A Research on Interbank Loan Interest Rate Fluctuation Characteristics and the VaR Risk of China’s Commercial Banks

doi:10.4236/me.2012.36097

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Modern Economy, 2012, 3, 759-765

http://dx.doi.org/10.4236/me.2012.36097 Published Online October 2012 (http://www.SciRP.org/journal/me)

A Research on Interbank Loan Interest Rate

Fluctuation Characteristics and the VaR Risk

of China’s Commercial Banks

Baoqian Wang, Cheng Wang, Xikun Zhang

Business School, Hohai University, Nanjing, China

Email: [email protected], hhucwa[email protected], [email protected]

Received June 20, 2012; revised July 22, 2012; accepted August 1, 2012

ABSTRACT

According to the historical time series data of commercial interbank, this paper examines the interest rate fluctuation

distribution characteristics, indicating that EGARCH Model can b etter fit the rate volatility of th e interbank market in-

terest. This paper calculates the value at risk (VaR) of five major commercial banks using EGARCH Model with such a

conclusion that the difference that major commercial banks face is various. The interest risk of state-owned commercial

banks and other financial institutions is more serious than the city commercial banks and foreign banks. The interest

risk of rural credit cooperatives is the least serious.

Keywords: GARCH Model; Interest Rate; VaR

1. Introduction

Since 1996, the speed of China’s market interest rate

process put fast gradually, letting go the interest rate of

the inter-bank market interest treasury bonds and policy

financial bonds. Domestic and foreign currency loans

and large foreign currency deposit rates are also involved.

Long-term RMB large deposit agreement is available and

at the same time china gradually expands the floating

range of RMB deposit and lending rates. With the market

operation of china’s interest rate, the issue of interest rate

risk measurement and management has become unavoi-

dable. By using statistical knowledge and VaR model,

this paper analyzes China’s interest rate market risk dis-

tribution patterns and quantifies the interest rate risk of

commercial banks in China.

2. Literature Review

Since 1978, china’s commercial banks have experienced

a series of management system reforms. But before 1993,

commercial bank interest rate has always been under

control, never out of the planned economic system. In

this period, domestic focus is on the research of the

regulation of commercial bank interest rate. Huang Jian-

feng (2001) systematically expounds on the normative

operations of the commercial bank deposit and loan in-

terest rate [1]. Ge Qi (2003) systematically introduces

foreign measurements and management methods on in-

terest rates. In practice, he actively explores the advanced

technologies and methods to be used in commercial

banks’ interest rate risk management approach [2]. Dai

Guoqiang (2005) uses the VaR method, the stochastic

analysis method and the option pricing method to put

forward the choice of benchmark interest rate of china’s

commercial banks, together with the interest rate trend

forecast in order to effectively control the interest rate

risk, and enhance their own competitiveness [3].

