Liquidity Crisis, Granularity of the Order Book and Price Fluctuations

TL;DR

This paper presents a microscopic model linking order book liquidity, measured by granularity, to price fluctuations, revealing a divergence in fluctuations as liquidity diminishes, which helps explain large market swings.

Contribution

The study introduces a novel microscopic model connecting order book granularity to price impact, highlighting the divergence of fluctuations as liquidity approaches zero.

Findings

Price impact surface depends on volume and granularity.

Power law relation between volume and impact with exponent ~0.59.

Price fluctuations diverge as granularity approaches zero.

Abstract

We introduce a microscopic model for the dynamics of the order book to study how the lack of liquidity influences price fluctuations. We use the average density of the stored orders (granularity $g$) as a proxy for liquidity. This leads to a Price Impact Surface which depends on both volume $\omega$ and $g$. The dependence on the volume (averaged over the granularity) of the Price Impact Surface is found to be a concave power law function $<\phi(\omega,g)>_g\sim\omega^\delta$ with $\delta\approx 0.59$. Instead the dependence on the granularity is $\phi(\omega,g|\omega)\sim g^\alpha$ with $\alpha\approx-1$, showing a divergence of price fluctuations in the limit $g\to 0$. Moreover, even in intermediate situations of finite liquidity, this effect can be very large and it is a natural candidate for understanding the origin of large price fluctuations.