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.

Over the years we have written multiple posts about the economic convergence phenomenon. We have also provided a couple of interesting apps, which could be used to study the real world data. Recently we have updated one of them with new data from World Bank (see this post or go straight to the related app).

Furthermore we have modified the old app to work with somewhat different data. Namely, the old app plotted GDP per capita series and the new app plots GDP per capita PPP series. GDP PPP is more interesting to some researchers as this GDP index is controlled for differing price levels between the countries.

We invite you to explore the data using the new app!

To open the interactive browser-based program, click on the image or here.