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CONTENTS
Part Ⅰ : The Contemporary Framework
1 Market Basics ... 3
2 To Rate A Tabula Rasa ... 17
3 The Actuarial Method ... 32
4 The Default Method ... 58
5 The Eclectic Method ... 69
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CONTENTS
Part Ⅰ : The Contemporary Framework
1 Market Basics ... 3
2 To Rate A Tabula Rasa ... 17
3 The Actuarial Method ... 32
4 The Default Method ... 58
5 The Eclectic Method ... 69
Part Ⅱ : Analyzing Structured Securities
6 Toward a Science of Ratings ... 79
7 Dynamic Asset Analysis ... 93
8 Liabilities Analysis and Structuring ... 106
9 The Average Life of Assets and Liabilities ... 124
10 PACs and TACs ... 138
Part Ⅲ : Applications of Numerical Methods to Structured Finance
11 The Art of Mathematical Modeling ... 155
12 Statistical Probability Density Functions ... 163
13 Eigenvalues and Eigenvectors ... 173
14 Markov Chains ... 180
15 Regression Analysis ... 196
16 Lower-Upper Decomposition ... 201
17 Covariance Matrix Simulation ... 204
18 The Newton-Raphson Nonlinear Optimization Method ... 208
19 Tchebychev Polynomials ... 211
Part Ⅳ : Case Studies
20 Automobile Receivable Securitizations ... 223
21 CDOs of ABS ... 272
22 Aircraft Receivable Securitizations ... 312
Part Ⅴ : Advanced Structural Features
23 Trigger Theory ... 357
Concluding Remarks ... 377
Appendices
Appendix A Numerical Experiments in Random Number Generation ... 383
Appendix B The Physics of Markov Chains ... 386
Appendix C The Markov Property and the Efficient Market Hypothesis ... 389
Appendix D An Example of Nonlinear Regression ... 392
Appendix E The Symmetry and Nonnegative Definiteness of Two Special Matrices ... 394
Appendix F Convergence Analysis for the Newton-Raphson Optimization Method ... 397
Appendix G Spline Function Interpolations ... 411
Appendix H Correlation Topics ... 420
Notes ... 429
Index ... 441
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