# Essay on Credit Risk Modelling

38375 Words Aug 26th, 2010 154 Pages
Statistical Methods in Credit Risk Modeling

by Aijun Zhang

A dissertation submitted in partial fulﬁllment of the requirements for the degree of Doctor of Philosophy (Statistics) in The University of Michigan 2009

Doctoral Committee: Professor Vijayan N. Nair, Co-Chair Agus Sudjianto, Co-Chair, Bank of America Professor Tailen Hsing Associate Professor Jionghua Jin Associate Professor Ji Zhu

c

Aijun Zhang

2009

To my elementary school, high school and university teachers

ii

ACKNOWLEDGEMENTS

First of all, I would express my gratitude to my advisor Prof. Vijay Nair for guiding me during the entire PhD research. I appreciate his inspiration, encouragement and protection through these
. . . . . . . . . . . . . . . . . . . . . . . . . LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CHAPTER I. An Introduction to Credit Risk Modeling . . . . . . . . . . . . 1.1 Two Worlds of Credit Risk . . . . . . . . 1.1.1 Credit Spread Puzzle . . . . . . 1.1.2 Actual Defaults . . . . . . . . . Credit Risk Models . . . . . . . . . . . . 1.2.1 Structural Approach . . . . . . 1.2.2 Intensity-based Approach . . . . Survival Models . . . . . . . . . . . . . . 1.3.1 Parametrizing Default Intensity 1.3.2 Incorporating Covariates . . . . 1.3.3 Correlating Credit Defaults . . . Scope of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ii iii vi ix x

1 2 2 5 6 6 9 11 12 13 15 18 24 24 28 30 32 36 38

1.2

1.3

1.4

II. Adaptive Smoothing Spline . . . . . . . . . . . . . . . . . . . . . 2.1 2.2 Introduction . . . . . . . . . . . . . AdaSS: Adaptive Smoothing Spline . 2.2.1 Reproducing Kernels . . . 2.2.2 Local Penalty Adaptation . AdaSS Properties . . . . . . . . . . Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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