Using Bell violations as an indicator for financial market crisis

The failure to identify and measure financial risk carries significant social and economic consequences. This paper introduces a novel framework for analyzing financial stress and crises, based on the Bell inequalities, a foundational framework in causal analysis, originally developed in quantum mechanics. Traditional approaches to crisis analysis do not, in general, adequately represent event-based dependencies and the distribution of tail risks inherent in complex financial systems. The proposed approach is underwritten by a generic causal framework, which we think is suitable for financial analysis: we offer an index for financial stress and we explore its value in detecting extreme market co-movements, which may serve as an early crisis warning signal.

Our analyses employ a rolling-window approach to analyze financial time series data. We utilize S&P 500 and STOXX Europe 600 stocks and consider three historical crises, namely the 2008 financial crisis, the EU debt crisis and the COVID-19 pandemic, which mark some of the largest downturns of financial markets in the last two decades. The findings demonstrate the framework's ability to align the number of observed Bell inequalities violations with observed peaks in market stress. In particular, the framework shows good performance against CDS spreads as a crisis indicator and is less erratic than the traditional Pearson correlation of price returns. It aligns well with implied equity option volatility as measured by VIX. Overall, we think the present causal framework has promising properties and merits further examination.