Construction of models for bounded price processes: the case of the HKD exchange rate

Abstract

This paper discusses construction of evolution models for financial time series evolving within a given interval. We calibrated a model for the case of the USD/HKD exchange rate after the separation of strong and weak side convertibility undertakings, in which the rate is confined to a specified corridor. This process represents an interesting example of a tradable bounded process. A 1D model was able to replicate the bounded distribution of the process, but a 2D model better captured dynamics as measured by the volatility without losing features of the 1D model. We briefly consider the ergodic properties of these models.