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Abstract

Introduction

Commercial banks at the present stage of the economic development are very important sector. They provide different services like lending and placement free money as deposits for entities and individuals. That is why commercial banks have become a very important element of modern economy.

Prediction of credit and deposit rates for commercial banks is very important stage of their work. If these interest rates are calculated correctly then commercial bank will receive maximum profit. Otherwise bank will lose some part of profit.

The aim of this work is analyzing means for building an econometric model for forecasting credit and deposit rates.

In order to accomplish this aim some problems have to be distinguished:

The object of research in this work is the process of formation credit and deposit rates.

The subject of research is interest rates in commercial banks.

This theme is very actual because the level of credit and deposit rates is important pledge of effective work of commercial bank and obtaining maximum profit.

To solve this problem methods of building and analysis of econometric models, methods of ranking objects using the multiset device can be used.

1. Building of econometric models

Econometric model which describes interrelations between phenomena or patterns of their development can be represented by next formula:

In formula (1.1) f(a,x) is functional which denotes form and structure of interrelations. Greatness y denotes the level of phenomenon which is studied and called the dependent variable; greatness x=(x1,x2...,xn) is avector of values of the independent variable xi; α=(α0,α1,α2,...,αn) is a vector of some arbitrary constants which are called the model parameters; ε – error of the model.

Error of the model ε characterizes the difference between the realized value of the variable y and calculated by the formula (1.1) in specific conditions. This error is a random greatness.

For calculating the numeric value of the parameters α0,α1,α2,...,αn previously accumulated an array of observations is used. One observation is the set of values (yt,x1t,x2t,...,xnt). Index t means individual observation.

The independent variable y is called the endogenous variable of model. Values of the dependent variable are determined by the values of the independent variables xi. The independent variables (factors) x1,x2,...,xn are called the exogenous variables.

By the character of connection of factors and varibale y models are divided into linear and nonlinear. By the properties of their parameters models are able to have constant and variable structure [1].

Procedure of building of econometric model may be divided into several stages:

  1. Analysis of the specific properties phenomena and processes which are studied, justification the class of models which can be used to describe them;
  2. Estimation of the parameters the variant of model that have chosen on the grounds of input data. These data denote levels of variables in different moments of time;
  3. Quality check of model that have been build. The answer to the question: is this model pertinently to use?;
  4. If the using of econometric model is beside the purpose then return to some previous stage is needed in oreder to try to build more qualitative model [2].

1.2 Analysis of econometric model

There are some indexes that is used for analysis the quality of econometric model

For example, the index of Student reresents statistical significance of coefficients of linear regression. Testing of the the model adequacy carried out using the index of Fisher. The overall quality of the equation estimated by the determination factor.

2. The rules of formation deposit and credit rates

Many factor influence on the level of deposit rate. For example, supply and demand of monetary assets on the market, demand for loans, the norms of required reserves for the obligations of banks, mandatory requirements of National Bank of Ukraine regarding ration between deposits of individuals and regulative capital of the bank, structure and conditions of deposits, accounting rules and taxation of income, overvalued level of interest rates tj the insidres of bank, the level of rivalry, dumping policy of banks which entering the market and seek to grab alcove by the unreasonable increase of deposit rates.

Basis of formation deposit rates is calculation the basic market rate which reflected minimal level of profitableness that satisfy investor in case of invest his money to bank. The following factors influence on the basic market rate:

The level of interset rate which take into consideration the paces of economic growth and inflation is called nominal risk-free rate. Nominal risk-free rate is calculated with the following formula

here FV – the future value of money, PV – the current value of investments, n – the number of investment periods (years).

Deposit rate of the bank basically a little lower than discount rate. Although sometimes supply and demand of money on the market and the competitive position of the bank lead to deviation of this rule.

The banks that do not have the reputation of safe and stabile institutions on the market have to offer high deposit rates to attract clients. In this case management of the bank have to know the directions and sizes of possible placement of money resources and their profitableness. Significant increase of the level of deposit rate may lead to unprofitable activity of the bank [3].

There are exist deveral methods that help commercial banks to determine deposit rate.

Pricing which is based on the method of the general fund requires accurate calculation of values each type of deposit services, calculation average value of deposit base and comparison it with level of interest rate on active operations. Loan rate have to satisfy next condition:

here Ya – loan rate, Ydi – expenses of deposit, Wdi – specific gravity of deposit in total amount of raised funds, Rdi – reserve deductions on deposit.

Many financial experts believe that for determination of deposit price should be taken into account not the weighted average but marginal expenses that means additional expenses which is connected with the leveraging new means. Economist James McNightly proposed the way of using the idea of marginal expenses or new value of money in the process of determination interest rates by banks for new deposit accounts. The essence of this method of price formation can be described by the following formulas:

here N – the norm of marginal expenses, Q – interest expenses on deposit, ΔQ – change in expenses on deposit, V – the amount of borrowed funds, ΔV – increment the volume of borrowed funds, Ya – loan rate [4].

Determination of credit rate is one of the most difficult problem of lending. Lender tries to set a high rate to make a profit on credit and compensate all expenses and risks. At the same time credit rate has to be low enough, then borrower will not turn to other lender and will be able to repay the loan.

