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請用此 Handle URI 來引用此文件: http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/93882
完整後設資料紀錄
DC 欄位值語言
dc.contributor.advisor管中閔zh_TW
dc.contributor.advisorChung-Ming Kuanen
dc.contributor.author陳昱元zh_TW
dc.contributor.authorYu-Yuan Chenen
dc.date.accessioned2024-08-09T16:09:34Z-
dc.date.available2024-08-10-
dc.date.copyright2024-08-09-
dc.date.issued2024-
dc.date.submitted2024-07-23-
dc.identifier.citationAndersen, L. and Sidenius, J. (2004). Extensions to the gaussian copula: Random recovery and random factor loadings. Journal of Credit Risk Volume, 1(1):05.
Chen, J., Liu, Z., and Li, S. (2014). Mixed copula model with stochastic correlation for cdo pricing. Economic Modelling, 40:167–174.
Choros, B., Härdle, W. K., and Okhrin, O. (2009). Cdo pricing with multifactor and copulae models. Technical report, Citeseer.
Choroś-Tomczyk, B., Härdle, W. K., and Overbeck, L. (2014). Copula dynamics in cdos. Quantitative Finance, 14(9):1573–1585.
Hull, J. et al. (2009). Options, futures and other derivatives/John C. Hull. Upper Saddle River, NJ: Prentice Hall,.
Hull, J., White, A., et al. (2004). Valuation of a cdo and an nth to default cds without monte carlo simulation. Journal of Derivatives, 12(2):8–23.
Jäckel, P. (2005). A note on multivariate gauss-hermite quadrature. London: ABN-Amro.Re.
Kalemanova, A., Schmid, B., Werner, R., et al. (2007). The normal inverse gaussian distribution for synthetic cdo pricing. Journal of derivatives, 14(3):80.
Li, D. X. (1999). On default correlation: A copula function approach. Available at SSRN187289.
McNeil, A. J. and Nešlehová, J. (2009). Multivariate archimedean copulas, d-monotone functions and ℓ 1-norm symmetric distributions.
Okhrin, O. and Xu, Y. F. (2017). A comparison study of pricing credit default swap index tranches with convex combination of copulae. The North American Journal of Economics and Finance, 42:193–217.
O'Kane, D. and Schloegl, L. (2003). An analytical portfolio credit model with tail dependence. Quantitative Credit Research, Lehman Brothers.
Sklar, M. (1959). Fonctions de répartition à n dimensions et leurs marges. In Annales del’ISUP, volume 8, pages 229–231.
Vasicek, O. (2002). The distribution of loan portfolio value. Risk, 15(12):160–162.
Wang, D., Rachev, S. T., and Fabozzi, F. J. (2009). Pricing tranches of a cdo and a cds index: Recent advances and future research. Risk Assessment: Decisions in Banking and Finance, pages 263–286.
Xu, G. (2006). Extending gaussian copula with jumps to match correlation smile. Wachovia Securities, online at http://www. defaultrisk. com.
Yang, R., Qin, X., and Chen, T. (2009). Cdo pricing using single factor mg-nig copula model with stochastic correlation and random factor loading. Journal of mathematical analysis and applications, 350(1):73–80.
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dc.identifier.urihttp://tdr.lib.ntu.edu.tw/jspui/handle/123456789/93882-
dc.description.abstractCDO(擔保債務憑證)的估值在近期疫情和經濟不確定性背景下,仍然是金融領域的一個重要課題。傳統的copula模型,如單因子高斯copula,存在相關性偏斜和缺乏厚尾特徵等問題,導致校準和市場擬合上有顯著誤差。儘管已有各種具有厚尾特性的copula模型被提出,如Double t copula和NIG copula,但這些模型有些只能以近似方式求得分布,有些涉及過多的參數,導致計算時間增加和效率低下。各自都有部分缺陷。

