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題名 Pricing kth-to-Default Swaps: Copula Methods
作者 賴偉聖
貢獻者 謝淑貞
賴偉聖
關鍵詞 信用違約交換
CDS
copula
kth-to-default swaps
日期 2006
上傳時間 11-Sep-2009 17:07:51 (UTC+8)
摘要 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.
參考文獻 1. Arvanitis A. and Gregory J. [2001], The Complete Guide to Pricing, Hedging and Risk Management, Risk Books.
2. Cherubini U., Luciano E. and Vecchiato W. [2004], Copula Methods in Finance, John Wiley & Sons, Ltd.
3. Duffie, D. and Singleton, K. [1999] Modeling Term Structures of Defaultable Bonds, Review of Finance Studies, 12, 4, pp. 687-720.
4. Elizalde A. [2005], Credit Risk Models: Default Correlation in Intensity Models, CMFI, working paper.
5. Elizalde A. [2005], Credit Risk Models: Default Correlation in Intensity Models, Kings College London, Department of Mathematics, working paper.
6. Embrechts P. and McNeil A. [2001], Modeling Dependence with Copulas and Applications to Risk Management, ETH Zurich, Department of Mathematics, working paper.
7. Galiani S.S. [2003], Copula Functions and their Application in Pricing and Risk Managing Multiname Credit Derivative Products, Kings College London, Department of Mathematics, working paper.
8. Houweling, P., and Vorst, T. [2005], Pricing Default Swaps: Empirical Evidence, Journal of international Money and Finance, pp. 1200-1225.
9. Hull, J. and White, A. [2000], Valuing Credit Default SwapsⅠ: No Counterparty Default Risk, Journal of Derivatives, 8, 1, pp. 29-40, 2000.
10. Hull, J. and White, A. [2000], Valuing Credit Default SwapsⅡ: Modeling default Correlations, Journal of Derivatives, 8, 3, pp. 12-22, 2000.
11. Hull, J. and White, A. [2004], Valuation of a CDO and an to Default CDS without Monte Carlo Simulation, Journal of Derivatives, 12, 2, 2004.
12. Jarrow, R. and Turnbull S. [1995], Pricing Derivatives on Financial Securities Subject to Credit Risk, The Journal of Finance, 50, 1, pp. 53-85.
13. Joe, H., [1997], Multivariate Models and Multivariate Dependence Concepts, Chapman and Hall, London.
14. Lando, D. [1998], On Cox Process and Credit Risk Securities, Review of Derivatives Research, 2, pp. 99-120.
15. Li, D.X. [2000], On Default Correlation: A Copula Function Approach, The Journal of Fixed Income, Mar, pp. 43-54.
16. Mashal, R. and Zeevi, A. [2002], Beyond Correlation: Extreme Co-movements Between Financial Assets, working paper, Columbia Graduate School of Business.
17. McNeil, A.J., Frey, R. and Embrechts, P. [2005], Quantitative Risk Management : concepts, techniques and tools, Princeton Series in Finance.
18. Merton, R.C. [1974], On the Pricing of Corporate Debt: The Risk Structure of Interest Rates, The Journal of Finance, 29, 2, pp.449-470.
19. Nelsen, R. [1999], An Introduction to Copulas, Springer, New York.
20. Roberto de Matteis [2001], Fitting Copulas to Data, ETH Zurich, Department of Mathematics, working paper.
21. Romano, C. [2002], Calibrating and Simulating Copula Functions: an Application to the Italian Stock Market, CIDEM, working paper.
22. Rose, C. and Smith, M.D. [2000], Symbolic Maximum Likelihood Estimation with Mathematica, The Statistician, 49, 2, pp. 229-240.
23. Schonbucher, P.J. [2003], Credit Derivatives Pricing Models: Models, Pricing and Implementation, Wiley.
24. Shreve, S. [2004], Stochastic Calculus for Finance, Springer.
25. Wu F., Valdez E. A., and Sherris M. [2005], Simulating Exchangeable Multivariate Archimedean Copulas and its Applications, Actuarial Research Symposium, November 2005.
