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An exchange rate target zone model with a terminal condition and mean-reverting fundamentals

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  • Ajevskis, Viktors

Abstract

This paper proposes a target zones exchange rate model with a terminal condition of entering a currency zone. It is assumed that the exchange rate is a function of the fundamental and time. Another essential assumptions of the model is that the fundamental process is bounded inside the band [-f,f] and that terminal condition for the exchange rate holds. Using Ito’s lemma, we obtain a parabolic partial differential equation for the exchange rate. The fundamental is specified in two ways: as a regulated Brownian motion and Ornstein-Uhlenbeck processes. For the case of the Brownian motion process the closed form solution of the problem is obtained, whereas for the Ornstein-Uhlenbeck process the closed form solution does not exist, therefore we had to use numerical method for solving of the problem. Both specifications are compared numerically.

Suggested Citation

  • Ajevskis, Viktors, 2015. "An exchange rate target zone model with a terminal condition and mean-reverting fundamentals," MPRA Paper 65078, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:65078
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    References listed on IDEAS

    as
    1. Viktors Ajevskis, 2011. "A target zone model with the terminal condition of joining a currency area," Applied Economics Letters, Taylor & Francis Journals, vol. 18(13), pages 1273-1278.
    2. Paul R. Krugman, 1991. "Target Zones and Exchange Rate Dynamics," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(3), pages 669-682.
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    Cited by:

    1. Arcand, Jean-Louis & Kumar, Shekhar Hari & Hongler, Max-Olivier & Rinaldo, Daniele, 2023. "Can one hear the shape of a target zone?," Journal of Mathematical Economics, Elsevier, vol. 107(C).

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    More about this item

    Keywords

    Exchange rate target zone; Ornstein-Uhlenbeck process; Ito’s lemma; Kumer function;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • F31 - International Economics - - International Finance - - - Foreign Exchange

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