Technische Universität München Credit as an Asset Class - risklab

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LIST OF FIGURES 5.8 Coupon payment structure of a coupon bond . . . . . . . . . . . . . . . . . 92 5.9 Possible cash flow structure of a FRN . . . . . . . . . . . . . . . . . . . . . 96 5.10 Coupon payment structure of a CDS . . . . . . . . . . . . . . . . . . . . . . 98 5.11 Compounding of recovery payment . . . . . . . . . . . . . . . . . . . . . . . 98 5.12 Compounding of recovery payments of a CDS index . . . . . . . . . . . . . 104 6.1 Efficient frontier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 7.1 US Treasury Strips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 7.2 US credit spreads, rating classes AA, A2, BBB1 . . . . . . . . . . . . . . . 118 7.3 Model fit of US zero rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 7.4 Key statistics US economy, Gaussian defaults . . . . . . . . . . . . . . . . . 124 7.5 Key statistics US economy, NIG defaults . . . . . . . . . . . . . . . . . . . . 125 7.6 Densities of financial instruments, 1 year time horizon, Gaussian defaults (left-hand side) and NIG defaults (right-hand side) . . . . . . . . . . . . . . 126 7.7 Left tail densities of financial instruments, 1 year time horizon, Gaussian defaults (left-hand side) and NIG defaults (right hand side) . . . . . . . . . 127 7.8 Densities of financial instruments without left tails, 1 year time horizon, Gaussian defaults (left-hand side) and NIG defaults (right-hand side) . . . . 127 7.9 Densities of financial instruments, 3 years time horizon, Gaussian defaults (left-hand side) and NIG defaults (right-hand side) . . . . . . . . . . . . . . 128 7.10 Left tail densities of financial instruments, 3 years time horizon, Gaussian defaults (left-hand side) and NIG defaults (right hand side) . . . . . . . . . 129 7.11 Densities of financial instruments without left tails, 3 years time horizon, Gaussian defaults (left-hand side) and NIG defaults (right-hand side) . . . . 129 7.12 Correlation of financial instruments in US economy, Gaussian defaults and NIG defaults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 7.13 Minimum-variance portfolio with Gaussian defaults (left-hand side) and NIG defaults (right-hand side) . . . . . . . . . . . . . . . . . . . . . . . . . 134 7.14 Results of mean-variance optimisation, 1 year investment horizon with Gaussian defaults (left-hand side) and NIG defaults (right-hand side) . . . . . . . . . 135 7.15 Results of mean-variance optimisation, 3 years investment horizon with Gaussian defaults (left-hand side) and NIG defaults (right-hand side) . . . . 136 7.16 Results of mean-variance optimisation, 5 years investment horizon with Gaussian defaults (left-hand side) and NIG defaults (right-hand side) . . . . 137 7.17 Minimum-CVaR portfolio with Gaussian defaults (left-hand side) and NIG defaults (right-hand side) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 7.18 Results of CVaR optimisation, 1 year investment horizon with Gaussian defaults (left-hand side) and NIG defaults (right-hand side) . . . . . . . . . 141 7.19 Results of CVaR optimisation, 3 years investment horizon with Gaussian defaults (left-hand side) and NIG defaults (right-hand side) . . . . . . . . . 142 7.20 Results of CVaR optimisation, 5 years investment horizon with Gaussian defaults (left-hand side) and NIG defaults (right-hand side) . . . . . . . . . 143 7.21 Results of score optimisation, 1 year investment horizon with Gaussian defaults (left-hand side) and NIG defaults (right-hand side) . . . . . . . . . 145 vii
LIST OF FIGURES 7.22 Results of score optimisation, 3 years investment horizon with Gaussian defaults (left-hand side) and NIG defaults (right-hand side) . . . . . . . . . 146 7.23 Results of score optimisation, 5 years investment horizon with Gaussian defaults (left-hand side) and NIG defaults (right-hand side) . . . . . . . . . 147 7.24 Results for risk-averse and risk-affine investor, 1 year investment horizon, Gaussian defaults (top) and NIG defaults (bottom) . . . . . . . . . . . . . . 148 7.25 Results for risk-averse and risk-affine investor, 3 years investment horizon, Gaussian defaults (top) and NIG defaults (bottom) . . . . . . . . . . . . . . 149 7.26 Results for risk-averse and risk-affine investor, 5 years investment horizon, Gaussian defaults (top) and NIG defaults (bottom) . . . . . . . . . . . . . . 150 7.27 Key statistics US economy, Gaussian defaults . . . . . . . . . . . . . . . . . 153 7.28 Key statistics US economy, NIG defaults . . . . . . . . . . . . . . . . . . . . 154 7.29 Densities of financial instruments, 1 year time horizon, Gaussian defaults (left-hand side) and NIG defaults (right-hand side) . . . . . . . . . . . . . . 155 7.30 Left tail densities of financial instruments, 1 year time horizon, Gaussian defaults (left-hand side) and NIG defaults (right hand side) . . . . . . . . . 156 7.31 Densities of financial instruments without left tails, 1 year time horizon, Gaussian defaults (left-hand side) and NIG defaults (right-hand side) . . . . 156 7.32 Densities of financial instruments, 3 years time horizon, Gaussian defaults (left-hand side) and NIG defaults (right-hand side) . . . . . . . . . . . . . . 157 7.33 Left tail densities of financial instruments, 3 years time horizon, Gaussian defaults (left-hand side) and NIG defaults (right hand side) . . . . . . . . . 158 7.34 Densities of financial instruments without left tails, 3 years time horizon, Gaussian defaults (left-hand side) and NIG defaults (right-hand side) . . . . 158 7.35 Correlation of financial instruments in US economy, Gaussian defaults and NIG defaults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 7.36 Minimum-variance portfolio with Gaussian defaults (left hand side) and NIG defaults (right-hand side) . . . . . . . . . . . . . . . . . . . . . . . . . 161 7.37 Results of mean-variance optimisation, 1 year investment horizon with Gaussian defaults (left-hand side) and NIG defaults (right-hand side) . . . . . . . . . 162 7.38 Results of mean-variance optimisation, 3 years investment horizon with Gaussian defaults (left-hand side) and NIG defaults (right-hand side) . . . . 163 7.39 Results of mean-variance optimisation, 5 years investment horizon with Gaussian defaults (left-hand side) and NIG defaults (right-hand side) . . . . 164 7.40 Minimum-CVaR portfolio with Gaussian defaults (left-hand side) and NIG defaults (right-hand side) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 7.41 Results of CVaR optimisation, 1 year investment horizon with Gaussian defaults (left-hand side) and NIG defaults (right-hand side) . . . . . . . . . 167 7.42 Results of CVaR optimisation, 3 years investment horizon with Gaussian defaults (left-hand side) and NIG defaults (right-hand side) . . . . . . . . . 168 7.43 Results of CVaR optimisation, 5 years investment horizon with Gaussian defaults (left-hand side) and NIG defaults (right-hand side) . . . . . . . . . 169 7.44 Results of score optimisation, 1 year investment horizon with Gaussian defaults (left-hand side) and NIG defaults (right-hand side) . . . . . . . . . 170 viii
Page 1 and 2: Technische Universität München Ze
Page 3 and 4: Danksagungen Zuallererst möchte ic
Page 5 and 6: CONTENTS 3.8.2 Synthetic CDO (Synth
Page 7: List of Figures 2.1 Basic structure
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
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Page 23 and 24: 2.3.2 Classification according to R
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Page 45 and 46: in detail. CHAPTER 2. CREDIT RISK T
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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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