China’s interbank market interest rate research begins

relatively late. In the early days; it is primarily based on

qualitative analysis, but in recent years it terms into

quantitative analysis. Tang Qiming and Gao Xiang

(2002): interbank market interest rate of different terms

is in line with the expectations of interest rate term

structure theory [4]. Xu Hanfei (2004): by using ECM

model, Xu studies the transmission mechanism of central

bank loan interest rate to interbank loan interest rate

transmission, and finds that the transmission mechanism

is asymmetric and dynamic, and the adjustment that cen-

tral bank transmits to refinancing interest rate is only

about 60% direct conducted to the inter-bank market

interest rates [5]. Lin Hai, Zheng Zhenlong (2003): by

integrating Vasicek model and CIR model into GARCH

model, Lin and Zhang discusses china’s interest rates,

but they don’t give a further research on rate volatility

[6]. Dong Le (2006): Dong validates the dual asymmetry

of china’s short-term interest rate in terms of mean ve-

locity and the conditio nal variance. He gives the features

that the correlation coefficient of the inter-bank market

B. Q. WANG ET AL.

760

interest buyback rates is close to 1a suppose, namely,

foreign classic model doesn’t create very effective results

about the prediction of the term structure of interest rate,

which will even worse than the random walk. But he has

no further validation [7]. Zhang Na, Huang Xinfei, Liu

Deng (2006): in the process of constructing GARCH

model to analysis China’s various term interbank market

interest rate volatility, they discover GARCH model can

better explain the interbank market interest rate fluctua-

tion. Such fluctuation and the lag period fluctuation are

smooth and show a smoothly decreasing trend, but the

volatility is not serious [8]. Zheng Yaotian, Du Ziping

(2007): Zheng and Du fit the inter-bank overnight rates

by using EGARCH model, finding out the EGARCH (1,

3) model the best fitting one, which fully embodies the

overnight lending market information asymmetry. They

also do the short term prediction by EGARCH (1, 3) and

obtain ideal forecasting effect, thereby determine a suit-

able model for China’s interbank market interest rate

forecasting [9]. Li Jie, Gao Ning, Chai Jun (2007): Li and

Gao establish AR (P)-EGARCH model in China’s in-

terbank market. From liquidity, transaction volume and

structural changes terms, they explore the various influ-

ence factors for daily overnight interest rates of varieties,

proving that the positive leverage effect exists for the

sequence fluctuation in overnight lending market [10].

Liu Xiangyun (2007): doing a theoretical and practical

analysis for china’s commercial bank interest rate risk in

terms of interest rate term structure on the basis of

drift—jumping methods. A mean reversion phenomenon

is discovered in the short term market interest rate, such

as 7-day period Chinese bond repurchase rate and 7 days

interbank rates [11 ].

The VaR method was first adopted in J. P. Morgan

risk management practice of the last 90th century. Phil-

ippe Jore (1995) publishes the master piece systemati-

cally introducing VaR and its application. Philippe Jore

dose the all round discussion about VaR’s mathematical

statistics basis, calculation process and ways of applica-

tion [12].

Chew & Lilian (1996): summing up the calculation

parameter method for VaR, historical simulation method

and the Moncaro simulation method [13]. Futher more,

Duffle & Pan (1 997) and Jorion (200 0) respectively does

profound summary in Risk Value and Value at Risk:

Risk Control Reference. Among them, the application of

various methods to compare the effects of the research is

particularly enlightening [14,15].

To sum up, foreign researches mainly focus on the

model application, while the domestic researches mainly

concentrate on the model selection , rarely on risk quanti-

tative analysis and forecast. China’s interbank offered

rate (CHIBOR) is China’s first market-oriented interest

rates, so it could sensitively react to the supply and de-

mand situation in monetary market. As a result, the in-

terbank interest rate can be regarded as the benchmark

interest rate for China’s monetary market. With this hy-

pothesis, the paper tests the applicability of GARCH

model and makes a short-term prediction for the 7 days’

interest rate. Given a certain degree of confidence of

china’s commercial banks, based on the fitted model an d

various periods of different variance, by using bank in-

terbank borrowing trading positions, the commercial

bank risk values can be measured and compared analysis

will be available.

3. The Selection and Construction of Interest

Rates Model

3.1.The Normality Test for the Sample of

Inter-Bank Interest Rate

This paper uses the interbank market interest rate as the

market interest rate (Shanghai Interbank Offered Rate,

referred to as Shibor )to inspect china’s commercial bank

lending position risk. The purpose is to reflect the inter-

est risk of China’s commercial banks under the back-

ground of market orientated interest. At present, been

announced Shibor varieties includes overnight, 1-week,

2-week, 1-month, 3-month, 6-month, 9-month and 1-year.

This paper analyzes the data from 2007 to 2011, accord-

ing to the 1-week Sh ibor.

Sample of this paper is from 01/01/2007 to 31/12/2011.

There is totally 1249 statistics of 1 -week Shib or. And the

fitting prediction sample is from the first quarter of 2012.

Data processed by Eviews software.

From 1-week Shibor wave pattern (Figure 1), it could

be seen that the market interest rate violates strongly, so

the sequence is not stable. In order to get a stable return

time series data, some techniques need to be done. Using

the equation 1t

log log

yrr





 for the logarithm of a

first-order differential treatment, and make its become

more stable income sequence (Figure 2).

0.0

0.5

1.0

1.5

2.0

2.5

200 400 600 8001000 1200

Figure 1. 1-week shibor rate fluctuation.

