On the Ollivier-Ricci curvature as fragility indicator of the stock markets

TL;DR

This paper investigates the use of Ollivier-Ricci curvature as an indicator of stock market fragility, analyzing its properties, parameter sensitivity, and proposing an alternative calculation method to improve crisis detection.

Contribution

It provides a detailed analysis of the Ollivier-Ricci curvature indicator, including heuristics for parameter selection and an alternative computation approach based on sub-graphs.

Findings

The indicator accurately signals financial crises under certain conditions.

Parameter choices significantly affect the indicator's responsiveness.

An alternative method using specific sub-graphs enhances the calculation of the curvature indicator.

Abstract

Recently, an indicator for stock market fragility and crash size in terms of the Ollivier-Ricci curvature has been proposed. We study analytical and empirical properties of such indicator, test its elasticity with respect to different parameters and provide heuristics for the parameters involved. We show when and how the indicator accurately describes a financial crisis. We also propose an alternate method for calculating the indicator using a specific sub-graph with special curvature properties.