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.
Highlights
IntroductionA “Black Swan” refers to a highly improbable event that lies significantly outside of normal expectations. For financial markets, such events typically manifest themselves as extreme price variations
There exists a well-developed statistical theory predicting extreme price values for financial markets known as extreme value theory (EVT)
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
Summary
A “Black Swan” refers to a highly improbable event that lies significantly outside of normal expectations. For financial markets, such events typically manifest themselves as extreme price variations. We use an extreme price increase variable as part of our mathematical formalism, this paper is careful to only claim a method for approximating price reductions This method is only potentially useful for markets that are robust and actively traded, and where the mean value of the price displacement ratio is close to zero. Even though these are not the standard probability methods of EVT, the paper’s conclusions offer an approximation of the magnitude of a price displacement extreme, which is a consistent element in traditional EVT analysis [16] [17] [18] In this way, the paper might make some substantive contribution to the EVT literature and market risk management [19] in addition to supporting the veracity of EVT’s.
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