The Study on Commercial Bank Loan Pricing Model based on Inverted DEA.doc

1、1The Study on Commercial Bank Loan Pricing Model based on Inverted DEAAbstract. This paper fixes lending rate by solving the output parameter of DEA inversely with dichotomy and ensures the lending rate optimal efficiency. The corresponding output parameter of DEA， lending rate， is determined when t

2、he DEA efficiency index z=1 through solving DEA model with dichotomy and the optimal efficiency of the lending rate is ensured. This model fixes the lending rate under the DEA optimal efficiency and provides a new way of loan pricing. The output parameter of DEA is fixed based on the dichotomy when

3、the DEA efficiency index z=1. This study provides a new way for the inverse solution to DEA. So it changes the condition that the efficiency is estimated only with the known data of input and output and develops the use of DEA. Key words： Lending Rate， Loan Pricing； Data Envelopment Analysis； Dichot

4、omy； Optimal Efficiency Introduction Time Domain Reflectometry， a common method used for PD location system in power cable The key of this method lies in 2determining the time difference. Furthermore，to find the time difference between them and to calculate the PD location. Currently ，the identifica

5、tion of the reflected wave and original wave mainly used the correlation analysis and wavelet analysis1，2. In this paper， by applying the short-time energy-DTW method for identifying the partial discharge pulses ，matching original and reflected wave. Firstly， to improve the signal to noise ratio， ad

6、d window and calculate the accumulated energy of each finite window Then， use DTW method to identify and match the original wave and reflected wave. Establishment of input and output index system The input indexes 1） Deposit interest expenditure rate： It refers to the deposit interest which should b

7、e paid for loan. 2） Expenditure rate： It refers to all kinds of expenditures in the business and management of banks except the deposit interest expenditure. 3） Default risk compensation rate： It refers to the proportion of bad loans in the sum of the capital and interest of receivable loan under th

8、e different trades and different decision appraisal ranks. 4） Maturity risk premium： It refers to some changes in 3the probability of loan default， liquidity risk and inflation risk because of the different loan periods. The periods of the interest rates of domestic bonds can be used to measure matu

9、rity risk premium. 5） Loan target rate of return： It refers to the planned minimum profit of every loan gained by the banks. The input indexes The benefit of the intermediary business is the sum of the derivative benefit of deposit， the deposit expense of different maturities and settlement deposit

10、earnings etc. In order to make the discount of every loan reasonable， the rate of return on the intermediary business of issued loans is calculated by the whole profit of the intermediary business of the previous year to the estimated credit total for clients of that year. The rate of return on the

11、intermediary business of new loans is calculated by the whole profit of the intermediary business of the previous year to the estimated credit total for clients of this year. Most banks always give the discount to clients according to the benefit of the intermediary business. This improves the compe

12、titiveness of loan price and gives the preference to the 4clients who have the high benefit of the intermediary business. The input indexes The lending rates of issued loans are known quantities and those of the new loans are dependent quantities. This is the double attribute of lending rate. But th

13、e purpose of this paper is to fix the lending rate of new loan. In DEA model， the lending rates of new loans are the output indexes of known data. In this model， the lending rates of new loans are dependent variables. The input/output indexes of loan pricing， as shown in table below. Loan p ricing m

14、 odel based on dea The Definition of The Input/Output Indexes Basic Data Assume that some bank has 15 loans issued， where the deposit interest expenditure rates x1j， the expenditure rates x2j， the default risk compensation rate x3j， the maturity risk premium x4j， the loan target rates of return x5j，

15、 the rates of return on the intermediary business y1j and the lending rates y2j （ j=1，15） are as shown in table . Assume that the bank increase 7 loans， where the deposit 5interest expenditure rates of the new loans x10， the expenditure rates x20， the default risk compensation rate x30， the maturity

16、 risk premiums x40， the rates of target return on loan x50 and the rates of return on the intermediary business y10 are as shown in table . Results With the data of table and table ， the loan rates calculated by the DEA model （model 1） exist in the first column of table . With the same date， the loa

17、n rates calculated by the cost-plus pricing model （model 2） exist in the second column. And the loan rates calculated by Customer Profitability Analysis Model （model 3） exist in the third column. Comparing the first column with the second column in table ， we can draw the conclusion that the lending

18、 rates calculated by model 2 are higher than those by model 1 because model 2 brings about the loan pricing on the high side without regard to the return of the intermediary business， so the loan pricing loan lacks of the competitiveness and is difficult for the clients to accept. Comparing the firs

19、t column with the third one in table ， we can draw the conclusion that the loan rates calculated by model 1 are higher than those by model 3， which shows that the 6banks offer too discount to the clients who have the intermediary business and do not get the maximum profit. So the DEA model guarantee

20、s the optimal efficiency of loan pricing， that is， the model gets the lending rate of the maximum return for banks within the scope of the acceptance of clients. References 1 A. H. Chen， S. C. Mazumdar， and Y. Yan， “Monitoring and bank loan pricing， ” Pacific-Basin Finance Journal， vol. 8， March 200

21、0， pp. 1-24. 2 V. Stango， “Pricing with Consumer Switching Costs： Evidence from the Credit Card Market， ” The Journal of Industrial Economics， vol. 12， 2002， pp. 475-491. 3 D. O. Cook， C. D. Schellhorn， and L. J. Spellman， “Lender certification premiums， ” Journal of Banking & Finance， vol. 27， Augu

22、st 2003， pp. 1561-1579. 4 I. E. Brick， and D. Palia， “Evidence of jointness in the terms of relationship lending， ” Journal of Financial Intermediation， vol. 16， July 2007， pp. 452-476. 5 G. Elliehausen， M. E. Staten， and J. Steinbuks， “The effect of prepayment penalties on the pricing of subprime mortgages， ” Journal of Economics and Business， vol. 60， 7January-February 2008， pp. 33-46.