A Theory of 'Auction as a Search' in speculative markets

TL;DR

This paper models high-frequency trading as a search process in an order book, using diffusion-based agent behavior to analyze how prices and volumes emerge in speculative markets.

Contribution

It introduces a total order book model with zero intelligence agents and analyzes different search dynamics like Levy and Brownian motion.

Findings

Diffusion mechanisms influence transaction price search.

Superdiffusive search can outperform Brownian in certain scenarios.

Analytic and numerical results clarify market dynamics.

Abstract

The tatonnement process in high frequency order driven markets is modeled as a search by buyers for sellers and vice-versa. We propose a total order book model, comprising limit orders and latent orders, in the absence of a market maker. A zero intelligence approach of agents is employed using a diffusion-drift-reaction model, to explain the trading through continuous auctions (price and volume). The search (levy or brownian) for transaction price is the primary diffusion mechanism with other behavioural dynamics in the model inspired from foraging, chemotaxis and robotic search. Analytic and asymptotic analysis is provided for several scenarios and examples. Numerical simulation of the model extends our understanding of the relative performance between brownian, superdiffusive and ballistic search in the model.