Arbitrage-free exchange rate ensembles over a general trade network

TL;DR

This paper analyzes the structure of arbitrage-free exchange rate ensembles over general trade networks, extending classical models to arbitrary graphs and discussing implications for digital currency markets.

Contribution

It introduces a framework for understanding no-arbitrage exchange rates over arbitrary trade networks, beyond complete graphs, and discusses minimal information requirements.

Findings

Exchange rate ensembles form a vector space over arbitrary graphs.

Complete graphs lead to trivial exchange rate ensembles.

Relevance to digital currency markets with regulated trade networks.

Abstract

It is assumed that under suitable economic and information-theoretic conditions, market exchange rates are free from arbitrage. Commodity markets in which trades occur over a complete graph are shown to be trivial. We therefore examine the vector space of no-arbitrage exchange rate ensembles over an arbitrary connected undirected graph. Consideration is given for the minimal information for determination of an exchange rate ensemble. We conclude with a topical discussion of exchanges in which our analyses may be relevant, including the emergent but highly-regulated (and therefore not a complete graph) market for digital currencies.