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Triangular arbitrage as an interaction among foreign exchange rates

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  • Aiba, Yukihiro
  • Hatano, Naomichi
  • Takayasu, Hideki
  • Marumo, Kouhei
  • Shimizu, Tokiko

Abstract

We first show that there are in fact triangular arbitrage opportunities in the spot foreign exchange markets, analyzing the time dependence of the yen–dollar rate, the dollar–euro rate and the yen–euro rate. Next, we propose a model of foreign exchange rates with an interaction. The model includes effects of triangular arbitrage transactions as an interaction among three rates. The model explains the actual data of the multiple foreign exchange rates well.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:310:y:2002:i:3:p:467-479
    DOI: 10.1016/S0378-4371(02)00799-9
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    References listed on IDEAS

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    Cited by:

    1. Paz Grimberg & Tobias Lauinger & Damon McCoy, 2020. "Empirical Analysis of Indirect Internal Conversions in Cryptocurrency Exchanges," Papers 2002.12274, arXiv.org.
    2. Jarosław Kwapień & Sylwia Gworek & Stanisław Drożdż & Andrzej Górski, 2009. "Analysis of a network structure of the foreign currency exchange market," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 4(1), pages 55-72, June.
    3. 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.
    4. Takayuki Mizuno & Shoko Kurihara & Misako Takayasu & Hideki Takayasu, 2003. "Time-scale dependence of correlations among foreign currencies," Papers cond-mat/0303306, arXiv.org.
    5. Daniel J. Fenn & Sam D. Howison & Mark McDonald & Stacy Williams & Neil F. Johnson, 2008. "The Mirage of Triangular Arbitrage in the Spot Foreign Exchange Market," Papers 0812.0913, arXiv.org.
    6. Stefanescu, Razvan & Dumitriu, Ramona, 2016. "Particularitǎţi ale evoluţiei variabilelor financiare [Some particularities of the financial variables evolution]," MPRA Paper 73481, University Library of Munich, Germany, revised 02 Sep 2016.
    7. Alberto Ciacci & Takumi Sueshige & Hideki Takayasu & Kim Christensen & Misako Takayasu, 2020. "The microscopic relationships between triangular arbitrage and cross-currency correlations in a simple agent based model of foreign exchange markets," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-19, June.
    8. Ye Wang & Yan Chen & Haotian Wu & Liyi Zhou & Shuiguang Deng & Roger Wattenhofer, 2021. "Cyclic Arbitrage in Decentralized Exchanges," Papers 2105.02784, arXiv.org, revised Jan 2022.
    9. Zura Kakushadze & Juan Andrés Serur, 2018. "151 Trading Strategies," Springer Books, Springer, number 978-3-030-02792-6, September.
    10. Aiba, Yukihiro & Hatano, Naomichi & Takayasu, Hideki & Marumo, Kouhei & Shimizu, Tokiko, 2003. "Triangular arbitrage and negative auto-correlation of foreign exchange rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 253-257.
    11. Takatoshi Ito & Kenta Yamada & Misako Takayasu & Hideki Takayasu, 2012. "Free Lunch! Arbitrage Opportunities in the Foreign Exchange Markets," NBER Working Papers 18541, National Bureau of Economic Research, Inc.
    12. Peter G. Szilagyi & Jonathan A. Batten, 2006. "Arbitrage, Covered Interest Parity and Long-Term Dependence between the US Dollar and the Yen," The Institute for International Integration Studies Discussion Paper Series iiisdp128, IIIS.
    13. Papadopoulos Konstantinos G., 2008. "Purchasing Power Parity with Strategic Markets," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 8(1), pages 1-32, June.
    14. Batten, Jonathan A. & Szilagyi, Peter G., 2007. "Covered interest parity arbitrage and temporal long-term dependence between the US dollar and the Yen," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 376(C), pages 409-421.
    15. Aiba, Yukihiro & Hatano, Naomichi, 2004. "Triangular arbitrage in the foreign exchange market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 174-177.

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