Using First-Passage-Time Density to Assess Realignment Risk of a Target Zone

Abstract

This paper proposes a path-dependent approach for estimating realignment probabilities of targeted exchange rates based on the first-passage-time (FPT) density instead of the commonly used path-independent approach. We consider that path dependency is an intrinsic characteristic of realignment risk because a realignment of an exchange rate can occur whenever a committed band by a central bank is breached. A mean-reverting lognormal process is considered in the FPT approach. Based on market data of the British pound and Italian lira during the ERM crisis of 1992, the realignment probabilities of the currencies estimated under the proposed approach show that path dependency is quantitatively significant, compared with the path-independent approach. The first-hitting time and the time of the maximum slope of the FPT density have forward-looking capability of assessing realignment risk of the pound and lira target zones.