Liquidity Crisis, Granularity of the Order Book and Price Fluctuations
英文摘要：
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 $ω$ 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 $<ϕ(ω,g)>_g\simω^δ$ with $δ\approx 0.59$. Instead the dependence on the granularity is $ϕ(ω,g|ω)\sim g^α$ with $α\approx-1$, 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.
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