Analysis of intermittence and log-periodicity of foreign exchange rates near a crash

Abstract

Many believe that financial indices near a crash exhibit a type of critical point characterized by log-periodic signatures. Models have been developed based on these ideas in an attempt to mathematically characterize financial data about to crash. Few of these models consider the property of intermittency. Intermittency is a concept borrowed from fluid dynamics that essentially implies that a system alternates between a stable, or predictable, state and unstable state. One model that attempts to characterize crashes incorporates intermittency in the form of log-stationary intervals. It models the asset price as a step function that follows an underlying power law. Like other models, the asset experiences faster than exponential growth at some critical price, which is time of the crash. However, it makes the further assumption, based on empirical evidence, that the price of an asset remains stable within some interval before jumping, usually at the announcement of some important piece of information. These stable periods correspond to the steps in the step function. The model has been applied, with some success, to various financial indices but it has yet to be applied to currencies. We believe the high variability of currencies and currency based assets will limit the model's ability to describe such assets before the time of the crash. We thus apply this model to foreign exchange rates that involve the Icelandic krona in order to test its ability to accurately and consistently describe a crash.