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Credit Risk : Modeling, Valuation and Hedging :  Modeling, Valuation and Hedging - Tomasz R. Bielecki

Credit Risk : Modeling, Valuation and Hedging

Modeling, Valuation and Hedging

Hardcover

Published: January 2002
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This volume will serve as a valuable reference for financial analysts and traders involved with credit derivatives. Some aspects of the book may also be useful for market practitioners engaged in managing credit-risk sensitive portfolios. Graduate students and researchers in areas such as finance theory, mathematical finance, financial engineering and probability theory will benefit from the book as well.

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)

Prefacep. V
Structural Approach
Introduction to Credit Riskp. 3
Corporate Bondsp. 4
Recovery Rulesp. 5
Safety Covenantsp. 6
Credit Spreadsp. 7
Credit Ratingsp. 7
Corporate Coupon Bondsp. 8
Fixed and Floating Rate Notesp. 9
Bank Loans and Sovereign Debtp. 11
Cross Defaultp. 11
Default Correlationsp. 11
Vulnerable Claimsp. 12
Vulnerable Claims with Unilateral Default Riskp. 12
Vulnerable Claims with Bilateral Default Riskp. 13
Defaultable Interest Rate Contractsp. 14
Credit Derivativesp. 16
Default Swaps and Optionsp. 18
Total Rate of Return Swapsp. 21
Credit Linked Notesp. 22
Asset Swapsp. 24
First-to-Default Contractsp. 24
Credit Spread Swaps and Optionsp. 25
Quantitative Models of Credit Riskp. 26
Structural Modelsp. 26
Reduced-Form Modelsp. 27
Credit Risk Managementp. 29
Liquidity Riskp. 30
Econometric Studiesp. 30
Corporate Debtp. 31
Defaultable Claimsp. 33
Risk-Neutral Valuation Formulap. 34
Self-Financing Trading Strategiesp. 37
Martingale Measuresp. 38
PDE Approachp. 40
PDE for the Value Functionp. 44
Corporate Zero-Coupon Bondsp. 47
Corporate Coupon Bondp. 50
Merton's Approach to Corporate Debtp. 51
Merton's Model with Deterministic Interest Ratesp. 51
Distance-to-Defaultp. 57
Extensions of Merton's Approachp. 58
Models with Stochastic Interest Ratesp. 59
Discontinuous Value Processp. 60
Buffet's Approachp. 64
First-Passage-Time Modelsp. 65
Properties of First Passage Timesp. 66
Probability Law of the First Passage Timep. 67
Joint Probability Law of Y and p. 69
Black and Cox Modelp. 71
Corporate Zero-Coupon Bondp. 71
Corporate Coupon Bondp. 79
Corporate Consol Bondp. 81
Optimal Capital Structurep. 82
Black and Cox Approachp. 82
Leland's Approachp. 84
Leland and Toft Approachp. 86
Further Developmentsp. 88
Models with Stochastic Interest Ratesp. 90
Kim, Ramaswamy and Sundaresan Approachp. 96
Longstaff and Schwartz Approachp. 98
Cathart and El-Jahel Approachp. 103
Briys and de Varenne Approachp. 104
Saá-Requejo and Santa-Clara Approachp. 107
Further Developmentsp. 113
Convertible Bondsp. 113
Jump-Diffusion Modelsp. 113
Incomplete Accounting Datap. 113
Dependent Defaults: Structural Approachp. 114
Default Correlations: J.P. Morgan's Approachp. 116
Default Correlations: Zhou's Approachp. 117
Hazard Processes
Hazard Function of a Random Timep. 123
Conditional Expectations w.r.t. Natural Filtrationsp. 123
Martingales Associated with a Continuous Hazard Functionp. 127
Martingale Representation Theoremp. 131
Change of a Probability Measurep. 133
Martingale Characterization of the Hazard Functionp. 137
Compensator of a Random Timep. 140
Hazard Process of a Random Timep. 141
Hazard Process p. 141
Conditional Expectationsp. 143
Semimartingale Representation of the Stopped Processp. 150
Martingales Associated with the Hazard Process p. 152
Stochastic Intensity of a Random Timep. 155
Martingale Representation Theoremsp. 156
General Casep. 156
Case of a Brownian Filtrationp. 159
Change of a Probability Measurep. 162
Martingale Hazard Processp. 165
Martingale Hazard Process p. 165
Martingale Invariance Propertyp. 166
Evaluation of : Special Casep. 167
Evaluation of : General Casep. 169
Uniqueness of a Martingale Hazard Process p. 172
Relationships Between Hazard Processes and p. 173
Martingale Representation Theoremp. 177
Case of the Martingale Invariance Propertyp. 179
Valuation of Defaultable Claimsp. 180
Case of a Stopping Timep. 182
Random Time with a Given Hazard Processp. 183
Poisson Process and Conditional Poisson Processp. 186
Case of Several Random Timesp. 197
Minimum of Several Random Timesp. 197
Hazard Functionp. 198
Martingale Hazard Processp. 198
Martingale Representation Theoremp. 200
Change of a Probability Measurep. 203
Kusuoka's Counter-Examplep. 209
Validity of Condition (F.2)p. 216
