Macroscopic Equity Markets Model: Towards Predicting Financial Crashes

Abstract

This research examines the structural properties of the macroscopic model introduced in [AlShelahi and Saigal, 2018]. We present a theoretical analysis of the behavior of the macroscopic variables. In particular, we show that the model exhibits shock-like solutions, providing a new narrative for financial shocks. To solve the system of stochastic nonlinear partial differential equations adaptively, an integrative algorithm is devised and tested on abnormal and normal trading days. The results suggest that abnormalities can be identified before crashes. Our findings warrant further investigation into the macroscopic structure of equity markets.