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No‐arbitrage matrices of exchange rates: Some characterizations

Author

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  • Wilfredo L. Maldonado
  • Juan José Egozcue
  • Vera Pawlowsky‐Glahn

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.

Suggested Citation

  • Wilfredo L. Maldonado & Juan José Egozcue & Vera Pawlowsky‐Glahn, 2021. "No‐arbitrage matrices of exchange rates: Some characterizations," International Journal of Economic Theory, The International Society for Economic Theory, vol. 17(4), pages 375-389, December.
    • Handle: RePEc:bla:ijethy:v:17:y:2021:i:4:p:375-389
    DOI: 10.1111/ijet.12249
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    References listed on IDEAS

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    1. Daniel J. Fenn & Sam D. Howison & Mark Mcdonald & Stacy Williams & Neil F. Johnson, 2009. "The Mirage Of Triangular Arbitrage In The Spot Foreign Exchange Market," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(08), pages 1105-1123.
    2. Juan José Egozcue & Vera Pawlowsky-Glahn & Matthias Templ & Karel Hron, 2015. "Independence in Contingency Tables Using Simplicial Geometry," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(18), pages 3978-3996, September.
    3. Stan Palasek, 2014. "Arbitrage-free exchange rate ensembles over a general trade network," Papers 1406.1547, arXiv.org.
    4. Aiba, Yukihiro & Hatano, Naomichi & Takayasu, Hideki & Marumo, Kouhei & Shimizu, Tokiko, 2002. "Triangular arbitrage as an interaction among foreign exchange rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 310(3), pages 467-479.
    5. Smith, R. P. & Hunter, J., 1985. "Cross arbitrage and specification in exchange rate models," Economics Letters, Elsevier, vol. 18(4), pages 375-376.
    6. Yukihiro Aiba & Naomichi Hatano & Hideki Takayasu & Kouhei Marumo & Tokiko Shimizu, 2002. "Triangular arbitrage as an interaction among foreign exchange rates," Papers cond-mat/0202391, arXiv.org, revised Mar 2002.
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    Cited by:

    1. Germ`a Coenders & N'uria Arimany Serrat, 2023. "Accounting statement analysis at industry level. A gentle introduction to the compositional approach," Papers 2305.16842, arXiv.org, revised Feb 2024.

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