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In banking, especially in risk management, portfolio management, and
structured finance, solid quantitative know-how becomes more and
more important. We had a two-fold intention when writing this book:
First, this book is designed to help mathematicians and physicists
leaving the academic world and starting a profession as risk or portfolio
managers to get quick access to the world of credit risk management.
Second, our book is aimed at being helpful to risk managers looking
for a more quantitative approach to credit risk.
Following this intention on one side, our book is written in a Lecture
Notes style very much reflecting the keyword “introduction” already
used in the title of the book. We consequently avoid elaborating on
technical details not really necessary for understanding the underlying
idea. On the other side we kept the presentation mathematically precise
and included some proofs as well as many references for readers
interested in diving deeper into the mathematical theory of credit risk
management.
The main focus of the text is on portfolio rather than single obligor
risk. Consequently correlations and factors play a major role. Moreover,
most of the theory in many aspects is based on probability theory.
We therefore recommend that the reader consult some standard text
on this topic before going through the material presented in this book.
Nevertheless we tried to keep it as self-contained as possible.
Summarizing our motivation for writing an introductory text on
credit risk management one could say that we tried to write the book we
would have liked to read before starting a profession in risk management
some years ago.
Contents
1 The Basics of Credit Risk Management
1.1.1 The Default Probability
1.1.1.1 Ratings
1.1.1.2 Calibration of Default Probabilities to
Ratings
1.1.2 The Exposure at Default
1.1.3 The Loss Given Default
1.1 Expected Loss
1.2.1 Economic Capital
1.2.2 The Loss Distribution
1.2.2.1 Monte Carlo Simulation of Losses
1.2.2.2 Analytical Approximation
1.2.3 Modeling Correlations by Means of Factor Models
1.2 Unexpected Loss
1.3 Regulatory Capital and the Basel Initiative
2 Modeling Correlated Defaults
2.1.1 A General Bernoulli Mixture Model
2.1.2 UniformDefault Probability and UniformCorrelation
2.1 The Bernoulli Model
2.2.1 A General Poisson Mixture Model
2.2.2 UniformDefault Intensity and UniformCorrelation
2.2 The Poisson Model
2.3 Bernoulli Versus Poisson Mixture
2.4.1 CreditMetricsTM and the KMV-Model
2.4.2 CreditRisk+
2.4.3 CreditPortfolioView
2.4.3.1 CPV Macro
2.4.3.2 CPV Direct
2.4.4 Dynamic Intensity Models
2.4 An Overview of Today’s Industry Models
©2003 CRC Press LLC
2.5.1 The CreditMetricsTM/KMV One-Factor Model
2.5.2 The CreditRisk+ One-Sector Model
2.5.3 Comparison of One-Factor and One-Sector Models
2.5 One-Factor/Sector Models
2.6.1 Copulas: Variations of a Scheme
2.6 Loss Distributions by Means of Copula Functions
2.7 Working Example: Estimation of Asset Correlations
3 Asset Value Models
3.1 Introduction and a Small Guide to the Literature
3.2.1 Geometric Brownian Motion
3.2.2 Put and Call Options
3.2 A Few Words about Calls and Puts
3.3.1 Capital Structure: Option-Theoretic Approach
3.3.2 Asset from Equity Values
3.3 Merton’s Asset Value Model
3.4.1 Itˆo’s Formula “Light”
3.4.2 Black-Scholes Partial Differential Equation
3.4 Transforming Equity into Asset Values: A Working Approach
4 The CreditRisk+ Model
4.1 The Modeling Framework of CreditRisk+
4.2 Construction Step 1: Independent Obligors
4.3.1 Sector Default Distribution
4.3.2 Sector Compound Distribution
4.3.3 Sector Convolution
4.3 Construction Step 2: Sector Model
5 Alternative Risk Measures and Capital Allocation
5.1 Coherent Risk Measures and Conditional Shortfall
5.2.1 Variance/Covariance Approach
5.2.2 Capital Allocation w.r.t. Value-at-Risk
5.2.3 Capital Allocations w.r.t. Expected Shortfall
5.2.4 A Simulation Study
5.2 Contributory Capital
6 Term Structure of Default Probability
6.1 Survival Function and Hazard Rate
6.2 Risk-neutral vs. Actual Default Probabilities
©2003 CRC Press LLC
6.3.1 Exponential Term Structure
6.3.2 Direct Calibration of Multi-Year Default Probabilities
6.3.3 Migration Technique and Q-Matrices
6.3 Term Structure Based on Historical Default Information
6.4 Term Structure Based on Market Spreads
7 Credit Derivatives
7.1 Total Return Swaps
7.2 Credit Default Products
7.3 Basket Credit Derivatives
7.4 Credit Spread Products
7.5 Credit-linked Notes
8 Collateralized Debt Obligations
8.1.1 Typical Cash Flow CDO Structure
8.1.1.1 Overcollateralization Tests
8.1.1.2 Interest Coverage Tests
8.1.1.3 Other Tests
8.1.2 Typical Synthetic CLO Structure
8.1 Introduction to Collateralized Debt Obligations
8.2.1 The Originator’s Point of View
8.2.1.1 Regulatory Arbitrage and Capital Relief
8.2.1.2 Economic Risk Transfer
8.2.1.3 Funding at Better Conditions
8.2.1.4 Arbitrage Spread Opportunities
8.2.2 The Investor’s Point of View
8.2 Different Roles of Banks in the CDO Market
8.3.1 Multi-Step Models
8.3.2 Correlated Default Time Models
8.3.3 Stochastic Default Intensity Models
8.3 CDOs from the Modeling Point of View
8.4 Rating Agency Models: Moody’s BET
8.5 Conclusion
8.6 Some Remarks on the Literature
©2003
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