B. Q. WANG ET AL. 761

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

200 400 600 800 1000 1200

Figure 2. The rate difference fluct uation f i gure. Data sources

: Time series of daily interbank interest rate market.

3.2. Inspection of ARCH Effects

of information in

ina’s commercial

3.2.1. Autocorrel at i on Test Y7 on a delay of 18 orders,

of Figures 1 and 2: http//:www.bba.org.uk/;

http//:www.chinamoney.com.cn/.

Do the normality test using the differential logarithmic

atistics and the results (Table 1) show that, in the 1-week

inter-bank lending market, the average rate of return is

0.001097; the skewness (S) is 0.419 660; t he k urt osi s (K) i s

42.33005; the statistic value of J-B test of normality is

81398.90 with a probability of 0. Information got from the

above statistical value is that the volatility of the return

rate is strong and the time series is not in line with the

normal distribution for the presentation of “fat-tail phe-

nomenon”. The intermediate portion contains a large

amount of statistical information. Therefore, we need to

use the GARCH model distribution instead of normal dis-

tribution so as to im prove the model fitting effect s.

Because of the different availability

different moments, financial time series usually has a

peak, thick tail and cluster characteristic. In order to deal

with these characteristic, Engle proposed “Conditional

Heteroscedasticity Regression Model” (Auto Regressive

Conditional Heteroscedasticity, ARCH Model) to deal

with such problems. The model uses a regression form

and all the available in formation to describe the variance

of the variance. In 1986, Bollerslev proposed “GARCH

Model” (Generalized Auto Regressive Conditional Het-

eroscedasticity Model), which was also called the gener-

alized autoregressive conditional heteroscedasticity mo-

del. It is the expansion from of the most basic conditional

variance function ARCH model, and it has a strong ad-

vantage in the explanation and establishment of variance

of time series. In 1990, Zakoian proposed “TARCH

Model” (Threshold ARCH), namely the asymmetric con-

ditional heteroscedasticity regression model. It explains

the phenomenon in the stock market that while the

crash and the roar margin are the same, the crash process

is always accompanied by the serious fluctuation. In

1991, Nelson propo sed “EGARCH Model”, it ef fectively

depict the conditional variance of positive, negative in-

terference of the asymmetric response.

The above analysis shows that ch

nk lending rate distribution does not conform to the

normal distribution hypothesis, therefore, through a vari-

ety of conditions heteroscedastic model comparison, we

need select the optimal GARCH model to fit china’s

commercial bank interb ank market interest rates.

Do the autoco rr elatio n test on

and the test results are shown in Table 2. On the 0.05

significance level, th e probability P valu e was 0, which is

less than 0.05. Inspection instructions show that until

higher-order sequence, the yields still remain a strong

correlation relationship. So now the return series auto-

regressive model is being fitted. Given the yield of the

sequence





after autocorrelation and partial auto-

correlation the following model is selected to fit the

sequence test,





. Use maximum likelihood estimation me-

thod to est the parameters.

112 2

yc yy

imate

33tttt



 



 



 (1)

3.2.2. The Stationary Test 3) to check the smooth of se-Use the unit root test (Table

quence. As the stationary of the sequence directly affect the

model fitting result, and the non-stationary data sequence

will produce a false return we have to test the stationary of

the sequence. Here we use the method of Augmented

Dickey-Fuller (ADF) to make unit root test for yield se-

quence





. The ADF value is –17.20466, which is less

than 1% 5% significance level. So the unit root

and

Table 1. Normal inspection result.

Mean Kurtosis st P value

Standard Partial J-B

deviation degree atistics

Y7 0 0.0020.050760.41955042.32008 81398.900.000000

D sof

Table 2. The autocorrelation test of yields.

ata ources: The result f the empirical study by using the software o

Eviews. Statictics database: Figures 1 and 2 http//:www.bba.org.uk/; http//:

www.chinamoney.com.cn/.

7 days lending of inter-bank

Delay in order e Q-statistic P valu

6 56.492 0.000

12 71.981 0.000

18 77.592 0.000

Data sour result of the estudy by using are of ces: Thempirical the softw

Eviews. Statictics database: Figures 1 and 2 http//:www.bba.org.uk/; http//:

www.chinamoney.com.cn/.

