Abstract: There exist two problems in the application of Logistic model to calculate corporate default probabilities. One is that Logistic model can not be estimated or the results calculated are incorrect on the condition the corporate default records database is unavailable or the database is not typical. The other is the differences in distribution characteristics of financial indicators between industries are usually ignored in current Logistic default probability models. It leads to the decrease in the accuracy of corporate default probability calculation. To solve the first problem, the corporate default probabilities implied in the corporate bond credit spreads are calculated. Then the parameters of Logistic regresion are estimated on the basis of Logistic transformation, so that the corporate default probabilities calculated conform to the actual situation of the credit market. To solve the second problem, it is confirmed there exist significant differences in distribution characteristics of key financial indicators between industries by singel factor variance analysis. It is also confirmed the accuracy of corporate default probabilites is improved significantly, calculated by the Logistic models established respectively for each industry. The process of establishment of Logistic default probability model is as follows. The financial indicators which reflect similar information are deleted through correlation analysis of financial indicators initially selected. The financial indicators with weak explanatory capacity to corporate default probability are deleted through coefficient significant test of financial indicators. According to the criterion of linear regression fitness, the key financial indicators of Logistic default probability model are selected for different industries. Logistic default probability models are established for 5 sample industries such as machinery and equipment industryetc, providing models and methods to calculate the corporate default probabilities accurately for sample industries. The innovations and characteristics of the paper are as follows. Firstly, the corporate default probabilities implied in the bond market are calculated according to the credit spreads of corporate bonds, and taken as the explained variable of the Logistic linear regression after Logistic transformation, solving the problem to estimate the parameters of Logistic default probability models without the corporate default records database. Secondly, through single factor variance analysis, it confirms that there exist significant differences in distribution characteristics of financial indicators between industries, and it indicates that the Logistic default probability model should be established respectively for each industry. Thirdly, through correlation analysis of financial indicators initially selected, the financial indicators which reflect similar information are deleted; through coefficient significant test of financial indicators, the financial indicators with weak explanatory capacity to corporate default probability are deleted, which ensures the key financial indicators selected finally are reasonable. Fourthly, the empirical study shows that the key financial indicators of Logistic default probability models are different between industries, and the parameters of the same financial indicators are distinctive in different Logistic default probability models. The empirical study also shows the goodness of fit and the adjusted goodness of fit are enhanced nearly one time when the Logistic default probability models are established respectively for each industry instead of being as a whole. The results of the study have reference value for improving the accuracy of corporate default probability calculation, and for loan pricing, corporate bond pricing and credit risk management of commercial banks.

Key words: corporate default probability, logistic regression, goodness-of-fit, credit spread

摘要： 用Logistic模型计算公司违约概率在实际应用中存在两个问题:一是在缺乏公司违约记录数据库或违约记录数据库不典型的情况下,无法应用该模型或模型计算结果不准确;二是现有Logistic违约概率模型忽视了不同行业财务指标分布特征的差异性,导致公司违约概率计算结果的准确性降低。针对问题一,本文通过公司债券信用利差计算市场隐含的公司违约概率,在Logistic变换的基础上进一步确定Logistic线性回归的参数,使得公司违约概率的计算结果符合债券市场的实际状况。针对问题二,通过不同行业关键财务指标的单因子方差分析,证实了行业间财务指标的分布特征具有显著性差异,通过拟合优度证实了区分行业建立Logistic违约概率模型可显著提高违约概率测算的准确性。本文Logistic违约概率模型的构建过程如下:通过初选财务指标的相关性分析,删除反映信息重复的财务指标;通过Logistic回归中财务指标系数的显著性检验,删除对违约概率解释能力弱的财务指标;以Logistic回归的拟合优度为标准,选取各样本行业Logistic违约概率模型的关键财务指标,建立了机械设备等5个样本行业的Logistic违约概率模型,为样本内行业公司违约概率的准确测算提供模型与方法。本文的创新与特色:一是在无套利条件下,通过公司债券信用利差计算市场隐含的公司违约概率,并对其进行Logistic变换,作为Logistic线性回归的被解释变量,解决了在缺乏公司违约记录数据情况下Logistic违约概率模型的参数估计问题;二是通过单因子方差分析方法,证实了行业间财务指标的分布特征具有显著性差异,说明应区分行业建立Logistic违约概率模型;三是通过财务指标间的相关分析删除反映信息重复的财务指标,通过财务指标系数的显著性检验删除对公司违约概率解释能力弱的财务指标,保证了Logistic违约概率模型中关键财务指标选取的合理性;四是实证研究结果表明,不同行业的Logistic违约概率模型的关键财务指标不同,同一财务指标的参数也存在显著差异。实证研究结果还表明,区分行业建立Logistic违约概率模型与不区分行业相比,前者可将拟合优度及调整后的拟合优度提高近1倍。本文研究结果对于提高公司违约概率测算的准确性具有重要参考意义,对于商业银行贷款定价、公司债券发行定价、银行信用风险管理具有重要参考意义。

关键词: 公司违约概率, Logistic回归, 拟合优度, 信用利差