We continue our series of posts on order book models by considering an order book model proposed by Cristelli et al. [1], which is able to reproduce power-law price change. Originally this model was develop to study order impacts on a price in case of finite liquidity (in case when the order book is not tightly packed). Indeed it seems that when there are noticeable gaps behind the best bids, going deeper into the respective order book side, a couple of consecutive orders may cause power-law fluctuations.

Long ago we have implemented a simple traffic model, Nagel-Schreckenberg model (see this post). This model demonstrates how small errors or perturbations to traffic flow could amplify and cause traffic jams.

While these errors are the reason for the jams, avoiding them is not that easy. Sometimes these errors are even useful as they help us drive safer. From individuals perspective it is obviously better to be overly cautious than overly bold. In this way you can avoid traffic accidents.

So how to fix traffic? It appears that obvious answers, such as building more roads or adding lanes, do not work that well. To understand why it is so and for some ideas on how to fix traffic we invite you to watch a video by SciShow.

Previously we have discussed what order book is. We have also discussed simplified model inspired by physics (here. Let us now consider another simple model [1], which appears to be a bit more realistic model of the order book.

Here on Physics of Risk we often are interested in the power spectral density of the time series. We have earlier provided a couple of interactive examples (see here, here and here) illustrating the concept as well as a brief introductory discussion. In this post we would like to suggest viewing a video by 3Blue1Brown in which an interesting intuition on this very topic is provided in a very fascinating manner.

Last time we have discussed what order book is, and now we will present a simple model for the order book [1], which was inspired by reaction-diffusion model from physics.

Note that the full model considered in [1] is more complex than we discuss in this post. Here we only reproduce the results of the model with "noise traders" only (as discussed in Section IV B of the article).