Liquidity Crisis, Granularity of the Order Book and Price Fluctuations

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 $<\varphi (\omega ,g){>}_g\sim {\omega }^{\delta }$ with $\delta \approx 0.59$. Instead the dependence on the granularity is $\varphi (\omega ,g|\omega )\sim g^{\alpha }$ 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.

18 pages, 7 figures

References in corpus (5)

• A theory for long-memory in supply and demand
• Minimal Agent Based Model for Financial Markets I: Origin and Self-Organization of Stylized Facts
• Minimal Agent Based Model for Financial Markets II: Statistical Properties of the Linear and Multiplicative Dynamics
• Critical comparison of several order-book models for stock-market fluctuations
• Mechanisms of Self-Organization and Finite Size Effects in a Minimal Agent Based Model

Cited by in corpus (6)

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• Asymmetric statistics of order books: The role of discreteness and evidence for strategic order placement
• Liquidity crises on different time scales