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).

All models of the financial markets we have presented on Physics of Risk to this date did not make any assumptions about the actual market microstructure. The previously discussed models assumed that some kind of market maker takes in the information about the market sentiments. This market marker sets a "fair" price and everyone is assumed to be happy with it. Similar price discovery mechanism was used in the past in various stock exchanges. In the literature this mechanism is referred to as the Walrasian Market. In contemporary stock exchanges Walrasian Market is replaced with the order book. This post is meant to explain some of the related terminology, which will be relevant in future posts about order book models.