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How to determine exchange rates under risk neutrality: A note

Author

Listed:
  • Stefano Bosi

    (EPEE - Centre d'Etudes des Politiques Economiques - UEVE - Université d'Évry-Val-d'Essonne)

  • Patrice Fontaine

    (EUROFIDAI - Institut Européen de données financières - ESSEC Business School - CNRS - Centre National de la Recherche Scientifique)

  • Cuong Le Van

    (IPAG Business School, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, TIMAS - Institute of Mathematics and Applied Science)

Abstract

The goal of this paper is to determine the exchange rates consistent with an equilibrium in the international assets and goods markets. We present a wealth model of a two-country economy where financial assets and goods are traded. We consider the case where the agents are risk neutral, a very common assumption in finance in order to have explicit solutions for prices, and, in particular, in international finance for exchange rates using the non-null Pareto optima. We show that the Pareto optima in the international assets and goods markets are found to coincide with the net trade allocations. More notably, under a no-arbitrage condition in the assets markets, we can define an exchange rates system for which PPP holds. We provide conditions to have a non-null Pareto optimum to compute the exchange rates. We give an example with a non-null Pareto optimum associated with the determination of the exchange rate. © 2017 Elsevier B.V.

Suggested Citation

  • Stefano Bosi & Patrice Fontaine & Cuong Le Van, 2017. "How to determine exchange rates under risk neutrality: A note," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-02877955, HAL.
    • Handle: RePEc:hal:cesptp:hal-02877955
    DOI: 10.1016/j.econlet.2017.05.015
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    References listed on IDEAS

    as
    1. Bosi, Stefano & Fontaine, Patrice & Le Van, Cuong, 2016. "Interest rates parity and no arbitrage as equivalent equilibrium conditions in the international financial assets and goods markets," Mathematical Social Sciences, Elsevier, vol. 82(C), pages 26-36.
    2. repec:hal:pseose:hal-01302524 is not listed on IDEAS
    3. Hart, Oliver D., 1974. "On the existence of equilibrium in a securities model," Journal of Economic Theory, Elsevier, vol. 9(3), pages 293-311, November.
    4. Dumas, Bernard, 1992. "Dynamic Equilibrium and the Real Exchange Rate in a Spatially Separated World," The Review of Financial Studies, Society for Financial Studies, vol. 5(2), pages 153-180.
    5. repec:dau:papers:123456789/13604 is not listed on IDEAS
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    Cited by:

    1. Bosi, Stefano & Fontaine, Patrice & Le Van, Cuong, 2021. "Long-run equilibrium in international assets and goods markets: Why is the law of one price required?," Journal of Economic Behavior & Organization, Elsevier, vol. 190(C), pages 891-904.
    2. Jun Wei, 2020. "Optimal Combination of Currency Assets and Algorithm Simulation under Exchange Rate Risk," Complexity, Hindawi, vol. 2020, pages 1-10, November.

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    More about this item

    Keywords

    Exchange rates; International asset pricing; No-arbitrage conditions; Returns on securities;
    All these keywords.

    JEL classification:

    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
    • F31 - International Economics - - International Finance - - - Foreign Exchange
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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