477
References	p. 479
Basic Notation	p. 495
Subject Index	p. 497
Table of Contents provided by Publisher. All Rights Reserved.

Credit Risk : Modeling, Valuation and Hedging

Modeling, Valuation and Hedging

At a Glance

Hardcover

Industry Reviews

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