|M.Sc Thesis||Department of Industrial Engineering and Management|
|Supervisor:||Prof. Avner Bar Ilan|
Studies of optimal holding reserve policy have typically assumed that countries have a desired level of reserves, and assumed that deviations of actual level of reserves from the desired one trigger a process of adjustment. Many studies have identified a stable demand function for foreign reserves held by central banks. So that, economists determined that optimal reserves holding is closely related to that of the demand for money by individuals or firms.
The purpose of my thesis is to determine the optimal reserves held by central banks within a continuous stochastic framework modeling in which, the control variable of drift (rate of reserves changing) is controlled by the central bank. The mechanism used to drift changes and controlling will be the interest ratio, that is, increasing of interest ratio causes consequent increase of net reserve flows into the country.
In this research, we will exhibit the analytical solution of the model by using numerical simulations and will examine which model describes better the behavior of holding reserves by using data on developed countries, Middle East countries, South American countries and South East Asian countries.
Accepted models used in literature are related to models that explain the demand for money, in which control variable is impulse control, whereas, drift considered as an exogenous variable. In these models, modifications or changing in conditional parameters (like money or reserves held) occurs within infinitesimal period of time. For example, when sum of reserves held is small, immediate process of net flows of foreign currency takes place, which causes accumulating reserves and consequently, reach higher levels of reserves.
In this thesis, we will demonstrate that the model of drift control describes better than another model the behavior of reserves and the determination of the optimal levels.