Measuring Black Swans in Financial Markets

Abstract

There exists a well-developed statistical theory predicting extreme price values for financial markets known as extreme value theory (EVT). This approach relies on the seemingly obvious, but rarely analyzed, assumption that price displacement extremes actually exist for various markets. This paper attempts to describe the behavior of financial markets as a set of functions in terms of the dynamic variables price and time based on the net difference between ask and bid volumes over a unit period, thereby offering evidence to support the assumption that price extremes exist. Yet, it’s not meaningful to show merely that extremes exist. If the extreme negative price displacement simply represents a complete market collapse then the assumption becomes trivial. Accordingly, the paper also introduces a method to determine whether price displacements are constrained by non-trivial extremes. This description might have implications for EVT and market risk management in approximating the magnitude of “Black Swan” events. The paper also shows that if one can closely approximate the magnitude of such a rare event, one cannot also predict when the event will occur with any meaningful degree of certainty.