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

Ajevskis, Viktors (2015): An exchange rate target zone model with a terminal condition and mean-reverting fundamentals.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Exchange rate target zone, Ornstein-Uhlenbeck process, Ito’s lemma, Kumer function
• Subjects: C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling; F - International Economics > F3 - International Finance > F31 - Foreign Exchange

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