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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.

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, January.
  • Handle: RePEc:bla:mathfi:v:9:y:1999:i:1:p:1-30
    DOI: 10.1111/1467-9965.00061
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    1. Duffie, Darrell & Zame, William, 1989. "The Consumption-Based Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 57(6), pages 1279-1297, November.
    2. Solnik, Bruno H., 1974. "An equilibrium model of the international capital market," Journal of Economic Theory, Elsevier, vol. 8(4), pages 500-524, August.
    3. Bakshi, Gurdip S & Chen, Zhiwu, 1996. "Inflation, Asset Prices, and the Term Structure of Interest Rates in Monetary Economies," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 241-275.
    4. Maurice Obstfeld & Kenneth S. Rogoff, 1996. "Foundations of International Macroeconomics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262150476, December.
    5. LeRoy, Stephen F, 1984. "Nominal Prices and Interest Rates in General Equilibrium: Endowment Shocks," The Journal of Business, University of Chicago Press, vol. 57(2), pages 197-213, April.
    6. Svensson, Lars E. O., 1985. "Currency prices, terms of trade, and interest rates: A general equilibrium asset-pricing cash-in-advance approach," Journal of International Economics, Elsevier, vol. 18(1-2), pages 17-41, February.
    7. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    8. Feenstra, Robert C., 1986. "Functional equivalence between liquidity costs and the utility of money," Journal of Monetary Economics, Elsevier, vol. 17(2), pages 271-291, March.
    9. LeRoy, Stephen F, 1984. "Nominal Prices and Interest Rates in General Equilibrium: Money Shocks," The Journal of Business, University of Chicago Press, vol. 57(2), pages 177-195, April.
    10. Huang, Chi-fu, 1987. "An Intertemporal General Equilibrium Asset Pricing Model: The Case of Diffusion Information," Econometrica, Econometric Society, vol. 55(1), pages 117-142, January.
    11. Lucas, Robert Jr., 1982. "Interest rates and currency prices in a two-country world," Journal of Monetary Economics, Elsevier, vol. 10(3), pages 335-359.
    12. Bekaert, Geert, 1996. "The Time Variation of Risk and Return in Foreign Exchange Markets: A General Equilibrium Perspective," Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 427-470.
    13. Bakshi, Gurdip S & Chen, Zhiwu, 1997. "Equilibrium Valuation of Foreign Exchange Claims," Journal of Finance, American Finance Association, vol. 52(2), pages 799-826, June.
    14. Zapatero, Fernando, 1995. "Equilibrium asset prices and exchange rates," Journal of Economic Dynamics and Control, Elsevier, vol. 19(4), pages 787-811, May.
    15. Stulz, ReneM., 1986. "Interest rates and monetary policy uncertainty," Journal of Monetary Economics, Elsevier, vol. 17(3), pages 331-347, May.
    16. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-384, March.
    17. Breeden, Douglas T., 1979. "An intertemporal asset pricing model with stochastic consumption and investment opportunities," Journal of Financial Economics, Elsevier, vol. 7(3), pages 265-296, September.
    18. Stulz, Rene M, 1986. "Asset Pricing and Expected Inflation," Journal of Finance, American Finance Association, vol. 41(1), pages 209-223, March.
    19. Ohashi, Kazuhiko, 1991. "A note on the terminal date security prices in a continuous time trading model with dividends," Journal of Mathematical Economics, Elsevier, vol. 20(2), pages 219-223.
    20. Bekaert, Geert, 1994. "Exchange rate volatility and deviations from unbiasedness in a cash-in-advance model," Journal of International Economics, Elsevier, vol. 36(1-2), pages 29-52, February.
    21. Stulz, Rene M, 1984. "Currency Preferences, Purchasing Power Risks, and the Determination of Exchange Rates in an Optimizing Model," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 16(3), pages 302-316, August.
    22. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    23. McCallum, Bennett T., 1983. "The role of overlapping-generations models in monetary economics," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 18(1), pages 9-44, January.
    24. Ioannis Karatzas & John P. Lehoczky & Steven E. Shreve, 1990. "Existence and Uniqueness of Multi-Agent Equilibrium in a Stochastic, Dynamic Consumption/Investment Model," Mathematics of Operations Research, INFORMS, vol. 15(1), pages 80-128, February.
    25. Dumas, Bernard, 1992. "Dynamic Equilibrium and the Real Exchange Rate in a Spatially Separated World," Review of Financial Studies, Society for Financial Studies, vol. 5(2), pages 153-180.
    26. Adler, Michael & Dumas, Bernard, 1983. "International Portfolio Choice and Corporation Finance: A Synthesis," Journal of Finance, American Finance Association, vol. 38(3), pages 925-984, June.
    27. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
    28. Stulz, Rene M, 1987. "An Equilibrium Model of Exchange Rate Determination and Asset Pricing with Nontraded Goods and Imperfect Information," Journal of Political Economy, University of Chicago Press, vol. 95(5), pages 1024-1040, October.
    29. Dumas, Bernard, 1989. "Two-Person Dynamic Equilibrium in the Capital Market," Review of Financial Studies, Society for Financial Studies, vol. 2(2), pages 157-188.
    30. Uppal, Raman, 1993. "A General Equilibrium Model of International Portfolio Choice," Journal of Finance, American Finance Association, vol. 48(2), pages 529-553, June.
    31. Jiang, Wang, 1996. "The term structure of interest rates in a pure exchange economy with heterogeneous investors," Journal of Financial Economics, Elsevier, vol. 41(1), pages 75-110, May.
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    Cited by:

