The analysis of dynamics model of a commercial bank capital in view of the random factors

Abstract

The dynamics of the behavior of bank’s deposits was considered in the article based on the model equation suggested by I. Voloshin, taking into account the interest rate risk, which is being implemented by means of the assumption of their random nature. A common approach to the calculation of the corresponding probability characteristics has been implemented, which is, in a sense, a universal character.

Investigation of the behavior of the mathematical expectation of bank’s deposit with the passage of time has shown that minor random deviations from the deterministic values doesn’t lead to significant changes in comparison with the deterministic case (small variance of interest rates). However, with increasing dispersion with the passage of time there may exist significant deviations that can lead to unbalance of the banking system. These results were obtained under the assumption of statistical independence interest rates.

The account of the statistical dependence of interest rates leads to further integration in the integral representation of the mathematical expectation that has no substantial effect on the numerical implementation, as the standard approximate methods of calculating double integrals are applicable when the domain of integration is specified by coordinate lines.

In case where at the law of three sigma corresponding interval falls on the negative part of the axis, the assumption of normality of the interest rates is in doubt, and then a statistical analysis must be carried out under the assumption of lognormal distribution or consider the truncated normal distribution.

It should be noted that there had not been obtained estimates of the distribution parameters in the article due to a lack of sufficient data on the behavior of deposits in a particular commercial banks, that is, it does not check the relevant hypotheses that can be the subject of further research.

Further analysis of the random behavior of the quantity of deposits must be linked to the generalization of the market model of Rendelman-Bartter, which describes the behavior of interest rates. Approach, that was proposed at this work, may be useful in the case when interest rates are stochastic processes, as well as the probability characteristics of the quantity of the deposit is considered the mathematical expectation and variance, which describe essentially non-stationary random process. The model of the bank’s deposit behavior, that was considered, can be used for finding the steady state, that is when the initial time be expected to infinity.