B. Q. WANG ET AL.

762

hypothesis are rejected by the test values, indicating that

the sequence of yield



is a stationary sequence.

3.2.3. ARC H T e st

In order to see whether the Conditional Heteroscedastic

exists in the return series





, the paper uses Lagrange

multiplier method to do thst. Make a 3 lag ARCH

effect test for the residuals of the regression equation,

and from the test results (Table 4), we could see that the

F-statistic and the LM-statistic probability value is rela-

tively 0.000227 and 0.000241, less than 0.05. The origi-

nal assumptions rejected hence ARCH effect exists in the

model.

3.3. Int

e te

erest Rate Model Selection

nd TARCH mo-

Compare ARCH, GARCH, EGARCH a

del in terms of the residuals, depending on the Akaike

Information Criterion (AIC), Schwarz (SC) guidelines

and the LL principle of maximum likelihood function

value, and hence select the most suitable model.

The modeling process: select the inter-bank lending of

1249 continuous-time series data and compare the re-

siduals of ARCH (1), GARCH (1, 1), TGARCH (1, 1)

and EGERCH (1, 1) (Appendix 1). The appendix shows

the AIC and SC of EGARCH (2, 1) is the smallest; the

LL value of TGARCH (1, 1) is smaller than EGARCH (2,

2); the fitting coefficients of EGARCH (2, 1) are higher

than TGARCH (1, 1). Consider the overall results;

EGARCH (2, 1) model is selected to fit the inter-bank

interbank of fer ed rat e seque n ce

According to the results of fitting model, the 7-day in-

ter-bank lending yield model is:

0.11742



  (2)

Table 3. The unit root test results.

alue ADF statistics Critical v

1% –3.4384

5% –2.8643

Inter-bank 7

day lending –17.20466

10%–2.5682

Data sources: The result of the empirical studyng e of

Eviews. Statictics database: Figures 1 and 2 http//:www.bba.org.uk/; http//:

4. ARCH effect test.

by usithe softwar

www.chinamoney.com.cn/.

Table

ARCH Test

F-stat 20709 P 0.000227

istics 4.8

Inter-bank 7

day lending L M-statistics23.76079 P 0.000241

Da reicasthf

Eviews. Statictics database: Figures 1 and 2 http//: www.bba.org.uk/; http//:

ta sources: The sult of the empirl study by uing e software o

www.chinamoney.com.cn/.

log0.642986 0.947445log



0.647886 0.125999

0.110117

















(3)

Do the ARCH effect test for the above model, and the

accom

lly

panied probability of the F-statistics and LM are

bigger than 0.05. Test results indicate that the model can

be accepted for there is not any Conditional Heterosce-

dastic.

In order to further empirically test the validity of

EGARCH (2, 1) model, we selected 72 data of inter-bank

lending ra te from January to March of 2012 to make p re-

diction. Compare the pred ictive value with the true value

(Figure 3). From the prediction results, we could see that

the predicted rates fluctuate around the real rates, and the

margin between them is very small. The trend of the fit-

ted curve is in line with the real rates curve, and the pre-

diction error is very small which also shows the applica-

bility of the model. Consequently, EGARCH (2, 1) pre-

diction is applicable in the lending and borrowing inter-

est rate risk management of china’s commercial banks.

4. VaR Estimation of China’s Commercial

Banks

The size of commercial bank interest rate risk is usua

measured by the value at risk VaR. The so-called value at

risk is the maximum possible loss given a certain confi-

dence interval and time interval. The equation is (given

confidence level









VaR WEr r



 (4)

In the equation, means the init

cial asset or 0

ial value of a finan-

portfolio;





Er means the expected rate of

Figure 3. Predictive value compared with the actual val-

ues.

B. Q. WANG ET AL. 763

return. Use Equation (1) to calculate the relative losses of

VaR equivalent to the expected rate of return.

If the yield submits to normal distribution

“



~0,rN t



”, we could calculate sub-sites



, and

then we could calculate “rZ







”. He the

following equation:



VaR WE

nce

r rWZ





 (5)

However, because of the peak, thick tail

tion c

onditions of Different Vari-

nce.

and aggrega-

haracteristics of financial time series, normal dis-

tribution will underestimate the interest rate risk.