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    3. Balduzzi, Pierluigi, 2007. "Money and asset prices in a continuous-time Lucas and Stokey cash-in-advance economy," Journal of Economic Dynamics and Control, Elsevier, vol. 31(8), pages 2713-2743, August.
    4. Basak, Suleyman, 2005. "Asset pricing with heterogeneous beliefs," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2849-2881, November.
    5. Duarte, Diogo & Saporito, Yuri F., 2019. "Endogenous asymmetric money illusion," Journal of Banking & Finance, Elsevier, vol. 109(C).
    6. Suleyman Basak & Hongjun Yan, 2010. "Equilibrium Asset Prices and Investor Behaviour in the Presence of Money Illusion," Review of Economic Studies, Oxford University Press, vol. 77(3), pages 914-936.
    7. 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.
    8. 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.
    9. Lioui, Abraham & Poncet, Patrice, 2003. "International asset allocation: A new perspective," Journal of Banking & Finance, Elsevier, vol. 27(11), pages 2203-2230, November.
    10. Chiarolla, Maria B. & Haussmann, Ulrich G., 2001. "Equilibrium in a stochastic model with consumption, wages and investment," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 311-346, April.
    11. Lioui, Abraham & Poncet, Patrice, 2005. "General equilibrium pricing of CPI derivatives," Journal of Banking & Finance, Elsevier, vol. 29(5), pages 1265-1294, May.
    12. 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.
    13. Lioui, Abraham & Poncet, Patrice, 2004. "General equilibrium real and nominal interest rates," Journal of Banking & Finance, Elsevier, vol. 28(7), pages 1569-1595, July.
    14. Anna Pavlova & Roberto Rigobon, 2010. "International Macro-Finance," NBER Working Papers 16630, National Bureau of Economic Research, Inc.
    15. 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.
    16. repec:ebl:ecbull:v:7:y:2003:i:4:p:1-11 is not listed on IDEAS
    17. Benjamin Croitoru & Lei Lu, 2015. "Asset Pricing in a Monetary Economy with Heterogeneous Beliefs," Management Science, INFORMS, vol. 61(9), pages 2203-2219, September.
    18. 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.
    19. 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.
    20. Travis D. Nesmith, 2005. "Solving stochastic money-in-the-utility-function models," Finance and Economics Discussion Series 2005-52, Board of Governors of the Federal Reserve System (U.S.).
    21. Basak, Suleyman, 2004. "Asset Prices with Heterogenous Beliefs," CEPR Discussion Papers 4256, C.E.P.R. Discussion Papers.

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