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Future exchange rates and Siegel's paradox

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  • Keivan Mallahi-Karai
  • Pedram Safari

Abstract

Siegel's paradox is a fundamental question in international finance about exchange rates for futures contracts and has puzzled many scholars for over forty years. The unorthodox approach presented in this article leads to an arbitrage-free solution which is invariant under currency re-denominations and is symmetric, as explained. We will also give a complete classification of all such aggregators in the general case. The formula obtained in this setting therefore describes all the negotiated no-arbitrage forward exchange rates in terms of a reciprocity function. Keywords: Siegel's paradox, forward exchange rates, discount bias.

Suggested Citation

  • Keivan Mallahi-Karai & Pedram Safari, 2018. "Future exchange rates and Siegel's paradox," Papers 1805.03347, arXiv.org.
    • Handle: RePEc:arx:papers:1805.03347
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    References listed on IDEAS

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    1. Jeremy J. Siegel, 1972. "Risk, Interest Rates and the Forward Exchange," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 86(2), pages 303-309.
    2. Maurice Obstfeld & Kenneth S. Rogoff, 1996. "Foundations of International Macroeconomics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262150476, April.
    3. Don E. Roper, 1975. "The Role of Expected Value Analysis for Speculative Decisions in the Forward Currency Market," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 89(1), pages 157-169.
    4. Edlin Aaron S., 2002. "Forward Discount Bias, Nalebuff's Envelope Puzzle, and the Siegel Paradox in Foreign Exchange," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 2(1), pages 1-11, September.
    5. Gollier, Christian & Weitzman, Martin L., 2010. "How should the distant future be discounted when discount rates are uncertain?," Economics Letters, Elsevier, vol. 107(3), pages 350-353, June.
    6. Edlin, Aaron S., 2002. "Forward Discount Bias, Nalebuff's Envelope Puzzle, and the Siegel Paradox in Foreign Exchange," Berkeley Olin Program in Law & Economics, Working Paper Series qt2wc1p9pw, Berkeley Olin Program in Law & Economics.
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    Cited by:

    1. Djeutem, Edouard & Dunbar, Geoffrey R., 2022. "Uncovered return parity: Equity returns and currency returns," Journal of International Money and Finance, Elsevier, vol. 128(C).

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    Keywords

    siegel's paradox; forward exchange rates; discount bias.;
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