Credit Risk New Approaches to Value at Risk 属于MBA性质的书,主要对业界常用的信用模型如kmv、credit matrix、credit++等模型进行介绍,没有太多的数学推导和理论,适合初学者
部分目录:
CHAPTER 1
Why New Approaches to Credit Risk Measurement
and Management? 1
CHAPTER 2
Traditional Approaches to Credit Risk Measurement 9
CHAPTER 3
The BIS Basel International Bank Capital Accord: January 2002 23
CHAPTER 4
Loans as Options: The KMV and Moody’s Models 46
CHAPTER 5
Reduced Form Models: KPMG’s Loan Analysis System and
第二本:Credit Risk Modeling 作者:david lando
介绍了Structured model 和 reduced form model。读完之后会对信用风险模型的框架和思路有清晰的认识。
目录:
1 An Overview 1
2 Corporate Liabilities as Contingent Claims 7
3 Endogenous Default Boundaries and Optimal Capital Structure
4 Statistical Techniques for Analyzing Defaults
5 Intensity Modeling
6 Rating-Based Term-Structure Models
7 Credit Risk and Interest-Rate Swaps
8 Credit Default Swaps, CDOs, and Related Products
9 Modeling Dependent Defaults
第三本:Credit Risk 作者 duffie 相信作者不用介绍了,不过在这本书中duffie一改往日的风格,该书没有太多的数学
推导,看起来比较轻松,该书的特点是对各类信用风险产品定价作了介绍。
1 Introduction
2 Economic Principles of Risk Management
3 Default Arrival:Historical
Patterns and Statistical Models
4 Ratings Transitions:Historical Patterns and Statistical Models
5 Conceptual Approaches to
Valuation of Default Risk
6 Pricing Corporate and Sovereign Bonds
7 Empirical Models of Defaultable Bond Spreads
8 Credit Swaps
9 Optional Credit Pricing
10 Correlated Defaults
11 Collateralized Debt Obligations
12 Over-the-Counter Default Risk and Valuation
13 Integrated Market and Credit Risk Measurement
第四本: CREDIT RISK MODELING,VALUATION AND HEDGING 作者: Marek Rutkowski
该书的主要侧重点是Hazard Process,主要从连续半鞅理论着手,数学要求较高,这本书也解释了
很多在以上两本书中在讲reduced form model 时没有讲清楚的地方。该书我只有扫描的版本。
第五本:CREDIT RISK MODELING 作者: Marek Rutkowski 这本书和上一本内容几乎对应,可以
作为上一本的数学附录,对上一本书很多省略的数学证明等作了很好的补充。
部分目录:
1 Structural Approach 9
1.1 Notation and De¯nitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.1.1 Defaultable Claims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.1.2 Risk-Neutral Valuation Formula . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.1.3 Defaultable Zero-Coupon Bond . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.2 Merton's Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3 First Passage Times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.3.1 Distribution of the First Passage Time . . . . . . . . . . . . . . . . . . . . . . 15
1.3.2 Joint Distribution of Y and ¿ . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.4 Black and Cox Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.4.1 Bond Valuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.4.2 Black and Cox Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.4.3 Corporate Coupon Bond . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.4.4 Optimal Capital Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
1.5 Extensions of the Black and Cox Model . . . . . . . . . . . . . . . . . . . . . . . . . 30
1.5.1 Stochastic Interest Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
1.6 Random Barrier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
1.6.1 Independent Barrier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2 Hazard Function Approach 35
2.1 Elementary Market Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.1.1 Hazard Function and Hazard Rate . . . . . . . . . . . . . . . . . . . . . . . . 36
2.1.2 Defaultable Bond with Recovery at Maturity . . . . . . . . . . . . . . . . . . 37
2.1.3 Defaultable Bond with Recovery at Default . . . . . . . . . . . . . . . . . . . 40
2.2 Martingale Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.2.1 Conditional Expectations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.2.2 Martingales Associated with Default Time . . . . . . . . . . . . . . . . . . . . 42
2.2.3 Predictable Representation Theorem . . . . . . . . . . . . . . . . . . . . . . . 46
2.2.4 Girsanov's Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.2.5 Range of Arbitrage Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.2.6 Implied Risk-Neutral Default Intensity . . . . . . . . . . . . . . . . . . . . . . 51
2.2.7 Price Dynamics of Simple Defaultable Claims . . . . . . . . . . . . . . . . . . 52
2.3 Pricing of General Defaultable Claims . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.3.1 Buy-and-Hold Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
2.3.2 Spot Martingale Measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.3.3 Self-Financing Trading Strategies . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.3.4 Martingale Properties of Arbitrage Prices . . . . . . . . . . . . . . . . . . . . 59
2.4 Single Name Credit Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
2.4.1 Stylized Credit Default Swap . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
2.4.2 Market CDS Spread . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
2.4.3 Price Dynamics of a CDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
2.4.4 Replication of a Defaultable Claim . . . . . . . . . . . . . . . . . . . . . . . . 64
2.5 Basket Credit Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
2.5.1 First-to-Default Intensities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
2.5.2 First-to-Default Representation Theorem . . . . . . . . . . . . . . . . . . . . 68
2.5.3 Price Dynamics of Credit Default Swaps . . . . . . . . . . . . . . . . . . . . . 70
2.5.4 Valuation of a First-to-Default Claim . . . . . . . . . . . . . . . . . . . . . . 73
2.5.5 Replication of a First-to-Default Claim . . . . . . . . . . . . . . . . . . . . . . 74
2.5.6 Conditional Default Distributions . . . . . . . . . . . . . . . . . . . . . . . . . 75
2.5.7 Recursive Valuation of a Basket Claim . . . . . . . . . . . . . . . . . . . . . . 77
2.5.8 Recursive Replication of a Basket Claim . . . . . . . . . . . . . . . . . . . . . 80
2.6 Applications to Copula-Based Models . . . . . . . . . . . . . . . . . . . . . . . . . . 80
2.6.1 Independent Default Times . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
2.6.2 Archimedean Copulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3 Hazard Process Approach 87
3.1 Hazard Process and its Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.1.1 Conditional Expectations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
3.1.2 Hazard Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3.1.3 Valuation of Defaultable Claims . . . . . . . . . . . . . . . . . . . . . . . . . 91
3.1.4 Defaultable Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.1.5 Martingales Associated with Default Time . . . . . . . . . . . . . . . . . . . . 93
3.1.6 F-Intensity of Default Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
3.1.7 Reduction of the Reference Filtration . . . . . . . . . . . . . . . . . . . . . . 97
3.1.8 Enlargement of Filtration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
3.2 Hypothesis (H) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
3.2.1 Equivalent Forms of Hypothesis (H) . . . . . . . . . . . . . . . . . . . . . . . 99
3.2.2 Canonical Construction of a Default Time . . . . . . . . . . . . . . . . . . . . 101
3.2.3 Stochastic Barrier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
3.3 Predictable Representation Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
3.4 Girsanov's Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
3.5 Invariance of Hypothesis (H) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
3.5.1 Case of the Brownian Filtration . . . . . . . . . . . . . . . . . . . . . . . . . . 107