Validity of Condition (M.1)p. 218
Reduced-Form Modeling
Intensity-Based Valuation of Defaultable Claimsp. 221
Defaultable Claimsp. 222
Risk-Neutral Valuation Formulap. 223
Valuation via the Hazard Processp. 225
Canonical Construction of a Default Timep. 227
Integral Representation of the Value Processp. 230
Case of a Deterministic Intensityp. 232
Implied Probabilities of Defaultp. 234
Exogenous Recovery Rulesp. 236
Valuation via the Martingale Approachp. 239
Martingale Hypothesesp. 242
Endogenous Recovery Rulesp. 243
Hedging of Defaultable Claimsp. 246
General Reduced-Form Approachp. 250
Reduced-Form Models with State Variablesp. 253
Lando's Approachp. 253
Duffie and Singleton Approachp. 255
Hybrid Methodologiesp. 259
Credit Spread Modelsp. 264
Conditionally Independent Defaultsp. 265
Basket Credit Derivativesp. 266
Mutually Independent Default Timesp. 267
Conditionally Independent Default Timesp. 268
Valuation of the ith-to-Default Contractp. 274
Vanilla Default Swaps of Basket Typep. 281
Default Correlations and Conditional Probabilitiesp. 284
Default Correlationsp. 284
Conditional Probabilitiesp. 287
Dependent Defaultsp. 293
Dependent Intensitiesp. 295
Kusuoka's Approachp. 295
Jarrow and Yu Approachp. 296
Martingale Approach to Basket Credit Derivativesp. 306
Valuation of the ith-to-Default Claimsp. 311
Markov Chainsp. 313
Discrete-Time Markov Chainsp. 314
Change of a Probability Measurep. 316
The Law of the Absorption Timep. 320
Discrete-Time Conditionally Markov Chainsp. 322
Continuous-Time Markov Chainsp. 324
Embedded Discrete-Time Markov Chainp. 329
Conditional Expectationsp. 329
Probability Distribution of the Absorption Timep. 332
Martingales Associated with Transitionsp. 333
Change of a Probability Measurep. 334
Identification of the Intensity Matrixp. 338
Continuous-Time Conditionally Markov Chainsp. 340
Construction of a Conditionally Markov Chainp. 342
Conditional Markov Propertyp. 346
Associated Local Martingalesp. 347
Forward Kolmogorov Equationp. 350
Markovian Models of Credit Migrationsp. 351
JLT Markovian Model and its Extensionsp. 352
JLT Model: Discrete-Time Casep. 354
JLT Model: Continuous-Time Casep. 362
Kijima and Komoribayashi Modelp. 367
Das and Tufano Modelp. 369
Thomas, Allen and Morkel-Kingsbury Modelp. 371
Conditionally Markov Modelsp. 373
Lando's Approachp. 374
Correlated Migrationsp. 376
Huge and Lando Approachp. 380
Heath-Jarrow-Morton Type Modelsp. 385
HJM Model with Defaultp. 386
Model's Assumptionsp. 386
Default-Free Term Structurep. 388
Pre-Default Value of a Corporate Bondp. 390
Dynamics of Forward Credit Spreadsp. 392
Default Time of a Corporate Bondp. 394
Case of Zero Recovery Ratep. 397
Default-Free and Defaultable LIBOR Ratesp. 398
Case of a Non-Zero Recovery Ratep. 400
Alternative Recovery Rulesp. 403
HJM Model with Credit Migrationsp. 405
Model's Assumptionp. 405
Migration Processp. 407
Special Casep. 408
General Casep. 410
Alternative Recovery Schemesp. 413
Defaultable Coupon Bondsp. 415
Default Correlationsp. 416
Market Prices of Interest Rate and Credit Riskp. 417
Applications to Credit Derivativesp. 421
Valuation of Credit Derivativesp. 421
Hedging of Credit Derivativesp. 422
Defaultable Market Ratesp. 423
Interest Rate Contracts with Default Riskp. 424
Default-Free LIBOR and Swap Ratesp. 424
Defaultable Spot LIBOR Ratesp. 426
Defaultable Spot Swap Ratesp. 427
FRAs with Unilateral Default Riskp. 428
Forward Swaps with Unilateral Default Riskp. 432
Multi-Period IRAs with Unilateral Default Riskp. 434
Multi-Period Defaultable Forward Nominal Ratesp. 438
Defaultable Swaps with Unilateral Default Riskp. 441
Settlement of the 1st Kindp. 442
Settlement of the 2nd Kindp. 444
Settlement of the 3rd Kindp. 445
Market Conventionsp. 446
Defaultable Swaps with Bilateral Default Riskp. 447
Defaultable Forward Swap Ratesp. 449
Forward Swaps with Unilateral Default Riskp. 449
Forward Swaps with Bilateral Default Riskp. 450
Modeling of Market Ratesp. 451
Models of Default-Free Market Ratesp. 452
Modeling of Forward LIBOR Ratesp. 452
Modeling of Forward Swap Ratesp. 458
Modeling of Defaultable Forward LIBOR Ratesp. 465
Lotz and Schlögl Approachp. 465
Schönbucher's Approachp. 469
A Guide to Referencesp. 477
Referencesp. 479
Basic Notationp. 495
Subject Indexp. 497
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540675938
ISBN-10: 3540675930
Series: Springer Finance
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 501
Published: January 2002
Publisher: SPRINGER VERLAG GMBH
Country of Publication: DE
Dimensions (cm): 23.93 x 16.46  x 3.38
Weight (kg): 0.89