臺灣博碩士論文加值系統

資產報酬相關係數在新巴賽爾資本協定的內部評等法之資本計提中是一個關鍵的變數，但許多文獻所提的結論都指出巴賽爾所提供資產報酬相關係數的範圍是有爭議的。在新巴賽爾資本協定2001年第二版諮詢文（CP2）中，並沒有將資產報酬相關係數列為變數，僅表示資產報酬相關係數均為0.2；而在2003年4月的第三版諮詢文（CP3），正式將資產報酬相關係數列為計算資本需求之重要變數，除了更改範圍為0.12~0.24外，更提出資產報酬相關係數與違約機率呈現負相關，且擁有一函數關係，但由於CP3對於這個函數並沒有提出一個理論的架構，因此引起許多學者熱烈討論。

本文即欲採用貝式方法中的吉氏抽樣法加在一因子模型上以探討資產報酬相關係數的分配，我們採用北美上市公司2001年至 2005年的股價報酬資料以及財報資料作分析，結果指出資產報酬相關係數是違約機率的遞減函數且是公司規模的增函數，並且提出資產報酬相關係數的公式可能忽略了某些重要且會影響相關系數範圍的因子。

The asset correlation is the key variable for calculating the regulatory capital in the IRB approach of New Basel Accord. However, the range of asset correlation has suffer a lot of controversy since the Second Consultative paper（CP2）in 2001. Then, the third Consultative paper（CP3）announced in April, 2003 formally introduced the asset return correlation as a decreasing function of default probability. CP3 not only defined that the range of asset correlation from 0.12 to 0.24 for corporations but also addressed a negative relationship between asset correlation and probability of default. As CP3 did not explain the theoretical concept for the formula of asset correlation, there were a lot of studies discuss the appropriateness of this formula. This study applied Bayesian method to ASRF model to estimate the posterior distribution of asset correlation. We use the data for the firms in the United State from year 2001 to 2005. The empirical results suggest that the asset correlation is a decreasing function of probability of default and an increasing function of firm size, and indicate that there may be some important factors impact the asset correlation were ignored.

1 Introduction 1
2 Literature review 4
2.1 Overview of Basel II . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 IRB approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3 Derivation of the Capital requirement . . . . . . . . . . . . . . . 6
2.4 Asset Correlation in the IRB Approach . . . . . . . . . . . . . . 9
2.4.1 Literature about Asset Correlation . . . . . . . . . . . . 10
3 Research Method 14
3.1 Bayesian Statistical Analysis . . . . . . . . . . . . . . . . . . . . 14
3.1.1 Gibbs Sampler . . . . . . . . . . . . . . . . . . . . . . . 16
3.2 The Asymptotic Single Risk Factor Model . . . . . . . . . . . . 17
3.3 ASRF Model with Bayesian Method . . . . . . . . . . . . . . . 19
3.4 Posterior distribution of asset correlation
— Application of Gibbs Sampler . . . . . . . . . . . . . . . . . 21
3.5 Data Description . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4 Empirical Results 24
4.1 Based on Z-score categories . . . . . . . . . . . . . . . . . . . . 25
4.2 Based on firm size categories . . . . . . . . . . . . . . . . . . . . 32
5 Conclusion 38
A Normal and Beta prior 42
A.1 Normal prior by Z-score category . . . . . . . . . . . . . . . . . 42
A.2 Beta prior by Z-score category . . . . . . . . . . . . . . . . . . . 44
A.3 Normal prior by firm size category . . . . . . . . . . . . . . . . . 45
A.3.1 Beta prior by firm size category . . . . . . . . . . . . . . 46

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