Financial instability from local market measures

TL;DR

This paper models how local market measures influence financial stability, revealing a phase transition from arbitrage-free to unstable markets driven by instrument diversity and heterogeneity.

Contribution

It introduces a stylized model analyzing the impact of heterogeneous local measures on market stability, deriving critical conditions for phase transition.

Findings

Market instability arises with increased instrument diversity and heterogeneity.

A sharp phase transition separates stable and unstable market regimes.

Analytical and numerical results confirm the critical thresholds for instability.

Abstract

We study the emergence of instabilities in a stylized model of a financial market, when different market actors calculate prices according to different (local) market measures. We derive typical properties for ensembles of large random markets using techniques borrowed from statistical mechanics of disordered systems. We show that, depending on the number of financial instruments available and on the heterogeneity of local measures, the market moves from an arbitrage-free phase to an unstable one, where the complexity of the market - as measured by the diversity of financial instruments - increases, and arbitrage opportunities arise. A sharp transition separates the two phases. Focusing on two different classes of local measures inspired by real markets strategies, we are able to analytically compute the critical lines, corroborating our findings with numerical simulations.