Bidirectional bond percolation model for the spread of information in financial markets

TL;DR

This paper models the spread of information in financial markets using a bidirectional bond percolation process on a Galton-Watson tree, providing explicit calculations of cluster size moments and decay properties.

Contribution

It introduces a novel bidirectional percolation model for information spread and derives explicit formulas for cluster size moments and decay behavior in this context.

Findings

Explicit formulas for the first and second moments of the information cluster size.

Proof of exponential decay of cluster diameter in the subcritical phase.

Modeling of information spread as a bidirectional bond percolation process.

Abstract

Information is a key component in determining the price of an asset in financial markets, and the main objective of this paper is to study the spread of information in this context. The network of interactions in financial markets is modeled using a Galton-Watson tree where vertices represent the traders and where two traders are connected by an edge if one of the two traders sells the asset to the other trader. The information starts from a given vertex and spreads through the edges of the graph going independently from seller to buyer with probability $p$ and from buyer to seller with probability $q$. In particular, the set of traders who are aware of the information is a (bidirectional) bond percolation cluster on the Galton-Watson tree. Using some conditioning techniques and a partition of the cluster of open edges into subtrees, we compute explicitly the first and second moments of the cluster size, i.e., the random number of traders who learn about the information. We also prove exponential decay of the diameter of the cluster in the subcritical phase.