Abstract
In this paper, the model formulated incorporated stochastic variables such as bank loans and deposits as well as some deterministic variables: cash available, depreciation, capital expenditure, tax and costs, comprising variable costs and fixed costs. This paper assumes that the dynamics of bank loans and deposits at time t follow a geometric Brownian motion, therefore, it satisfies certain stochastic differential equations (SDEs) formulated on some probability space. On the other hand, the growth rate μL(t) in loan at time t, growth rate μD(t) in deposit at time t, and the variable cost η(t) at time t are assumed to be driven by mean-reverting Ornstein-Uhlenbeck processes. The SDEs of the dynamics of bank loans, growth rate in loans, bank deposits, growth rate in deposits and variable cost arising from the model were solved by means of the ItO Lemma. Discrete time approximations of the exact solutions of the SDEs were derived and used in a Monte Carlos simulation software.
Highlights
In recent times, there has been a high level of bank consolidations especially in the emerging markets
According to [1], bank management focuses on four operational concerns
The bank has to be liquid enough to finance its obligations to depositors
Summary
There has been a high level of bank consolidations especially in the emerging markets. The bank has to be liquid enough to finance its obligations to depositors. This aspect of bank management is called liquidity management and it involves the acquisition of sufficient liquid assets to meet the demand from deposit withdrawals and depositors payment. Banks must have incentives to invest in assets that have a reasonably low level of risk associated with them. This process is known as assets management and aims to encourage investment in assets that have low default probability and strategies that are sufficiently diverse. Capital adequacy management involves the decision about the amount of capital the bank should hold and how it should be accessed
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