Real-time identification of the onset of financial rogue waves

Extreme events in financial systems, often captured by indicators such as volatility, remain difficult to identify close to their onset. Volatility shares many statistical properties with other natural, complex systems which experience extreme events, which we explore in this manuscript. We extend the analogy between rogue waves in optical and hydrodynamical systems to financial volatility by identifying rogue-wave-like peaks with similar statistical properties. We use a Schr\"odinger equation where the potential follows the shape of a Kerr nonlinearity to examine the properties of financial volatility indices within a moving time window. We see evidence of Anderson localisation as a rogue peak approaches in the VIX, and show that the numerical gradient of the system's minimum eigenvalue reliably spikes at the onset of an extreme event. We adapt our methodology to simulate the real-time arrival of data, and show that all but one of the VIX's major peaks can be detected given a reasonable amount of history. We then perform two out-of-sample tests, one for the VXO index, and one for the VSTOXX index, and successfully replicate our initial results, identifying all but one major peak (87.5% or 7/8) in both cases. This method of analysis shows considerable promise as a tool for identifying potential financial crises, aiding in their mitigation.