Bidirectional bond percolation model for the spread of information in financial markets
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 GaltonWatson 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 GaltonWatson 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.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.04958
 Bibcode:
 2021arXiv210904958C
 Keywords:

 Mathematics  Probability;
 60K35
 EPrint:
 14 pages, 1 figure