Unique Fundamental Dynamics of Target-zone Exchange Rates

Abstract

We have provided a rigorous derivation of the asymmetric mean-reverting fundamental dynamics proposed by Lo and coworkers (2015) for target-zone exchange rates, and have shown that the proposed fundamental dynamics is the unique choice and described by the Rayleigh process. By analogy, such a fundamental can be treated as a one-dimensional overdamped Brownian particle moving in a logarithmic-harmonic potential well. In addition, we have demonstrated that the predicted exchange rate distributions can take several different shapes, which may correspond to possible realignments and widely different (marginal and intra-marginal) intervention policies. The shapes of these distributions represent the predicted distributions discussed in previous theoretical models which only generate one or two shapes. Moreover, we have succeeded in performing explicit calibration of the proposed fundamental dynamics, thus confirming the validity of our model. Unlike the Krugman model, our model is capable of explaining the empirical observations that the exchange rate dynamics is sticky near the edges of the band, and that both positive and negative interest rate differentials can appear in the entire target zone.