No‐arbitrage matrices of exchange rates: Some characterizations

Abstract

Abstract We provide some characterizations of the absence of triangular arbitrage in the spot exchange rates of a group of countries. When the matrix of exchange rates of the group does not fulfill the conditions given in those characterizations, we provide a measure of distance to the space of matrices of exchange rates that are triangular arbitrage‐free. Using this distance, we compute the closest no‐arbitrage matrix of exchange rates of the group. We apply the methodology developed to the exchange rates between the currencies of Brazil (real), European Union (euro), Great Britain (pound sterling), and USA (dollar) to analyze the possibility of triangular arbitrage in those foreign exchange markets.

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