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研究生:陳珮瑜
研究生(外文):Pei-yu Chen
論文名稱:信用評等轉置矩陣之穩定度探討
論文名稱(外文):A Study of the Stability in Credit Rating Transition Matrix
指導教授:張揖平張揖平引用關係
指導教授(外文):Yi-ping Chang
學位類別:碩士
校院名稱:東吳大學
系所名稱:財務工程與精算數學系
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2011
畢業學年度:99
語文別:中文
論文頁數:15
中文關鍵詞:第三版新巴塞爾協定新版巴塞爾資本協定內部評等法信用評等轉置矩陣稀疏性。
外文關鍵詞:Basel IIIBasel IIInternal Ratings Based ApproachCredit ratingTransition matrixSparse.
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巴塞爾銀行監理委員會 (Basel Committee on Banking Supervision)
於 2010 年 9 月 12 日宣布了第三版新巴塞爾協定 (New Basel Capital Accord, 簡稱 Basel III),
在 Basel III 關於內部評等法 (Internal Ratings Based Approach) 議題未修改之部分,
將承襲在 2004 年 6 月底公布之新版巴塞爾協定 (New Basel Capital Accord, 簡稱 Basel II) 的規定實施。
本文針對 Basel II 內部評等法中的信用評等 (credit rating) 轉置矩陣 (transition matrix) 之穩定性進行探討,
參考 H\"{o}se et al. (2002) 提出的檢定統計量,
由於信用評等轉置矩陣常具有稀疏性 (sparse),
本文亦參考 Zelterman (1987) 在稀疏轉置矩陣時所提出的修正檢定統計量,
並應用在信用評等轉置矩陣上且增加期初評等之維度。
根據本文結果顯示,
原本在檢定信用評等轉置矩陣是否具有穩定度之檢定統計量過於保守,
並限制了資料必須為非稀疏性。
當信用評等轉置矩陣具有稀疏性時,
使用修正的檢定統計量結果較準確,
且應用在實證資料上顯示 Standard & Poor's 信用評等轉置矩陣資料並不具有穩定度。
Basel Committee on Banking Supervision on September 12,
2010 announced the third edition of the new Basel Capital Accord,
the unmodified part of the Internal Ratings Based Approach of Basel III that it will follow the Basel II published the end of June 2004.
In this paper,
we will focus on credit rating transition matrix of the Internal Ratings Based Approach of Basel III to explore the stability.
We made reference to Hose et al. (2002) proposed the test statistic,
and due to credit rating transition matrix often with sparse,
so this article also made reference to Zelterman (1987),
it proposed the modified test statistic under sparse transition matrix,
apply the modified test statistic on the credit rating transition matrix and increase the dimensions of initial rating.
According to this result shows that the credit rating transition matrix is sparse,
the results of use modified test statistics will more accurate,
and apply it on empirical data shows that the Standard & Poor's credit rating transition matrix does not have stability.
1.緒論...1
2.文獻回顧...2
3.研究方法...3
3.1檢定統計量近似 Chi-square 分配...3
3.2修正檢定統計量近似 Normal 分配...4
4.信用評等轉置矩陣之檢定方法的表現...6
5.實證分析...12
6.結論...12
參考文獻...14
1.Anatoliy, A. and Yanka, Y. (2004).
Transition matrix generation,
International Conference on Computer Systems and Technologies.

2.Basel Committee on Banking Supervision. (2004).
Basel II: International Convergence of Capital Measurement and Capital Standards: a Revised Framework.
http://www.bis.org/publ/bcbs107.htm

3.Basel Committee on Banking Supervision. (2010).
Basel III: A global regulatory framework for more resilient banks and banking systems.
http://www.bis.org/publ/bcbs189_dec2010.htm

4.Cressie, N. and Read, T. R. C.(1989). Pearson's X^2 and The Loglikelihood Ratio Statistic G^2:
A Comparative Review,
International Statistical Instatitute,
Vol. 57, No. 1, pp. 19-43.

5.Hose, S., Huschens, S. and Wania, R. (2002). Rating migrations. In Applied Quantitative Finance,
edited by Hardle, W., Kleinow, T. and Stahl, G.,
Springer, Heidelberg, pp. 105-123.

6. Jafry, Y. and Schuermann, T. (2004).
Measurement estimation and comparison of credit migration matrices,Journal of Banking &Finance,
Vol. 28, pp. 2603-2639.

7.Lando, D. and Skodeberg, T. (2002).
Analyzing rating transitions and rating drift with continuous observations,
Journal of Banking & Finance,
Vol. 26, pp. 423-444.

8. Parshall, C. G., Kromrey, J. D. and Dailey, R. (1999).
Comparative performance of three statistical tests of homogeneity for sparse I*J contingency tables,
Communications in Statistics-Simulation and Computation,
Vol. 28, No. 1, pp. 275-289.

9. Pamela, N., William P. and Simone, V. (2000).
Stability of rating transitions,
Journal of Banking & Finance,
Vol. 24, pp. 203-227.

10. Trueck, S. and Rachev, S. T. (2009).
Rating Based Modeling of Credit Risk: Theory and Application of Migration Matrices,
Elsevier Academic Press, Amsterdam, London.

11. Zelterman, D. (1987). Goodness-of-fit tests for large sparse multinomial distributions,
Journal of the American Statistics Association,
Vol. 82, No. 398, pp. 624-629.

12. Zelterman, D. (2006).Models for Discrete Data,
Clarendon Press, Oxford, New York.
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