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

Viktors Ajevskis ()

MPRA Paper from University Library of Munich, Germany

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.

Keywords: Exchange rate target zone; Ornstein-Uhlenbeck process; Ito’s lemma; Kumer function (search for similar items in EconPapers)
JEL-codes: C02 C6 F31 (search for similar items in EconPapers)
Date: 2015-06-16
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https://mpra.ub.uni-muenchen.de/65078/1/MPRA_paper_65078.pdf original version (application/pdf)

Related works:
Working Paper: An Exchange Rate Target Zone Model with a Terminal Condition and Mean-Reverting Fundamentals (2015) Downloads
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