Technische Universität München Credit as an Asset Class - risklab

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Contents 1 Introduction 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Objectives and Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Credit Risk Transfer 4 2.1 Credit Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.1.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.1.2 Credit Risk and Regulation . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Traditional credit related Instruments . . . . . . . . . . . . . . . . . . . . . 6 2.2.1 Loans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2.2 Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 Credit Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3.1 Definition and Functionality . . . . . . . . . . . . . . . . . . . . . . . 10 2.3.2 Classification according to Risk Category . . . . . . . . . . . . . . . 12 2.3.3 Reasons for the Utilisation of Credit Derivatives . . . . . . . . . . . 12 2.3.4 Chances and Risks related to Credit Derivatives Markets . . . . . . 15 2.3.5 Transaction Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.3.6 Market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.4 Securitisations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.4.1 Definition and Functionality . . . . . . . . . . . . . . . . . . . . . . . 24 2.4.2 Classification according to the Underlying Asset . . . . . . . . . . . 26 2.4.3 Reasons for the Utilisation of Securitisations . . . . . . . . . . . . . 27 2.4.4 Risks related to Securitisation Markets . . . . . . . . . . . . . . . . . 28 2.4.5 Transaction Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.4.6 Market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3 Credit Risk Transfer Instruments 35 3.1 Derivatives- or Securitisation-based Instruments . . . . . . . . . . . . . . . . 35 3.2 Credit Default Swap/Credit Default Option . . . . . . . . . . . . . . . . . . 36 3.3 Total Return Swap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.4 Credit Spread Option . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.5 Basket Credit Default Swap . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.6 Portfolio Credit Default Swap . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.7 Credit Linked Note . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.8 Collateralised Debt Obligation . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.8.1 Traditional CDO (True Sales Securitisation) . . . . . . . . . . . . . . 46 iii
CONTENTS 3.8.2 Synthetic CDO (Synthetic Securitisation) . . . . . . . . . . . . . . . 48 3.8.3 Classification of CDO Transactions . . . . . . . . . . . . . . . . . . . 49 3.9 CDS Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 3.9.1 iTraxx Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.9.2 DJ CDX Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.9.3 Motivations for Investors . . . . . . . . . . . . . . . . . . . . . . . . 57 3.9.4 Market Participants . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 4 Data Analysis 59 4.1 A Note on Return Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.2 US Aggregates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.3 Euro-Aggregates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 5 Simulation and Pricing Framework 67 5.1 A Note on Interest-Rate Modelling . . . . . . . . . . . . . . . . . . . . . . . 67 5.2 Model of Zagst for Economic Scenario Generation . . . . . . . . . . . . . . 69 5.3 Fitting of the Interest-Rate Curve . . . . . . . . . . . . . . . . . . . . . . . 75 5.4 Simulation of Correlated Default Times . . . . . . . . . . . . . . . . . . . . 75 5.4.1 Migration Matrices Approach . . . . . . . . . . . . . . . . . . . . . . 76 5.4.2 One-Factor Copula . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 5.5 Pricing of Financial Instruments . . . . . . . . . . . . . . . . . . . . . . . . 90 5.5.1 Zero-Coupon Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 5.5.2 Coupon Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 5.5.3 Excursus: Default Intensity Model . . . . . . . . . . . . . . . . . . . 93 5.5.4 Floating Rate Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 5.5.5 Funded CDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 5.5.6 Funded CDS Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 6 Portfolio Selection 106 6.1 Traditional Portfolio Selection . . . . . . . . . . . . . . . . . . . . . . . . . . 106 6.1.1 Mean-Variance Approach . . . . . . . . . . . . . . . . . . . . . . . . 106 6.1.2 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 6.2 Conditional Value at Risk Optimisation . . . . . . . . . . . . . . . . . . . . 109 6.2.1 A Note on Value at Risk . . . . . . . . . . . . . . . . . . . . . . . . . 109 6.2.2 Conditional Value at Risk . . . . . . . . . . . . . . . . . . . . . . . . 110 6.3 Performance Measure Omega . . . . . . . . . . . . . . . . . . . . . . . . . . 111 6.4 Portfolio Selection with Measure Score . . . . . . . . . . . . . . . . . . . . . 112 7 Simulation and Simulation Results 114 7.1 US Economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 7.1.1 Calibration of the Economic Scenario Generator . . . . . . . . . . . 114 7.1.2 Fit to Market Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 7.1.3 Simulation of Correlated Default Times . . . . . . . . . . . . . . . . 119 7.1.4 Return Characteristics of Financial Instruments . . . . . . . . . . . 120 7.1.5 Mean-Variance Approach . . . . . . . . . . . . . . . . . . . . . . . . 131 iv
Page 1 and 2: Technische Universität München Ze
Page 3: Danksagungen Zuallererst möchte ic
Page 7 and 8: List of Figures 2.1 Basic structure
Page 9 and 10: LIST OF FIGURES 7.22 Results of sco
Page 11 and 12: List of Tables 2.1 Risks in credit
Page 13 and 14: CHAPTER 1. INTRODUCTION based simul
Page 15 and 16: Chapter 2 Credit Risk Transfer To o
Page 17 and 18: CHAPTER 2. CREDIT RISK TRANSFER ins
Page 19 and 20: CHAPTER 2. CREDIT RISK TRANSFER bon
Page 21 and 22: CHAPTER 2. CREDIT RISK TRANSFER •
Page 23 and 24: 2.3.2 Classification according to R
Page 27 and 28: CHAPTER 2. CREDIT RISK TRANSFER Ris
Page 29 and 30: CHAPTER 2. CREDIT RISK TRANSFER exa
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Page 45 and 46: in detail. CHAPTER 2. CREDIT RISK T
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Page 53 and 54: Product Variations CHAPTER 3. CREDI
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CHAPTER 3. CREDIT RISK TRANSFER INS
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Definition 4.1 (Simple Return) CHAP
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Figure 4.2: Histogram of US aggrega
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CHAPTER 4. DATA ANALYSIS Aggregate
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4.4 Summary CHAPTER 4. DATA ANALYSI
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Definition 5.1 (Interest-Rate) CHAP
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CHAPTER 5. SIMULATION AND PRICING F
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with and Proof: A d (t, T ) = D d (
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Theorem 5.12 (Log-Expansion) CHAPTE
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and CHAPTER 5. SIMULATION AND PRICI
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5.5.4 Floating Rate Notes CHAPTER 5
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epeat the adjusted formulas here in
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Chapter 6 Portfolio Selection After
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CHAPTER 6. PORTFOLIO SELECTION µ(x
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above definition of the VaR can als
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L� −∞ FR(r)dr = L� −∞ C
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Chapter 7 Simulation and Simulation
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CHAPTER 7. SIMULATION AND SIMULATIO
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7.1.6 Conditional Value at Risk CHA
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7.1.7 Score CHAPTER 7. SIMULATION A
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7.1.8 Comparison of Optimal Portfol
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7.2.2 Mean-Variance Approach CHAPTE
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7.2.4 Score CHAPTER 7. SIMULATION A
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CHAPTER 8. SUMMARY AND OUTLOOK fact
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Appendix A Mathematical Preliminari
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APPENDIX A. MATHEMATICAL PRELIMINAR
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APPENDIX A. MATHEMATICAL PRELIMINAR
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Appendix B Ratings Rating Descripti
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APPENDIX C. CALCULATION OF THE DYNA
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Appendix E List of Abbreviations AB
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BIBLIOGRAPHY [Das06] Das, S. (2006)
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BIBLIOGRAPHY [NS87] Nelson, C.R., S
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Technische Universität München Credit as an Asset Class - risklab

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