本研究引入了高斯分佈和雙指數分佈混合(G-DE)copula模型,以解決過往copula模型的局限性。G-DE copula模型保留了厚尾特徵,並具有卷積特性,消除了數值近似的需求,並減少了參數估計的複雜性,從而提高了計算效率。更甚是透過混合高斯分布,使其大幅提升市場報價擬合度。我們的研究將G-DE模型與傳統copula模型進行比較,展示其在校準準確性、計算效率和整體性能方面的優勢。研究結果顯示,G-DE copula模型是CDO定價和風險管理的一個強有力的替代方案。
zh_TW
dc.description.abstractThe valuation of Collateralized Debt Obligations (CDOs) remains a crucial financial topic, especially in the context of the recent pandemic and economic uncertainties. Traditional copula models, such as the one-factor Gaussian copula, suffer from issues like correlation skew and lack of heavy-tailed characteristics, leading to biases in calibration and market fit. Although various heavy-tailed copula models have been proposed, including the double t copula and NIG copula, they either require complex numerical approximations or involve excessive parameters, resulting in increased computational times and inefficiencies.

This study introduces the Mixtures of Gaussian distribution and Double Exponential distribution (G-DE) copula model, addressing the limitations of previous copula models. The G-DE copula model retains heavy-tailed characteristics while possessing convolution property, eliminating the need for numerical approximations and reducing the complexity of parameter estimation. This results in improved computational efficiency and better market quote fitting. Our research compares the G-DE model with traditional copula models, demonstrating its advantages in calibration accuracy, computational efficiency, and overall performance. The findings highlight the G-DE copula model as a robust alternative for CDO pricing and risk management.
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dc.description.tableofcontents論文口試委員審定書. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
致謝. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv
Chapter 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Chapter 2 Methodology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1 Copula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.1 Mathematical Definition of copula . . . . . . . . . . . . . . . . . . 7
2.1.2 Types of copula . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 CDO pricing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3 Gaussian copula model . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3.1 One-factor Gaussian copula model . . . . . . . . . . . . . . . . . . 13
2.3.2 Gaussian Hermite Quadrature . . . . . . . . . . . . . . . . . . . . . 15
2.3.3 LHP Approximation Method . . . . . . . . . . . . . . . . . . . . . 15
2.3.4 Two-factor Gaussian copula model . . . . . . . . . . . . . . . . . . 18
2.3.5 Two dimensional Gaussian Hermite Quadrature . . . . . . . . . . . 20
2.4 Double t copula model . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.5 NIG copula model . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.6 G-NIG copula model . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.7 G-DE copula model . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.7.1 DE copula model . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.7.2 G-DE copula model . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Chapter 3 Data and Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.1 Synthetic CDO Data . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2 Data Quotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3 Calibration Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Chapter 4 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.1 Simulation Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Chapter 5 Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.1 Calibration Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.2 Calibration Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 63
Chapter 6 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Appendix A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
A.1 Derivation of cdf of 2DE Distribution . . . . . . . . . . . . . . . . . 71
A.2 Proof of central moments of 2DE Distribution . . . . . . . . . . . . . 72
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dc.language.isoen-
dc.title以混合雙指數copula模型定價合成型CDOzh_TW
dc.titlePricing synthetic CDO with mixed double exponential copula modelen
dc.typeThesis-
dc.date.schoolyear112-2-
dc.description.degree碩士-
dc.contributor.coadvisor繆維中zh_TW
dc.contributor.coadvisorWei-Chung Miaoen
dc.contributor.oralexamcommittee張森林;王之彥zh_TW
dc.contributor.oralexamcommitteeSan-Lin Chung;Jr-Yan Wangen
dc.subject.keyword混合雙指數,Copula,因子模型,合成型CDO,組別相關性,zh_TW
dc.subject.keywordMixed Double Exponential,Copula,Factor model,Synthetic CDO,Grouped Correlation,en
dc.relation.page73-
dc.identifier.doi10.6342/NTU202402011-
dc.rights.note未授權-
dc.date.accepted2024-07-25-
dc.contributor.author-college管理學院-
dc.contributor.author-dept財務金融學系-
顯示於系所單位:財務金融學系

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