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| 研究生： |
賴偉聖 |
|---|---|
| 論文名稱： |
Pricing kth-to-Default Swaps: Copula Methods |
| 指導教授： | 謝淑貞 |
| 學位類別： |
碩士
Master |
| 系所名稱： |
商學院 - 國際經營與貿易學系 Department of International Business |
| 論文出版年： | 2007 |
| 畢業學年度： | 95 |
| 語文別： | 英文 |
| 論文頁數： | 57 |
| 中文關鍵詞： | 信用違約交換 |
| 外文關鍵詞： | kth-to-default swaps |
| 相關次數： | 點閱：200 下載：0 |
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Credit derivatives are instruments that transfer the credit risk from one party to another one. The most common credit derivative is the single entity credit default swap (CDS).A basket default is similar to a single entity CDS except that the underlying obligation is a basket of entities rather than a single reference asset. The copula methods play an important role while we price a multiname product since the assets in the portfolio are not independent. We need to model the correlated default times by using copula functions. In this article, we develop a copula based methodology for pricing -to-default swaps by using market CDS quotes. In order to know the influence of changing price drivers such as correlations and intensities on spreads, we also discuss the sensitivity analysis in this article.
1. INTRODUCTION 4
2. RELATED LITERATURES 6
3. COPULA FUNCTIONS 7
3.1. DEPENDENCE MEASURES 7
3.2. BASIC DEFINITIONS AND PROPERTIES 10
3.3. MULTIVARIATE COPULA FUNCTIONS 12
3.3.1. The Multivariate Gaussian Copula 13
3.3.2. The Multivariate Student's t Copula 13
3.3.3. Archimedean Copulas 14
3.4. TAIL DEPENDENCE 17
3.5. ESTIMATING PARAMETERS OF COPULAS 19
3.6. EMPIRICAL RESULTS 20
4. CONSTRUCTION OF THE CREDIT CURVE 24
4.1. HAZARD RATE FUNCTION 24
4.2. POISSON PROCESS AND COX PROCESS 25
4.3. CALIBRATION OF HAZARD RATE FUNCTION 29
4.4. EMPIRICAL RESULTS 31
5. SIMULATING CORRELATED DEFAULT TIMES 35
5.1. SIMULATION FROM ELLIPTICAL COPULAS 35
5.2. SIMULATION FROM ARCHIMEDEAN COPULAS 36
5.3. THE DISTRIBUTION OF DEFAULT TIMES 40
6. BASKET DEFAULT SWAP SPREADS 41
6.1. PRICING OF -TO-DEFAULT SWAPS 41
6.2. EMPIRICAL RESULTS 43
6.3. SENSITIVITY ANALYSIS RESULTS 45
7. CONCLUSION 49
APPENDIX 54
Table List
TABLE 1 UPPER AND LOWER TAIL COEFFICIENTS OF ARCHIMEDEAN COPULA 17
TABLE 2 THE CORRELATION MATRIX OF THE PORTFOLIO 21
TABLE 3 THE MARKET QUOTES FOR CREDIT DEFAULT SWAPS (BPS) 32
TABLE 4 THE RESULTS OF -TO-DEFAULT SWAPS (BPS) 44
TABLE 5 THE RESULTS OF CHANGING THE INTENSITIES (BPS) 46
TABLE 6 THE RESULTS OF CHANGING THE CORRELATIONS (BPS) 47
Figure List
FIGURE 1 ESTIMATION OF DEGREES OF FREEDOM 22
FIGURE 2 ESTIMATION OF GUMBEL COPULA 22
FIGURE 3 ESTIMATION OF CLAYTON COPULA 23
FIGURE 4 ESTIMATION OF FRANK COPULA 23
FIGURE 5 THE CALIBRATED HAZARD RATES FOR THE PORTFOLIO. 34
FIGURE 6 SPREADS OF -TO-DEFAULT SWAPS WITH DIFFERENT INTENSITIES 46
FIGURE 7 SPREADS OF -TO-DEFAULT SWAPS WITH DIFFERENT CORRELATIONS. 48
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