臺灣博碩士論文加值系統

在做擔保債權憑證的定價時，資產間的相關性是一個不容易處理的問題。資產總損失的分配是由一個很多維的聯合機率分配來決定，但是因為太過於複雜，因此有計算上的困難。本文延伸了前人的文獻，利用兩個主要的元素來解決這個問題：分別是因素模型以及傅立葉轉換，以期能夠達到快速的計算出擔保債權憑證個各分券的合理價格。

In pricing CDOs, the correlation between assets is a major issue. A multi-asset joint distribution function is too complicated to transform to a loss distribution. Chen and Zang developed a method to price a large credit portfolio. This method is composed of two elements: Factor model and Fourier inversion. This thesis generalizes their method. We assume that there are two common factors, and all assets have their own correlations with the common factors. Since the assets in a pool are not affected by only one common factor, and each asset has different degrees of influence over that common factor, we generalize the one-factor model with more accurate performance.

誌謝.........................................i
中文摘要....................................ii
英文摘要...................................iii
第一章 論文介紹..............................1
1.1 簡介......................................1
1.2 論文架構................................. 7
第二章 文獻回顧..............................8
2.1 Merton模型................................8
2.2 Chen-Zang 模型............................9
2.2.1 一因子模型..............................9
2.2.1 傅立葉轉換.............................11
2.3 Yeh-Liao-Tao 模型........................13
第三章 研究方法.............................14
3.1 一般化...................................14
3.2 模型架構.................................16
第四章 實證分析.............................19
4.1 環境設定結果.............................19
4.2 比較.....................................24
第五章 結論.................................27
參考文獻.....................................28

[1] CHEN, REN-RAW AND ZANG, JUN. “Pricing Large Portfolios with Fourier Inversion.” Working paper, October 17, 2004.

[2] HULL, J. Options, Futures, and Other Derivatives. 5th Edition, Prentice Hall, Englewood Cliff, NJ, 2003.

[3] HULL, J. AND A. WHITE. “Valuation of a CDO and an n-th to default CDS without Monte Carlo simulation.” Journal of Derivatives, Vol. 12. No. 2. (2004). pp. 8-48.

[4] LAURIE S. GOODMAN. “Synthetic CDOs: An Introduction.” Journal of Derivatives, Vol. 9. No. 2. (2002). pp. 8–23.

[5] MERTON, ROBERT. “On the Pricing of Cooperate Debt: The Risk Struture of Interest Rates.” Journal of Finance, 28, 1974, pp. 449–470.

[6] Tao, M. C. AND Liao, H. H. AND Yeh, S. C. “Collateralized Bond Obligation Credit Risk Evaluation: An Integration of Intrinsic Valuation and Fourier Transform Method.”