The Framework of Hammer Credit Rating System for Enterprises in Capital Markets of China with International Standards

Abstract

The goal of this paper is to discuss how we establish the “Hammer Credit System” by applying Gibbs sampling algorithm under the framework of bigdata approach to extract features in depicting proxy default (bad) samples or illegal behaviors by following the “five step principle”. Our study shows that the Hamer Credit System is able to resolve three problems of the current credit rating market in China which rate: “1) the rating is falsely high; 2) the differentiation of credit rating grades is insufficient; and 3) the poor performance of predicting early warning and related issues”; and in addition the CAFÉ credit is supported by clearly defining the “BBB” as the basic investment level with annualized rate of default probability in accordance with international standards in the practice of financial industries, and the credit transition matrix for “AAA-A” to “CCC-C” credit grades.

Appendix: The Framework for the Extraction of Features Based on Gibbs Algorithms

The following is the framework for the extraction of risk features by using Gibbs sampling algorithms (see Yuan et al. [23] for more in details).

Step 1: Assuming that the characteristic indicators depicting financial fraud follow the Bernoulli distribution, the characteristic space formed by the characteristic factors is initialized. Based on random sampling, the characteristics are classified according to whether the coefficient is 0: those who are not 0 are recorded as 1:

$$A_0 = \left( {0,1,1, \ldots ,0} \right) \in \left\{ {0,1} \right\}^m .$$

(1)

where, $m$ represents the number of features in the initialized feature space, and represents ${A}_{0}$ a subset in the initialized feature space.

Step 2: Via BIC (Bayesian Information Criterions) construct a standard that supports random sample counting, and construct a distribution function for features, to:

$$P_{BIC} {(}i_n = 1{|} I_{ - n} ) = \frac{{exp\left( { - BIC{(}i_n = 1{|}I_{ - n} } \right))}}{{exp\left( { - BIC{(}i_n = 0{|}I_{ - n} } \right)) + exp\left( { - BIC{(}i_n = 1{|}I_{ - n} } \right))}}$$

(2)

where ${P}_{BIC}(i)$ the indicator transfer probability function, representing the nth feature, ${I}_{-n}$ is in addition to ${i}_{n}$ the other feature sets, the number of features in the initialized feature space, ${I}_{0}$ represents a subset in the initialized feature space, using the formula to ensure that the feature subset shifts to a higher degree of fit, As a result, the salience of the characteristic indicators that ultimately characterize financial fraud behavior can be revealed.

Step 3: Determine the number of sample counts for the sample. The number of sampling calculations is determined to reduce the computational complexity and ensure that the results of the final indicator significance are achieved within the tolerable margin of error. At this point, we need to set the error range due to the sample size. In order to ensure the significance of the extracted feature calculation results, the sample size error is usually recommended to be no more than 5%, and the corresponding formula is as follows:

$$Std\left( p \right) = \sqrt {\frac{{p\left( {1 - p} \right)}}{M}} < \sqrt{\frac{1}{4M}} .$$

(3)

When the analog error is controlled within 2 times of $Std\left(p\right)$ by not bigger than 5% (for 2 standard deviations (i.e., 2 $Std\left(p\right)$), the number of sampling counts can be obtained by the above formula $M$ is 400 (times), In this way, the number of sample counts can have the effect of reducing the computational complexity and ensuring the distinctiveness of the features.