JOURNAL OF COMPUTER SCIENCE AND ENGINEERING, VOLUME 11, ISSUE 2, FEBRUARY 2012

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© 2012 JCSE

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The Application of Catastrophe Theory in the Credit Risk Assessment Of Famers’

Microfinance Gang Lv1, Longyi Zhu1, Jing Wang1,2, Zongfang Zhou1

Abstract—The famers’ microfinance is of highly risk because it doesn’t need any collateral and guarantees. So it’s important to

assess and control the credit risk of the microfinance. Based on the establishment of the evaluation index, this paper used

catastrophe theory to assess the credit risk of the farmers. In the end, we took ten farmer families as samples to carry the

empirical study. The result shows that it’s an objective and reasonable way to assess the credit risk of famer.

Key words—catastrophe theory; farmers’ microfinance; credit risk

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1 INTRODUCTION

he famers’ microfinance was originated from Bangla-desh in 1970s and aimed at helping poor women. Due to its unique advantages---easy to get, need no mort-

gage, etc, the famers’ microfinance spread rapidly and soon became general accepted. In 2000, the People’s Bank of China introduced the famers’ microfinance into China. However, because the awareness of credit of farmers in China was so weak and seldom of farmers has the ability to handle the risk, the farmers’ microfinance in China was confronted with huge credit risk. This had seriously af-fected the loan’s quality of the rural financial institution which loaned the microfinance and the further develop-ment of the farmers’ microfinance. Therefore, how to as-sess the credit risk of the farmers’ microfinance has a fo-cus of attention.

The credit risk assessment of farmers’ microfinance is to evaluate the credit level of farmers by analyzing the data of relative indexes of farmers. The mature credit risk assessment methods at present mainly involve these four methods: (i) Regression model method, e.g. Logistic mod-el, it relies on a large number of actual data, but it’s diffi-cult to express the complex relationship between subject and object accurately by only using a simple regression analysis. (ii) System analysis method, such as AHP and fuzzy mathematics method, they have a clear analysis process and are strongly supported by the theory. How-ever, these two methods both involve the expert evalua-tion method which is highly subjective, and that make the assess result less objective. (iii) BP neural network me-thod. Because of the BP method’s defects that it is easy to

local convergence and is with slow convergence. It’s hard to modeling during the actual operation. (iv) Other credit risk assessment methods, such as gray theory and attribute theory method, etc. The calculation of attribute theory method is complicated and not easy to accomplish. The gray theory is subjective to some degree because the weight of some indexes, the threshold and clustering coefficient depends on experience.

When using these methods above, the weight of each index is generally determined artificially. But for the over-all credit risk of farmers’ microfinance, when some particu-lar indicators is extremely important, it might be neutra-lized by other index no matter what kind of assess methods are using. And this may lead to the lack of objectivity. Rela-tive to the above methods, the assessment method based on catastrophe theory don’t need to consider the weight of each index, because the importance of each index is deter-mined by the internal mechanism of the catastrophe sys-tem. Therefore, using catastrophe theory to assess the cre-dit risk of farmers’ microfinance can overcome the defects that the weight of index doesn’t vary with the change of index value and the subjectivity bringing by the artificial index weight.

This paper used catastrophe theory to assess the credit risk of the farmers comprehensively, and then took ten farmer families as samples to carry the empirical study. Main contents are as follows: Section II will give a brief introduction about the catastrophe theory and how to use catastrophe theory to evaluate the credit risk of farmers; Section III will select ten farmer families as an evaluation object to carry the empirical study by establishing the index system and normalizing the original data; Section IV will be the summary of the paper.

2 CATASTROPHE THEORY AND ITS APPLICATION

The catastrophe theory is a mathematic theory created by the French mathematician Rene Thom in 1972. The theory mainly studies how do the continuous gradient cause

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Gang Lv, Longyi Zhu and Zongfang Zhou is with the School of manage-ment and economics, University of Electronic Science and Technology of China,, Chengdu 610054, China

Jing Wang is with Northwest A&F University, Yangling, Shaanxi 712100, China

This research has been supported by National Natural Science Foundation of China (No. 70971015, 70973097).

Corresponding author: Zhou Zongfang, professor.

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mutations or leap in nature and human society, and seeks to use a unified mathematical model to describe and pre-dict these mutations or leap[1]. At present, catastrophe theory generally refers to the seven primary catastrophe models generalized by Rene Thom[2]. Catastrophe evaluation method is a comprehensive as-sessment method formed on the basis of catastrophe theory. The main steps are as follows: (1) Establish the index system and clarify the system type. As the general mutation system controls no more than 4 variables, so the decomposition of the corresponding in-dex can’t be more than four. Assuming x is state variable, a, b, c, d is control variable. There are three common types of catastrophe system: cusp catastrophe system, swallowtail catastrophe system and butterfly catastrophe system[3].

Cusp catastrophe system: when there are two control variables and one state variable, the catastrophe system is called cusp catastrophe system. The potential function of

this system is 4 2f x x ax bx , the normalization for-

mula is 3,a bx a x b .

