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Currency Prices, the Nominal Exchange Rate, and Security Prices in a Two‐Country Dynamic Monetary Equilibrium

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  • Suleyman Basak
  • Michael Gallmeyer

Abstract

This paper examines a continuous‐time two‐country dynamic monetary equilibrium in which countries with possibly heterogeneous tastes and endowments hold their own money for the purpose of transaction services formulated via money in the utility function. Given a price system, no‐arbitrage pricing results are provided for the price of each money and the nominal exchange rate. Characterizations are provided for equilibrium prices for general time‐additive preferences and non‐Markovian exogenous processes. Under a Markovian structure of model primitives, the currency prices are shown to solve a bivariate system of partial differential equations. Assuming that each country is endowed with heterogeneous separable power utility and the exogenous quantities all follow geometric Brownian motions, an equilibrium is shown to exist and additional characterization is provided. A further example of nonseparable Cobb-Douglas preferences is investigated. The additional features over the customary environment of homogeneous logarithmic preferences are emphasized. Copyright Blackwell Publishers Inc 1999.

Suggested Citation

  • Suleyman Basak & Michael Gallmeyer, 1999. "Currency Prices, the Nominal Exchange Rate, and Security Prices in a Two‐Country Dynamic Monetary Equilibrium," Mathematical Finance, Wiley Blackwell, vol. 9(1), pages 1-30.
  • Handle: RePEc:bla:mathfi:v:9:y:1999:i:1:p:1-30
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    Cited by:

    1. Vincenzo Costa, 2004. "Risk neutral valuation and uncovered interest rate parity in a stochastic two-country-economy with two goods," Economics Bulletin, AccessEcon, vol. 3(43), pages 1-10.
    2. Anna Pavlova & Roberto Rigobon, 2007. "Asset Prices and Exchange Rates," Review of Financial Studies, Society for Financial Studies, vol. 20(4), pages 1139-1180.
    3. Evans, Lynne & Kenc, Turalay, 2004. "FOREX risk premia and policy uncertainty: a recursive utility analysis," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 14(1), pages 1-24, February.
    4. Dibooglu, Sel & Kenc, Turalay, 2009. "Welfare cost of inflation in a stochastic balanced growth model," Economic Modelling, Elsevier, vol. 26(3), pages 650-658, May.
    5. Apte, Prakash & Sercu, Piet & Uppal, Raman, 2004. "The exchange rate and purchasing power parity: extending the theory and tests," Journal of International Money and Finance, Elsevier, vol. 23(4), pages 553-571, June.
    6. Keiichi Tanaka, 2003. "Indeterminacy of equilibrium price of money, market price of risk and interest rates," Economics Bulletin, AccessEcon, vol. 7(4), pages 1-11.
    7. Lioui, Abraham & Poncet, Patrice, 2003. "International asset allocation: A new perspective," Journal of Banking & Finance, Elsevier, vol. 27(11), pages 2203-2230, November.
    8. Lioui, Abraham & Poncet, Patrice, 2005. "General equilibrium pricing of CPI derivatives," Journal of Banking & Finance, Elsevier, vol. 29(5), pages 1265-1294, May.
    9. Bakshi, Gurdip & Carr, Peter & Wu, Liuren, 2008. "Stochastic risk premiums, stochastic skewness in currency options, and stochastic discount factors in international economies," Journal of Financial Economics, Elsevier, vol. 87(1), pages 132-156, January.

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