Markov and long-memory modelling of bounded financial processes: the case of a currency band

Abstract

This work constructs evolution models for financial time series evolving within a bounded interval. They are calibrated using the USD/HKD exchange rate when the rate is confined to a specified corridor. Within the general Markov framework, a 1D model replicated the bounded distribution of the process, but a 2D model better captured dynamics as measured by the volatility. By estimating the Hurst exponent using the rescaled range method, fractional Brownian motion could be employed.