Mathematical Exchange Rates Modeling: Equilibrium and Nonequilibrium Dynamics

Abstract

The development of the author’s concept of the International Flows Equilibrium Exchange Rate (IFEER) is the basis for the mathematical exchange rate modeling of two interconnected equal economies. IFEER-concept allows modeling the exchange rate dynamics of relatively medium-term equilibrium and short- and long-term disequilibrium. Discrete and integral versions of the concept are the basis for further modeling. New structural models of medium-, short- and long-term dynamics and new final structural dependencies of the exchange rate on the system of fundamental factors are the main results. The models include mathematically formalized export-import and capital flows and international competitive advantages indicators. The modeling allowed the revealing of the structural pricing mechanism of the exchange rate dynamics from new positions. We verify the US dollar to the Russian ruble exchange rate modeling during periods of financial and economic crises in recent Russian history, based on a systematic analysis of the exchange rate policy. Because of the analysis, the fall in export prices of oil and other energy carriers in international markets, the rise in consumer prices within the country, and the fall in aggregate output are the main reasons for the fall of the Russian ruble. The conducted modeling allows for the evaluation of the short-term contribution to the crisis depreciation dynamics. The mathematical tools allow for the development of the decision-making process on the exchange rate regulation.

Investigating Statistical Features of the FX Bid Ask Series in a Small Economy with a Sizeable Informal Economy

“…The situation becomes even more complicated if the foreign currency is used in the role of the national currency in direct transactions. Additionally, the Equation 2 has a saddle point solution (𝑒 * , 𝑝 * ) for economicfinancial circumstances where centrifugal effects inflicted by inflation pressure are present, which are common [5,23,24]. It followed that depending on the money supply disturbances for a given foreign currency, the dynamics of nominal exchange rates (e) would be completely different.…”

“…The FX rates are the result of interactions between several endogenous economic variables, such as the balance of payments, purchasing power, prices' index, interest rates, productivity measures, import-export balances, etc., and exogenous disturbances mostly related to money supply [1,2]. Concrete relationships between those variables are given in detailed econometric models shown in standard econometric literature or dedicated works as in [3][4][5], etc., which are based on the typical behavior of variables that are presumed measurable and known. Every disturbance or fluctuation of those cause-factors would be mirrored on the spot value of FX rates, and in principle, the trend of exchange rates is predictable and manageable theoretically.…”