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| 研究生： |
黃柏翰 Huang,Po Han |
|---|---|
| 論文名稱： |
評價擔保債權憑證與避險－隱含連繫結構模型 Valuing and Hedging Collateralized Debt Obligations with the Implied Copula Model |
| 指導教授： |
廖四郎
Liao,Szu Lang |
| 學位類別： |
碩士
Master |
| 系所名稱： |
商學院 - 金融學系 Department of Money and Banking |
| 論文出版年： | 2007 |
| 畢業學年度： | 95 |
| 語文別： | 英文 |
| 論文頁數： | 54 |
| 中文關鍵詞： | 西低歐 、隱含連繫結構 、避險 |
| 外文關鍵詞： | implied copula |
| 相關次數： | 點閱：114 下載：88 |
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Collateralized debt obligations (CDOs) represent one of the fastest-growing credit derivatives of the structured finance world. In January 2007, the law has been promoted so that CDOs can be issued in Taiwan, including CLOs and CBOs. Thus, we can expect that these two kinds of CDOs will be main products in short future.
There are many approaches to valuing CDOs, such as structural models, reduced-form models and credit barrier models. Copula models, which are sometimes classified as reduced-form models, represent the market standard for pricing CDOs. In this paper, we discuss the “implied copula model”, one approach implied from copulas. This is first written by John Hull and Alan White in October, 2006. Here, we discuss how the assumptions in the implied copula model can be released or changed. In our study, we use the CDX IG data on June 8, 2007, for calibration.
Besides valuing CDOs with implied copula, we use the adjusted implied copula approach to hedge. Since credit default swap (CDS) has become one of the basic credit products and CDOs are based from some set of CDSs, the CDO tranches and the CDSs must be arbitrage-free. By taking this idea into our model, our study shows that this approach can be used to hedge CDOs with CDSs. Moreover, we use implied copula to eliminate the arbitrage opportunity in Gaussian copula/base correlation approach. As valuing, we also use the CDX IG data on June 8, 2007, for calibration in our hedging model. Consequently, our results suggest that there is a hedging approach with better hedging effect, which is constructed according to Greeks of CDO tranches or according to classification by industries and credit ratings of the CDS names for CDOs.
I. Introduction...................................................................................................................1
II. CDO and CDO-related Models...................................................................................3
2.1 CDS and CDO Structure.....................................................................................3
2.2 Structural Models................................................................................................4
2.3 Reduced-form Models.........................................................................................5
2.4 Credit Barrier Models.........................................................................................5
2.5 Copula Model.......................................................................................................6
2.5.1 One Factor Copula Model........................................................................6
2.5.2 The Standard Market Model...................................................................8
2.5.3 Probability Bucketing...............................................................................8
2.6 The Implied Correlation......................................................................................8
2.6.1 The Compound Correlation.....................................................................9
2.6.2 The Base Correlation................................................................................9
2.7 Correlation Trading...........................................................................................11
III. The Implied Copula Model.......................................................................................12
3.1 Intuition behind Implied Copula Model..........................................................12
3.2 Correlation, Hazard Rates, and the Gaussian Copula...................................13
3.3 Implementation of Model..................................................................................15
3.3.1 Choosing the λ’s......................................................................................18
3.3.2 Choosing the π’s......................................................................................18
3.3.3 Bespoke CDO Tranches..........................................................................19
3.3.4 Arbitrage-free with CDSs.......................................................................19
IV. Empirical Analysis of CDX IG Data.........................................................................21
4.1 The Data of the CDO Indices............................................................................21
4.2 The Result of Calibration of CDX IG Data.....................................................22
4.3 Comparison of the Base Correlation and Implied Copula Approach...........24
4.3.1 On-the-run CDO Tranches....................................................................25
4.3.2 Off-the-run CDO Tranches....................................................................25
V. Greeks of CDO Tranches and Hedging Approaches................................................27
5.1 Comparison of Flat Term Structure Model and Implied Copula Model......28
5.2 Sensitivity Analysis of Greeks for Dynamic Hedging.....................................31
5.3 Delta of One Single Name..................................................................................35
5.3.1 The Nonhomogeneous Model.................................................................36
5.3.2 Deltas of a Single Name in the Nonhomogeneous Model....................36
5.4 Hedging Models..................................................................................................38
5.4.1 The First Model for Hedging.................................................................39
5.4.2 The Second Model for Hedging.............................................................41
VI. Conclusion..................................................................................................................44
Reference.........................................................................................................................45
Appendix 1........................................................................................................................46
i
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