An Exchange Rate Target Zone Model with a Terminal Condition and Mean-Reverting Fundamentals

TL;DR

This paper develops a model for exchange rates within target zones incorporating a terminal condition, analyzing bounded mean-reverting fundamentals with both analytical and numerical solutions.

Contribution

It introduces a novel exchange rate model with a terminal condition and compares solutions for bounded Brownian and Ornstein-Uhlenbeck processes.

Findings

Closed-form solution for Brownian motion case.

Numerical solutions for Ornstein-Uhlenbeck process.

Comparison of fundamental process specifications.

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 a band and that terminal condition for the exchange rate holds. 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.