非參數統計方法應用在新巴塞爾資本協定之信用風險模型

The Application of Nonparametric Estimate Smoother to the Credit Risk Model of New Basel Accord-Focusing on the Calculation of Asset Return Correlation

鍾麗英(Ly-Inn Chung) ； 郭台達(Tai-Ta Kuo)

《統計與資訊評論》 12卷 (2010/09) Pp. 39-52

https://doi.org/10.29862/JSC.201009.0003

摘要

資產報酬相關係數與違約機率為計算信用風險權重的主要參數。許多文獻所提的結論都顯示新巴塞爾資本協定中計算資產報酬相關係數的公式有修正的必要性。本研究利用在不給予任何參數化的前提假設下，揭露變數間函數相關的非參數估計統計方法建立違約距離與預期違約機率的關係模型，以估計借款公司之違約機率。接著應用違約相關模型估算資產報酬相關係數，並與新巴塞爾資本協定建議的資產報酬相關係數做比較，探討「新巴塞爾資本協定」中關於資產報酬相關係數計算公式的適切性。在使用美國2000年到2003年上市公司為研究資料，以實證研究探討資產報酬相關係數對於違約機率與公司資產規模間的關係。實證結果中我們發現資產報酬相關係數分別與違約機率具有一反向關係，而與公司資產規模大小呈現一正向關係，這兩個實證結果都與新巴塞爾資本協定中資產報酬相關係數與違約機率以及公司資產規模關係一致，不過由研究估算出的資產報酬相關係數值顯示出新巴塞爾資本協定對於資產報酬相關係數似乎具有過於高估傾向，仍有修改的空間與必要。實證研究中亦發現違約機率的變異數對資產報酬相關係數應該同樣具有影響，因此建議新巴塞爾資本協定規定的資產報酬相關係數公式可將違約機率的變異數列入評估考量。

關鍵字

違約機率 ； 資產報酬相關係數 ； 新巴塞爾資本協定

並列摘要

Asset return correlation and default probability are key factors for determining the regulatory capital requirement in credit risk model of New Basel Accord. In this paper, we apply the nonparametric estimate smoother to estimate default probability using distance to default. The asset correlation is calculated using the estimated default probability first and then extracting the implied asset return correlation from the joint default probability. Using data of American listed companies between 2000 and 2003, we empirically examine the relationship among asset return correlation, default probability, and firm asset size. Furthermore, we also compare the implied asset return correlation in this study with the correlation calculated from the definition in New Basel Accord. The empirical results indicate that the relationship between asset return correlation and default probability is negative, and asset return correlation is an increasing function of firm size. This finding is consistent with the result of quantitative impact study in New Basel Accord. However, the implied asset return correlation from this paper are much smaller than those calculated according to New Basel Accord. It shows that New Basel Accord tends to overestimate asset return correlation. It also suggests that the variance of default probability should be considered as a factor for calculating asset return correlation.

並列關鍵字

asset return correlation ； default probability ； New Basel Accord