The main factors that commercial banks take into consideration in the process of setting loan charge:

  1. average interest rate which bankpays out to it clients on deposit account;
  2. structure of loan resources of the bank;
  3. supply and demand on loans from the clients;
  4. period and type of loan;
  5. stability of monetary circulation in the country;
  6. average interest rate on interbank credit [5].

When commercial banks conclude a credit agreement they reach agreement with borrowers about value of interest rate. Macroeconomic factors influence on the value and dynamics of rates. individual factors also influence on this parameters. Macroeconomic factors are ratio supply and demand credit resources, monetary and credit policy of central bank, level of inflation and others. Individual factors are determined by the conditions of functioning of the bank, it position on the market, chosen credit and interest policy, the degree of riskiness of performed operations.

Level of interest rates of the bank is formed on the base of supply and demand of borrowed funds. The following factors also significantly influence on this level: prime cost of the loan, the amount, purpose and period of repayment, creditworthiness [6].

On the value of supply and demand of bank loans influence the following factors:

  1. pace of inflation;
  2. standards of credit regulation of the country;
  3. amount of money savings of legal entity and individuals;
  4. seasonal nature of formation and allocation of loan resources [7].

3. The multiset device for ranking factors which influence on rates

A multiset (also called a bag) is the known notion in combinatorial mathematics. A multiset A drawn from a crisp set G={x1,x2,...,xj,...} with different elements, which is called a domain, is defined as the following collection of elements, groups: A={kA(x1)⋅x1, kA(x2)⋅x2,...}= (kA(x)⋅x|x∈G}.

Here kA:G→Z+={0,1,2,...} is called a counting function of multiset, which defines the number of times that the element xi∈G occurs in the multiset A, and this is indicated with the symbol ⋅. The multiset Z is named as the maximal if kZ(x)=maxkA(x). A multiset A becomes an ordinary set when kA(x)=χA(x), where χA(x)=1 if x∈A, and χA(x)=0 if x∉A. The cardinality |A|=ΣxkA(x) and dimensionality |A|=ΣxχA(x) of the multiset A are defined as a total number of all element copies, and as a total number of different elements.

The following operations with multisets may be defined:

3.2 The rules of ranking

On of the approach to structure a set of objects A={A1,...,Ak} is strict or not srict regulation. The most used methods to regulate objects are ordinal classification, ranking, pairwise comparisons.

When we use ranking to regulate objects we calculate for each object Ai natural number ri that is called rank. Regulation of objects is a regulation of ranks r1<r2<...ri<rc.

There are different ways to ranking objects. For example, objects may be shown to expert all together or by turn. If the number of objects is not very big and there is only one criterion for evaluating then ranking is not veru difficult for experts. Ranking is more labor-intensive method compared to methods of ordinal classification [9].

3.3 The example of using

Let,s look to the example of ranking competitor in order to definition the rank of competitiveness using multiset.

We have different input data. For example:

  1. The level of competitiveness of company,s product on the market;
  2. The effectiveness of product that is analyzed;
  3. Public image of the company;
  4. The effectiveness of advertising;
  5. The effectiveness of ways to stimulate sales;
  6. The quality of product [10].

A companyAi activity in any market sector is estimated simultaneously by n experts upon m criteria Q1,...,Qm. Criterion estimates qses, es=1,...,hs, s=1,...,m may be numerical or verbal, and are ordered from the best to the worst as qs1>qs2>...>qshs. Need to order all companies from the best to the worst.

The rule for an objects, comparison looks as follows: the bigger the weighted sum SAi1=ΔsωskAi(qs1) of the first objects, estimates by all criteria Qs, the bigger the object Ai [8] .

4 Prognostication with the help of econometric models

Prognostication is a receiving of estimates of the dependent variable for some array of independent variables that is miss in input data. There are point and interval prognostification. In the first case estimate is a number, in the second case - interval which contains true value of dependent variable with prescribed level of significance.

The error of prognostication is a difference between prognosticated and real value and is calculated with the following formula:

here Sp – standard error of prognostication; S – standard error of regression; n – amount of data pairs that is used for regression analysis; xp – value of independent variable; ¯x – sample average of variable x; var(x) – variation of variable x [11].

Interval (a,b) that contain unknown parameter Θ with given probability β is called confidence interval. α=1-β is called significance level.

Stages of building confidence intervals:

  1. Find statistics η(X→,Θ) that depend on unknown parameter Θ which distribution law is unknown .
  2. Find quantiles η1 и η2 of statistic distribution η(X→,Θ) that satisfy the condition P(η1<η(X→,Θ)<η2)= β.
  3. After solution of inequality η1<η(X→,Θ)<η2 find the bounds of confidence interval [12].

Conclusion

During the process of study the theme of master, work factors that influence on deposit and loan rates of commercial banks have been dedicated. In future ranking of these factors with the help of multiset, building of econometric model and quality control test of it using criteria are planned. If model will be sub-quality then it is needed to improve. Then functioning of model has to be checked with the help of real data.

References

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