The detailed simulations and analysis we provide in "Quantum Walk model of extreme price events" suggest that algorithm inspired by quantum physics provide a powerful framework for predictive modelling of these events. As quantum physics suggest that extreme events will occasionally occur, a quantum walk (QW) is a more appropriate choice for simulation than classical probability distributions.

We further illustrate here using the price simulation of the Japanese price crash on August 5, 2024. The price turning point is identified to allow for a reversal in the crash direction within the model. We find that the abnormal rise then sudden drop in market depth structure positions occur at the turning point in all the crashes analysed with this method. Further results in the paper include simulations of several CME futures contracts including the E-mini S&P 500 flash crash on May 5, 2010, the ETF August 2015 flash crash, the Bitcoin flash crashes in 2019 and 2023. In addition, we simulate large price increases in the case of the US Treasury flash rally back in October 2015. Across all these events, the collapse of market depth was used as an indicator for the major price turning point and consequently the point at which the direction would reverse within the simulation. 

We model flash events using machine learning. We build a Long Short Term Memory (LSTM) model that generates a particular Quantum Walk distribution at each time. The subsequent price is randomly selected from this distribution. The QW LSTM model is trained on existing flash crash, to be able to capture changes in liquidity conditions due to selling pressure through the training parameters: top-of-book depth with trading volume. An out-of-sample test suggests that the model is able to provide a warning signal of an upcoming crash, which could be useful for policy analysis.