違約機率預測與極端值

本研究建議一個預測這約械率（Probability of Default，以下簡稱PO）的新方法，即使用Logit Model且考慮極端值，在本文為之為Robust Logistic Regression（穩健羅吉斯迴歸），首先，在模型的解釋能力上，Robust Logit Model的Pseudo-R-square值顯著地高於Logit Model，表示使用Robust Logistic Regression能讓模型的解釋能力提升。其次，本研究在樣本內預測的實證結果顯示，不論使用CAP、ROC、KS、Brier Score及交叉分類表，使用Robust Logistic Regression對於整個模型的預測效力會有大幅提升的效果，這表示離群值的存在的確降低核型的預測效力，所以在進行PO的預測時，是必須要考慮昌在群值的影響的，而本研究所提出的這個PO估計方法，的格可以消彌離群值所造成的不良影響，進而提升模型的預測效力。第三，在樣本外的CAP及KS檢定，Robust Logit Model的表現只略優於Logit，而就ROC及Brier Score言，並未得到較佳的預測結果，而使用交叉分類表，則在型一錯誤較佳，在型二錯誤較弱，可能是因為使用Robust Logistic Regression的模型雖然能得到較高的TP%，但卻得到較低的TN%，代表Robust Logistic Regression的模型可以降低型一錯誤，但卻提高了型二錯誤。

關鍵字

違約機率；羅吉斯模型；穩健迴歸；離群值

並列摘要

A new method for predicting the probability of default (PD) is suggested in this paper. This method, which is named ＂Robust Logistic Regression＂ in this paper, is based on Logit Regression but takes outlier into consideration. Firstly, comparing the explainatory power of Robust Logistic Model and Logit Model, the Pseudo-R-square of the former is outstandingly higher than the latter. Secondly, as the empirical study for the insample data shows, CAP, ROC, KS test, Brier Score and classification table all indicate that Robust Logistic Regression can strikingly increase the model's predictive power. It means the existences of the outlier indeedly weaken model's prediction power and the method suggested in this paper can eliminate the negative influences caused by the outlier. Thirdly, as the empirical study for the outsample data shows, Robust Logit Model is better than Logit Model in CAP and KS test but in ROC and Brier Score is not. For the classification table, Robust Logit Model performs better in Type one error but worse in Type two error. It shows Robust Logistic Regression may get higer percentage of TP but lower percentage of TN and means that Robust Logistic Regression can decrease Type one error but increase Type two error.