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姓名	呂其倫(Chi-Lun Lu)  查詢紙本館藏	畢業系所	財務金融學系
論文名稱	一般化non-square Cholesky 分解演算法運用在擔保債權憑證(CDO)之標的資產選擇 (A generalized non-square Cholesky Decomposition Algorithm with Applications to choose the underlyings for Collateralized Debt Obligations)
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摘要(中)	擔保債權憑證(CDO)是一種相關性的商品。這個商品的各切層價格反映多資產間聯合違約機率的相關性，因此投資人面臨相關性的風險。投資人必須去衡量這些風險，才能正確的去決定各層的公平價值。在CDO的產品中，去分解相關性矩陣來計算相關性，最常見的技巧是使用Cholesky分解。然而，Cholesky分解只能在矩陣為正定時使用。在本篇論文中，我們認為Spectral分解將可以克服上述的缺點。使用Spectral分解將一定可以獲得多資產蒙地卡羅模擬所需要的矩陣。在Cholesky分解和Spectral分解均可執行時，他們所獲的的模擬結果也將是一致的。而當Cholesky 分解不能執行時(矩陣有負的eigenvalue), Spectral分解可以獲得模擬所需的矩陣，也可以清楚的衡量出模擬結果的好壞。
摘要(英)	CDO is a correlation product. The investors of this product involve correlation risks since the prices of respective tranches depend on joint default correlations. To determine a fair return for bearing the correlation risks, the investors must be able to measure these risks. The most common skill used to decompose the correlation matrix for CDO products is the Cholesky decomposition. However, the Cholesky decomposition can only work for the case of a positive matrix. In this paper, we propose a Spectral decomposition which can overcome the shortcomings of the Cholesky decomposition. Spectral decomposition can always obtain matrix that Monte Carlo simulations need. Spectral decomposition will have consistent results if Cholesky decomposition can work. If Cholesky decomposition can not work (matrix has negative eigenvalues), Spectral decomposition can still obtain a matrix that is able to measures the simulation results not matter good or bad.
關鍵字(中)	★ 關聯結構 ★ 擔保債權憑證 ★ Cholesky分解 ★ Spectral分解	關鍵字(英)	★ Collateralized Debt Obligation ★ Copula ★ Cholesky Decomposition ★ Spectral decomposition
論文目次	Contents 1. Introduction .................................1 2. Copula Function and Pricing Synthetic CDO .................................4 2.1 Hazard Rate and Default Time .................................4 2.2 Standard Copula Functions .................................5 2.3 Monte Carlo Simulation .................................7 2.4 Fair Spread of CDO .................................10 3. Spectral Decomposition and Error Measure .................................11 3.1 Spectral decomposition .................................11 3.2 Error measure .................................13 4. Numerical example .................................15 4.1 Default Correlation and Fair Spread .................................15 4.2 Default Correlation and First/Second-to-Default .................................18 4.3 Change Credit Spread of CDS .................................19 5. Conclusion .................................20 References .................................22 Appendix A: The Frobeninus Norm Positive Approximant .................................24 Appendix B: Table and Figure .................................26
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指導教授	張傳章(Chuang-Chang Chang)	審核日期	2005-6-27
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