存活分析模型應用在信用卡使用者之違約風險研究

Abstract

摘要 存活分析模型在生物統計與公司財務領域已有多年研究，但運用它來判斷個人信用風險的違約機率並估計其未來之存活時間的文獻為數極少。本研究內容係利用信用卡使用者的信用卡歷史資料建立衡量違約風險之模型，研究對象為金融聯合徵信中心所蒐集之信用卡資料，選取2004年12月為觀測時點往前後各涵蓋12個月為資料研究期間，可取得的變數包含人口資料變數、持卡人歷史資料變數、持卡人短期、短中期、中期行為變數、及持卡人行為變數異動程度，並進一步以主成份分析法萃取出82個主成份投入Cox模型，從中決定顯著的共變量進而建立預測模型。 透過Cox模型，參數可直接由樣本資料來估計而無需假設樣本資料的分配。本研究結果顯示：當存活率判別值等於0.98時，正確分類為違約樣本或者正常樣本的比例皆在80%左右。隨著存活率判別值下降，正確分類為違約樣本的比例也會跟著降低，而正確分類為正常樣本的比例會上升。本模型除了可以觀察固定時點的樣本存活機率之外，亦可隨著時點移動觀察存活率遞減的情況，進而判斷該樣本在未來會在何時發生違約。預測違約時點是存活分析模型與其他模型最大的差異處，這項能力使得模型採用者可以更加掌握信用卡使用者的未來資訊，增加風險控管的積極性。

關鍵字：存活分析、Cox模型、個人信用風險

Abstract Survival Analysis was originally adopted for in Biological and Actuarial sciences. In the recent decades this method is also used to perform the company failure prediction model. However, it is still in the early stage to apply survival analysis to predict credit risk in the personal credit card market while it is the main purpose of this study. Thank to the dataset provided by Joint Credit Information Center, there are demographic information as well as the credit card holder’s usage histories and the consuming behavior difference between short-term and medium term. By applying Principal Component Analysis, the 82 Principal Components are therefore obtained to be the inputs in the Cox Model. The Cox Model provides advantage that the parameters can be directly estimated without specifying distribution of data. The result of the proposed method shows that the accuracy ratio of classification is around 80% when the cut-point of survival probability is made as 0.98. If the cut-point is lower, there will be lower accuracy ratio in the default sample but higher in the normal sample. By using Cox Model, one can also get the information of when will credit card holder defaults. The ability of default timing prediction makes the Cox Model different from other models and it can also improve the ability of credit risk management.

Keyword: Survival Analysis, Cox Model, Personal Credit Risk