Forecasting Flash Crashes with Subordinated Lévy Processes

Abstract

We develop a novel intraday crash forecasting framework for the S&P 500 index using one-minute returns and advanced Lévy process modeling. A double subordinated Lévy process with Generalized Inverse Gaussian (GIG) subordinators replaces the tempered stable processes used in prior research, enabling richer dynamics in tail behavior. We show that this model provides early warning signals of "flash crashes"-sudden intraday price collapses-with up to a 30-minute lead time, significantly improving over the warnings achievable by earlier approaches. The model captures both the heavytailed distribution of returns and time-varying volatility, allowing us to estimate the probability of extreme drawdowns in real time. We integrate early warning indicators-a Chow test for structural breaks, a tail-loss ratio, and a Mahalanobis distance metric-into our forecasting scheme to corroborate impending market stress. In an empirical application to S&P 500 index data, our approach would have flagged the Aug 24, 2015 flash crash. The ability to anticipate crashes even by half an hour has profound implications for risk management and market regulation: armed with advance warning, portfolio managers can de-risk positions and liquidity providers or regulators can take preemptive measures to dampen a crash's impact. Our findings underscore the importance of modeling return distributions beyond classical assumptions and demonstrate a practical path toward mitigating the damage from rapid market meltdowns.

Keywords: Flash Crashes, Subordinated Lévy Processes, Early Warning Indicators