Electronic Foreign-Exchange Markets and Passage Events of Independent Subordinators

Abstract

We set up a model for electronic foreign-exchange markets, suggesting subordinators to represent sellers' and buyers' offers. Its analysis naturally leads to the study of level passage events. The classical level passage event concerns the joint law of the time, height, and jump size observed when a real-valued stochastic process first exceeds a given level h. We provide an up-to-date treatment in the case when this process is a subordinator, and extend these results to a multivariate setting.