CABEM

Current Account Based Exchange Rate Mechanism

A Mathematical Protocol for Endogenous Trade Equilibrium and Sovereign Debt Discipline.

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Abstract

The Current Account Based Exchange Rate Mechanism (CABEM) is a mathematical framework for exchange-rate determination based on current-account balances and monetary expansion. The protocol derives exchange rates as endogenous outputs of observable macroeconomic variables and provides a globally consistent, transitive, and non-discretionary currency valuation system.


The Exchange Rate Problem

Exchange rates occupy a central position within the international economic system. They influence trade, capital allocation, sovereign financing and the distribution of purchasing power between nations. Despite this importance, the theoretical foundations of exchange-rate valuation remain fragmented. Contemporary approaches frequently incorporate variables such as economic output, domestic growth, interest-rate differentials or market expectations. These variables describe conditions within national economies. Exchange rates, however, govern economic relationships between national economies. This distinction is not merely conceptual. It determines which measurable quantities possess direct relevance for currency valuation.


External Economic Relations

Gross Domestic Product measures economic activity within a monetary area and is therefore denominated in the currency whose valuation is ultimately being examined. While such variables may describe the scale or dynamics of domestic production, they do not directly quantify economic exchange between sovereign currency areas. The current account occupies a different position within the system of national accounts. It records the net balance of goods, services, primary income and secondary income exchanged between an economy and the rest of the world. Unlike domestic aggregates, current-account balances represent observable external relationships. They describe the net transfer of economic value across monetary boundaries and therefore directly reflect the balance of international economic exchange.


A Balance-Based Perspective

CABEM is based on the proposition that persistent external balances contain structurally relevant information for currency valuation. Rather than deriving exchange rates from variables describing internal economic activity, the framework begins with measurable external-account positions and their interaction with monetary expansion. In this interpretation, exchange rates emerge as expressions of relative external economic balances rather than merely as outcomes of financial-market transactions. The objective is not to explain every short-term movement of foreign-exchange markets. The objective is to establish a coherent accounting framework through which currency valuations can be derived from observable macroeconomic relations.


CABEM Framework

The Current Account Based Exchange Rate Mechanism (CABEM) formalizes this perspective through a mathematical valuation framework based on current-account balances and monetary aggregates. Currency-specific valuation factors are derived from observable macroeconomic quantities. Bilateral exchange rates emerge from the relative relationship between these factors, producing a reciprocal and transitive exchange-rate system without requiring anchor currencies or discretionary adjustments. The resulting framework provides a globally consistent reference structure for the analysis of exchange rates and external economic imbalances.

The Core Mathematical Framework

CABEM Mathematical Framework

Currency-specific valuation factors are derived directly from relative current-account positions. Bilateral exchange rates emerge from the ratio between these valuation factors, ensuring reciprocity, transitivity and strictly positive exchange rates.

Key Properties

Reciprocity

Every exchange rate maintains exact inverse symmetry.

Transitivity

All currency pairs remain mathematically consistent.

Monetary Neutrality

The framework remains independent of privileged issuers.

External Balance

Persistent surpluses and deficits create endogenous adjustment pressure.

Scientific Release

Author Kay Schroeder Version 1.4 (Scientific Release) Publication Type Preprint Repository Zenodo DOI 10.5281/zenodo.23451367 mailto info(at)cabem.org

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