描述 碩士
國立政治大學
國際經營與貿易研究所
94351030
95
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0094351030
資料類型 thesis
dc.contributor.advisor 謝淑貞zh_TW
dc.contributor.author (Authors) 賴偉聖zh_TW
dc.creator (作者) 賴偉聖zh_TW
dc.date (日期) 2006en_US
dc.date.accessioned 11-Sep-2009 17:07:51 (UTC+8)-
dc.date.available 11-Sep-2009 17:07:51 (UTC+8)-
dc.date.issued (上傳時間) 11-Sep-2009 17:07:51 (UTC+8)-
dc.identifier (Other Identifiers) G0094351030en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/30049-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 國際經營與貿易研究所zh_TW
dc.description (描述) 94351030zh_TW
dc.description (描述) 95zh_TW
dc.description.abstract (摘要) 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.en_US
dc.description.tableofcontents 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
zh_TW
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0094351030en_US
dc.subject (關鍵詞) 信用違約交換zh_TW
dc.subject (關鍵詞) CDSen_US
dc.subject (關鍵詞) copulaen_US
dc.subject (關鍵詞) kth-to-default swapsen_US
dc.title (題名) Pricing kth-to-Default Swaps: Copula Methodszh_TW
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) 1. Arvanitis A. and Gregory J. [2001], The Complete Guide to Pricing, Hedging and Risk Management, Risk Books.zh_TW
dc.relation.reference (參考文獻) 2. Cherubini U., Luciano E. and Vecchiato W. [2004], Copula Methods in Finance, John Wiley & Sons, Ltd.zh_TW
dc.relation.reference (參考文獻) 3. Duffie, D. and Singleton, K. [1999] Modeling Term Structures of Defaultable Bonds, Review of Finance Studies, 12, 4, pp. 687-720.zh_TW
dc.relation.reference (參考文獻) 4. Elizalde A. [2005], Credit Risk Models: Default Correlation in Intensity Models, CMFI, working paper.zh_TW
dc.relation.reference (參考文獻) 5. Elizalde A. [2005], Credit Risk Models: Default Correlation in Intensity Models, Kings College London, Department of Mathematics, working paper.zh_TW
dc.relation.reference (參考文獻) 6. Embrechts P. and McNeil A. [2001], Modeling Dependence with Copulas and Applications to Risk Management, ETH Zurich, Department of Mathematics, working paper.zh_TW
dc.relation.reference (參考文獻) 7. Galiani S.S. [2003], Copula Functions and their Application in Pricing and Risk Managing Multiname Credit Derivative Products, Kings College London, Department of Mathematics, working paper.zh_TW
dc.relation.reference (參考文獻) 8. Houweling, P., and Vorst, T. [2005], Pricing Default Swaps: Empirical Evidence, Journal of international Money and Finance, pp. 1200-1225.zh_TW
dc.relation.reference (參考文獻) 9. Hull, J. and White, A. [2000], Valuing Credit Default SwapsⅠ: No Counterparty Default Risk, Journal of Derivatives, 8, 1, pp. 29-40, 2000.zh_TW
dc.relation.reference (參考文獻) 10. Hull, J. and White, A. [2000], Valuing Credit Default SwapsⅡ: Modeling default Correlations, Journal of Derivatives, 8, 3, pp. 12-22, 2000.zh_TW
dc.relation.reference (參考文獻) 11. Hull, J. and White, A. [2004], Valuation of a CDO and an to Default CDS without Monte Carlo Simulation, Journal of Derivatives, 12, 2, 2004.zh_TW
dc.relation.reference (參考文獻) 12. Jarrow, R. and Turnbull S. [1995], Pricing Derivatives on Financial Securities Subject to Credit Risk, The Journal of Finance, 50, 1, pp. 53-85.zh_TW
dc.relation.reference (參考文獻) 13. Joe, H., [1997], Multivariate Models and Multivariate Dependence Concepts, Chapman and Hall, London.zh_TW
dc.relation.reference (參考文獻) 14. Lando, D. [1998], On Cox Process and Credit Risk Securities, Review of Derivatives Research, 2, pp. 99-120.zh_TW
dc.relation.reference (參考文獻) 15. Li, D.X. [2000], On Default Correlation: A Copula Function Approach, The Journal of Fixed Income, Mar, pp. 43-54.zh_TW
dc.relation.reference (參考文獻) 16. Mashal, R. and Zeevi, A. [2002], Beyond Correlation: Extreme Co-movements Between Financial Assets, working paper, Columbia Graduate School of Business.zh_TW
dc.relation.reference (參考文獻) 17. McNeil, A.J., Frey, R. and Embrechts, P. [2005], Quantitative Risk Management : concepts, techniques and tools, Princeton Series in Finance.zh_TW
dc.relation.reference (參考文獻) 18. Merton, R.C. [1974], On the Pricing of Corporate Debt: The Risk Structure of Interest Rates, The Journal of Finance, 29, 2, pp.449-470.zh_TW
dc.relation.reference (參考文獻) 19. Nelsen, R. [1999], An Introduction to Copulas, Springer, New York.zh_TW
dc.relation.reference (參考文獻) 20. Roberto de Matteis [2001], Fitting Copulas to Data, ETH Zurich, Department of Mathematics, working paper.zh_TW
dc.relation.reference (參考文獻) 21. Romano, C. [2002], Calibrating and Simulating Copula Functions: an Application to the Italian Stock Market, CIDEM, working paper.zh_TW
dc.relation.reference (參考文獻) 22. Rose, C. and Smith, M.D. [2000], Symbolic Maximum Likelihood Estimation with Mathematica, The Statistician, 49, 2, pp. 229-240.zh_TW
dc.relation.reference (參考文獻) 23. Schonbucher, P.J. [2003], Credit Derivatives Pricing Models: Models, Pricing and Implementation, Wiley.zh_TW
dc.relation.reference (參考文獻) 24. Shreve, S. [2004], Stochastic Calculus for Finance, Springer.zh_TW
dc.relation.reference (參考文獻) 25. Wu F., Valdez E. A., and Sherris M. [2005], Simulating Exchangeable Multivariate Archimedean Copulas and its Applications, Actuarial Research Symposium, November 2005.zh_TW