A note on estimating realignment probabilities – A first-passage-time approach

This paper proposes a path-dependent approach for estimating realignment probabilities of targeted exchange rates based on first-passage-time distributions 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 first-passage-time approach. Based on market data of the British pound and mark during the ERM crisis of 1992, the realignment probabilities of the pound estimated under the proposed approach show that path dependency is quantitatively significant, compared with the path-independent approach.