| Asset pricing theory and model is one of the three pillars in the field of modern finance. Among which, loan pricing is one of the core decisions as to a commercial bank. How to make a reasonable loan pricing decision to the small enterprise is a urgent problem to be solved. If the interest rate price of loan is too high, customers maybe request loan for other commercial banks, which would cause the loss of quality customer resources. If the interest rate price of loan is too low, the loan income can not cover the operation cost of bank and bear the risk, which would cause a loss for commercial banks. With the liberalization of interest rate control, the competition of interbank market is becoming increasingly fierce, which request the commercial banks to improve the ability of loan pricing as quickly as possible. The key to determining loan pricing is measuring the risk premium of loan exposured accurately.Small enterprises have become the main driving force for the national economy growth, and it is the basic strength to relieve the employment pressure and maintain the social stability. However, due to the weak financial strength of small enterprise, financial information unperfect and other factors which results in the lack of reasonable pricing for small enterprises and obtaining a loan from the commercial bank diffcultly, the problem of financing difficulties and loan difficulties has become the bottleneck of the development of small enterprises. Through pricing to the small enterprises loans in a reasonable manner, the quality small enterprises can get the necessary financing support for development, which is good to relieve the current situation of the short of the development capital for small enterprises. Therefore, the issue of small enterprise loan pricing is a very important social problem.Risk premium in small enterprise loan pricing refers to three aspects:the first one is default risk premium; the second one is benchmark interest rate risk premium; the third one is term structure of interest rate risk premium.Default risk premium refers to the credit risk premium which is caused that small enterprisees can not return capital and interest on schedule. As long as default risk premium is measured inaccurately, the loss of default risk of small enterprises will not get a reasonable compensation.Benchmark interest rate risk premium refers to a risk premium that is caused by the benchmark interest rate change of the central bank, such as the Federal Reserve or the people's Bank of China. If the benchmark interest rate risk premium is ignored as the popular study, when the country's benchmark interest rate adjustment, the loan profit and loss of small enterprise is uncertain.Term structure of interest rate risk premium refers to this part risk premium which compensates the uncertainty arising from the yield to maturity changes over time. Term structure of interest rate risk premium contains liquidity risk premium and inflation risk premium. As is known to all. the interest rate for the three-year loan should be different from the five-year loan, liquidity risk must be compensated. It is self-evident that inflation is an economic phenomenon that price rises continuously on the basis of the last year. Small enterprise loan pricing must take the inflation risk into account for compensating inflation risk in successive years.Risk premium calculation of small enterprise loan pricing is difficult, that is reflected in the following three aspects:First, default risk premium calculation of small enterprise loan pricing is difficult. The information of small enterprise financial is more untrue relatively, more vulnerable to the impact of macroeconomic conditions, resulting in the credit risk of small enterprise being higher and the default risk premium of the loan being more difficult.Second, benchmark interest rate risk premium calculation of small enterprise loan pricing is difficult. Benchmark interest rates in financial markets are always changing and the parameters such as the rate jump time, jump amplitude, jump frequency and so on are not easy to measure, these factors result in the calculation of benchmark interest rate risk premium being difficult.Third, term structure of interest rate risk premium calculation of small enterprise loan pricing is difficult. The term structure of interest rates is always changing, when the economic situation improves, the term structure of interest rates will rise and the decline in the economic situation, the interest rate term structure will fall. The term structure of interest rates is difficult to accurately fit, resulting in the calculation of term structure of interest rate risk premium being difficult.The loan pricing model for small enterprise and its application based on risk premiums consists of three main contents. The first content is the model establishment of small enterprise default probability measurement based on K-S testing and logistic regression analysis, which is mainly to solve the problem of the default risk premium. The second content is the loan pricing model establishment for small enterprises based on benchmark interest rate risk premium, which is mainly to solve the problem of benchmark interest rate risk premium. The third content is the loan pricing model establishment for small enterprises based on term structure of interest rate risk premium, which is mainly to solve the problem of term structure of interest rate risk premium.The contributions of this paper are in three aspects.(1) The contribution of jumping parameters measurement of benchmark interest rate: Through auto regressive model AR measuring time-varying jump numbers of benchmark interest rates, jumping probability of benchmark interest rate can be measured, and then the benchmark interest rate risk premium is determine. Finally, a small enterprise loan pricing model based on the benchmark interest rate risk premium is set up.Through auto regressive model AR measuring time-varying jump numbers of benchmark interest rates, jumping probability of benchmark interest rate can be measured. The jump time period of the benchmark interest rate can be calculated by gamma distribution, and the jump amplitude of the benchmark interest rate can be calculated by normal distribution. The benchmark interest rate risk premium can be calculate by the jump times, the jump time period and the jump amplitude, that makes sure the benchmark interest rate risk in the small enterprise loan pricing model is adequately compensated. Throug the accumulation calculation of the risk premium of benchmark interest rate and the risk premium of default, the paper establishes a loan pricing model for small enterprise, which taking full consideration of financial cost, benchmark interest rate risk and default risk, which solves the determination problem of benchmark interest rate risk premium in loan pricing, and overcomes the disadvantages of the existing researches ignoring the benchmark interest rate risk premium resulting in unreasonable loan pricing.(2) The contribution of term structure of interest rates fitting:By solving the nonlinear programming model with the minimization of rate error between theoretical yield rate y, of bond and the actual yield rate y, of bond, the optimum piecewise point Jm and the optimum coefficient ak are deduced inversely, and than the optimal term structure of interest rates is fited. Finally, a small enterprise loan pricing model based on term structure of interest rates risk premium is set up.Since the characteristic that the theoretical rate yi of return is the function of piecewise point Jm and discount function coefficient ak, by solving the nonlinear programming model with the minimization of rate error between theoretical yield rate yi of bond and the actual yield rate y, of bond, the optimum piecewise point Jm and the optimum coefficient ak are deduced inversely, the optimal term structure of interest rates is fited and term structure of interest rates risk premium is measured, that makes sure term structure of interest rates risk in the small enterprise loan pricing model is adequately compensated. Throug the accumulation calculation of the risk premium of term structure of interest rates, the risk premium of benchmark interest rate and the risk premium of default, the paper establishes a loan pricing model for small enterprise, which taking full consideration of term structure of interest rates risk, benchmark interest rate risk and default risk, the status has been changed that existing researches determine piecewise point Jm artificially resulting in over high error between theoretical yield rate of bond and actual yield rates of bond and loan pricing unaccurate.(3) The contributions of indicator screening for the measurement of default probability: According to the thinking that the index should be kept as long as the index distinguishes default situation more significantly, the index which can identify default situation of small enterprise significantly be selected, and this paper establishes measure model of default probability which reflects default situation of small enterprise significantly.The data of the ith index of all customers is divided into two categories, default sample and non default sample, according to the thinking that the difference between distribution function of default sample and distribution function of non default sample is more larger as long as the K-S test statistics is more larger, and the insdex distinguishes default situation more significantly, by means of K-S test the index be selected which can identify default situation of small enterprise significantly, and the measure model of default probability is established which assure that the index for measuring default probability can distinguishes default situation more significantly and the accuracy of default probability measurement, the default probability measurement model overcomes the malpractice that selected indicator standard has nothing to do with small enterprise default situation in the existing researches. |
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