Thus according to the previous analysis, the EGARCH

(2, 1) conditional variance model is used to measure the

VaR of interest rate market in order to solve the underes-

timated interest rate risk.

According to EGARCH (2, 1), this paper calculates

the different variance in lending and borrowing market

conditions (Table 5). Take conditional standard devia-

tion into Equation (2), and dynamic VaR estimation will

be got according to the net position of the main five

commercial banks given the condition of 99% confidence

level. And according to the daily VaR of the first quarter

of five commercial banks, the dynamic VaR map (Figure

4) can be got. From the figure, the interest risk of China’s

commercial banks is intense.

Table 5. 2012 First 1uarter C

r1 0.019198 r21 0.000714 r41 0.001287

r2 0.012258 r22 0.000530 r42 0.001630

r3 0.008530 r23 0.000906 r43 0.001971

r4 0.006222 r24 0.000542 r44 0.002027

r5 0.005144 r25 0.000478 r45 0.002202

r6 0.003876 r26 0.000516 r46 0.002645

r7 0.002743 r27 0.000403 r47 0.003544

r8 0.001922 r28 0.000446 r48 0.002305

r9 0.001886 r29 0.000560 r49 0.001849

r10 0.002054 r30 0.000621 r50 0.001699

r11 0.001352 r31 0.000515 r51 0.001951

r12 0.001609 r32 0.000411 r52 0.001609

r13 0.001127 r33 0.000330 r53 0.001699

r14 0.001250 r34 0.000353 r54 0.001644

r15 0.000828 r35 0.000384 r55 0.029758

r16 0.000821 r36 0.000424 r56 0.018808

r17 0.000628 r37 0.000574 r57 0.013634

r18 0.000506 r38 0.000524 r58 0.009183

r19 0.000396 r39 0.001812 r59 0.006265

r20 0.000900 r40 0.001438 r60 0.004414

So Ch(w hin)rdom-

mbaositi lcuuday

urce:

ercial ina currency

nk lending pww.c

on caamoney.com.cn

lation of first q, a cco

arter ing to the c

510 15 20 25 30 35 40 45 50 55 60

VAR1 VAR4

VAR2

VAR3 VAR5

Figure 4. Dynamic VaR value of the interbank mark

he above VaR of the first quarter of dif-

onclusions

(2, 1) model can

lending position.

According to t

ferent commercial banks, by using Eviews software this

paper could draw the VaR statistical analysis of China’s

interbank borrowing position on the 7-day dynamic for

china’s commercial banks (Appendix 2).

According to the statistical results of Appendix1, the

standard deviation of the national commercial banks and

other financial institutions is 2.168015 and 2.098728,

indicating the dramatic violations in its VaR, and the

correspondingly larger risks. The VaR of city comercial

banks and foreign banks is relatively small, with the

standard deviation of 0.380789 and 0.353807 respec-

tively and the performance is relatively stable. The VaR

of the rural credit cooperatives are the most minimum

with a standard deviation of 0.023426, which is the most

stable one in terms of the performance.

Through the analyses, it could be seen that the scale of

assets and liabilities of China’s rural credit cooperatives

and foreign banks is relatively small, with a small

amount of money lending and more borrowing money

from the capital side, which means a small corresponding

dynamic VaR. For national commercial banks, city com-

mercial banks and other financial institutions, their scale

of assets and liabilities is larger and more dynamic, so it

has the higher risk in VaR (Appendix 3).

The results of the analysis in Appendix 1 are consis-

tent with Appe ndix 2.

5. Summary and C

This article has proved that EGARCH

better describe the characteristics of interest rates distri-

bution in china’s commercial interbank loan market

through theoretical and empirical research. Therefore, it

B. Q. WANG ET AL.

764

success

rket conditions heteroscedastic. Take the condi-

tio

e of statistical description, it can be

could be a useful tool for commercial banks to undergo

the risk management by using VaR estimation.

