Liquidity Crisis, Granularity of the Order Book and Price Fluctuations

Matthieu Cristelli, V. Alfi, L. Pietronero and A. Zaccaria

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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 $ _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.

Date: 2009-02, Revised 2009-07
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Journal Article: Liquidity crisis, granularity of the order book and price fluctuations (2010)
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