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How to determine exchange rates under risk neutrality: A note

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  • Bosi, Stefano
  • Fontaine, Patrice
  • Le Van, Cuong

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.

Suggested Citation

  • Bosi, Stefano & Fontaine, Patrice & Le Van, Cuong, 2017. "How to determine exchange rates under risk neutrality: A note," Economics Letters, Elsevier, vol. 157(C), pages 92-96.
    • Handle: RePEc:eee:ecolet:v:157:y:2017:i:c:p:92-96
    DOI: 10.1016/j.econlet.2017.05.015
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    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

    International asset pricing; Returns on securities; Exchange rates; No-arbitrage conditions;
    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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