Establish the model of ARCH (1), GARCH (1, 1),

TGARCH (1, 1) and EGARCH (2, 1) and make- [2

ve comparison. The AIC and SC of EGARCH (2, 1) is

the smallest, the LL value of TGARCH (1, 1) is smaller

than EGARCH (2, 1) but the fitting coefficient of

EGARCH (2, 1) is larger than TGARCH (1, 1). In com-

prehension, EGARCH (2, 1) can better describe the dis-

tribution of the series of the interest rate of inter lending

and borrowing market in china’s commercial banks, and

as a result, EGARCH (2, 1) could be used as the fitting

model.

Use EGARCH (2, 1) model to calculate the interest

rate ma

ns heteroscedastic into VaR model so that the dynamic

VaR estimation of night and 7-day lending position could

be figured out according to the daily net trading positions,

on the confidence level of 99%. From the final results, it

could be seen that the fluctuation of china’s interest rate

in the interbank lending and borrowing market is serious

and violate, indicating china’s interest rate in the inter-

bank lending and borrowing market has been fully mar

ket-oriented.

From the Bank lending and borrowing yields dynamic

the VaR valuseen [9] Y.-T. Cheng and Z. P. Du, “EGARCH Model in the In-

terbank Offered Rate Forecast,” Hubei Institute for Na-

tionalities, Vol. 1, No. 6, 2007, pp. 234-237.

at the risk value and the standard deviation of national

commercial Banks and other financial institutions is big-

ger, and dramatically changed. City commercial Banks

and foreign banks’ interest rate risk value is smaller, the

performance was stable. The risk of rural credit coopera-

tives is the smallest and the most stable. According to the

value, the risk of china’s state-owned commercial Banks

and other financial institutions is the largest, followed by

city commercial banks and foreign banks and finally are

the rural credit cooperatives the scale of assets and li-

abilities of China’s rural credit cooperatives and foreign

banks is relatively small, with a small amount of money

lending and more borrowing money from the capital side,

which means a small corresponding dynamic VaR. For

national commercial banks, city commercial banks and

other financial institutions, their scale of assets and li-

abilities is larger and more dynamic, so it has the higher

risk in VaR.

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B. Q. WANG ET AL. 765

Appendix

Appendix1. The inter-bank lending mode l c ompar ison.

Project CH (1, 1) EGARCH (2, 1) Coefficient ARCH (2) GARCH (1, 1) TGAR

AR (2) 2



–0.288315 –0.095982 –0.117429

AR (3) 3



–0.143736 –0.088460 –0.154973

C 0



0.000612 6.24E-05 2.36E-05 –0.643986

ARC) H (11



0.000612 0.415604 0.171395

ARCH (2) 2



0.596140

GARCH (1) 1



0.723542 0.771214

(RESID<0)

)*ARCH (1



0.514711

|RES|/SQR[GARCH] (1) 1



0.647886

RES/SQR[GARCH] (1) 1



–0.

|RES|/S

065162

QR[GARCH] (2) 2



–0.125999

RES/SQR[GARCH] (2) 2



–0.110117

EGARCH (1)



0.947445

AIC –3.634324 –3.861316 –3.914027 –3.

R-squared

940930

SC –3.613932 –3.845002 –3.889557 –3.912399

LL 2294.624 2436.629 2471.837 2491.757

0.018445 0.006557 0.024882 0.027082

ppendix 2. Commrcial intertions dyR value (Uillion).

dard Deviation

Aebank posinamic Vanit: 100 M

Mean Minimum Maximum Stan

National commercial banks 0.804891 0.005253 13.65921 2.168015

City commercial banks 0.255048 0.000601 1.917143 0.380789

Foreign banks 0.198768 0.002183 1.910912 0.353807

Rural credit cooperatives

VAR value

0.019253 0.000434 0.166527 0.023426

Other financial institutions 0.524792 0.001202 15.86409 2.098728

sitions of theer-bag (Unllion).

in Max

Appendix 3. Net po 7-day intnk lendinit: 100 Mi

Net Position Mean M

National commercial banks –243.197.–4691.1640 –78.18607 2900 0000

City commercial banks 2943.8800 49.06467 –9.800000 105.9300

Foreign banks 1529.3140 25.48857 –42.72000 132.7900

Rural credit cooperatives

Lending position

–266. –228.

215.7400 3.595667 –8.10000 25.64000

Other financial institutions 7100 –4.445167 8000 201.4400