Swallowtail catastrophe system: when there are three control variables and one state variable, the system is called swallowtail catastrophe system. The potential func-

tion is 5 3 2f x x ax bx cx , and the normalization

formula is 3 4, ,a b cx a x b x c .

Butterfly catastrophe system: when there are four con-trol variables and one state variable, the system is called butterfly catastrophe system. The potential function

is 6 4 3 2 +f x x ax bx cx dx , and the normalization

formula is 3 54, , ,a b c dx a x b x c x d .

(2) Standardization of original data. Different indexes generally have different dimensions and types like posi-tive and reverse index. Therefore, the data need to be standardized to eliminating the impact brought by the different dimensions and types of the indexes before the assessment started. (3) Use the normalization formula to assess the credit risk level. After the standardization of original data and the clarification of the catastrophe system, put the data into the corresponding normalization formula to get the in-termediate value of each index. If the index is comple-mentary, then take the average value; if it’s not, take the minimum value. According to this method, do the recur-sive operation from the bottom of the index system to the top and get the final catastrophe series. And thus make the comprehensive assessment of the object. The greater the mutation series is, the better situation the object is in[4],[5].

3 EMPIRICAL ANALYSIS OF THE CREDIT RISK

ASSESSMENT OF FARMERS’ MICROFINANCE

(1) Sample selection In this paper, we took ten farmer families as samples to carry the empirical study and accessed their credit risk-related data of 2010.

(2) Establishment of the index system of the credit risk assessment of farms Combining with the characteristics of the credit risk of famers’ microfinance and the characteristics of farmer and referring the index of the credit risk assessment of indi-viduals, this paper choose index from these three aspects: farmers’ solvency, management ability and their personal situation[6-8]. Furthermore, according to the internal me-chanism of the catastrophe evaluation method, the impor-tance of each index decrease from left to right. Then after being filtered and sorted, the index system of credit risk assessment of farmers’ microfinance is as shown:

Picture 1: Index system of credit risk assessment of farmers

As we can see, the index system composed by the solven-cy, management ability and personal situation is a swal-lowtail catastrophe system. Among it, the solvency is consist of total assets, net income and credit status over the years; Income-generating capacity and operational stability consist the management ability which is a cusp catastrophe system; The personal situation is a butterfly catastrophe system, and is divided into the ratio of labor population to dependent population, the proportion of owned money in needed money for the production, law-abiding and moral condition and guarantees1. (3) Standardization of the original data Based on the original data of ten typical farmers who ap-ply for the farmers’ microfinance (as shown in table 1) and the credit risk assessment situation of the farmers in the rural credit union, the qualitative data can be quanti-fied and as shown in table 2:

Note: ①is total asset; ② is net income per year; ③ is credit

status over years; ④ is income-generating capacity; ⑤ is opera-

1 All the index in the system are seen as complementary

Table 1: Original Data

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tional stability; ⑥ is the ratio of labor population to dependent

population; ⑦ is the proportion of owned money in needed

money for the production; ⑧ is law-abiding and moral condi-

tion; ⑨ is guarantees. Table 2: Quantification of the qualitative data

Note: In the index of Operational stability, “salary, shop” is

very good; “truck driver, contractor, construction worker, taxi driver” is good; “consignment, cultivation, part-time work” is ordinary; “odd jobs” is poor. In the index of the proportion of owned money in needed money for the production, more than 50% is very good, 30%~50% is good, less than 30% is poor.

According to the characteristics of the catastrophe evaluation method, we need to convert the original data into numbers between 0-1. This paper adopts the com-mon linear non-dimensional method to convert the origi-nal data. For the indicators which the bigger the better,

the method is as follow: min

max min

a ar

a a, the a is the

original data, r is the standardized data, mina indicate the

minimum of the data under one index, maxa indicate the

maximum of the data under one index[9]. The standardized data is as shown in table 3 below:

Table 3：Standardized data

(4) Use the normalization formula to give the compre-

hensive assessment After getting the standardized data, we put the data in-

to the corresponding catastrophe system and calculate from the bottom to the top. The final assessment result of the farmers and the ranking of the households is as be-low:

Table 4：Final assessment result and rank of farmers

The ranking result of the households above is coin-

cided with the actual condition. This indicates that the result of the catastrophe evaluation method is reliable and can reflect the credit risk status of the farmers. Besides, this method doesn’t need to consider the weight of the index and has a simple calculation process.

4 CONCLUSION

As a huge agricultural country, China has a massive number of poor rural populations and its rural economy is not developing well. At the same time, the farmers are facing big difficulties in getting loans. This severely re-stricts the development of the rural economy. The ap-pearance of the farmers’ microfinance solves this problem preferably. However, the farmers’ microfinance is facing a large credit default risk, so the assessment of credit risk of farmers is particularly important.

As a new risk assessment method, catastrophe evalua-tion method doesn’t need to consider the weight of the index, and this avoids the subjectivity brought by the ar-tificial weight. What’s more, catastrophe evaluation me-thod combines the advantages of the fuzzy analysis me-thod and the AHP method. Its calculation process is sim-ple and the result is visualized. In summary, the catastro-phe evaluation method can be an effective method of the credit risk assessment of farmers.

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