Efficiency of the Price Formation Process in Presence of High Frequency Participants: a Mean Field Game analysis

TL;DR

This paper models price formation in order-driven markets with heterogeneous traders, including HFTs and institutional investors, using mean field game theory to analyze liquidity, prices, and spreads, revealing efficiency differences.

Contribution

It introduces a mean field game framework to analyze the impact of high frequency traders and institutional investors on market efficiency and liquidity.

Findings

Markets with only institutional investors show liquidity imbalances and price deviations.

Presence of HFTs alleviates macro liquidity issues but benefits HFTs more than institutional investors.

Market efficiency improves with HFTs, but institutional investors face higher trading costs.

Abstract

This paper deals with a stochastic order-driven market model with waiting costs, for order books with heterogenous traders. Offer and demand of liquidity drives price formation and traders anticipate future evolutions of the order book. The natural framework we use is mean field game theory, a class of stochastic differential games with a continuum of anonymous players. Several sources of heterogeneity are considered including the mean size of orders. Thus we are able to consider the coexistence of Institutional Investors and High Frequency Traders (HFT). We provide both analytical solutions and numerical experiments. Implications on classical quantities are explored: order book size, prices, and effective bid/ask spread. According to the model, in markets with Institutional Investors only we show the existence of inefficient liquidity imbalances in equilibrium, with two symmetrical situations corresponding to what we call liquidity calls for liquidity. During these situations the transaction price significantly moves away from the fair price. However this macro phenomenon disappears in markets with both Institutional Investors and HFT, although a more precise study shows that the benefits of the new situation go to HFT only, leaving Institutional Investors even with higher trading costs.