We continue our series of posts on order book models by considering an order book model proposed by Tobias Preis [1], which is able to reproduce log-normal order book side profile. There are more modifications of this model considered in the aforementioned paper [1]. One of them is simpler and reminiscent of the order book model by Cristelli, which was discussed in a previous post, couple of them are more sophisticated and able to reproduce other interesting stylized facts.

It is quite possible that we will discuss some of the modifications sometime later on Physics of Risk, but now let us describe the chosen version of the model proposed by Tobias Preis.

Though this topic and the way it is presented differs from the usual way we write our posts, but this TED talk by a historian Y. N. Harari shares similar foundations. Y. N. Harari talks about the possible political phase transition (from democracy to fascism) and how the Big data could empower it. We invite you to ponder about this material.

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.