The authors develop a prediction framework on the premise that the self-exciting pattern of stock returns around a market crash is similar to that of seismic activity around an earthquake. By exploring similarities between stock market crashes and earthquakes, the authors develop an early warning system (EWS) that they use to predict crash days within a given period. They begin with a discussion of the causes of market crashes and examine why the self-exciting nature of financial crashes is comparable to activity leading up to earthquakes.

Next, they specify their model and estimation method, review the estimation results, give an assessment of the model simulations, and compare the effectiveness of the EWS with that of traditional volatility models. The authors conclude with a review and suggestions for future research.

Following the credit crisis, there has been heightened interest in predicting the next crash. Financial market regulators are increasingly concerned with systemic risk and have implemented policies designed to reduce disorderly crashes. There is also great interest from risk managers in assessing the risk of large negative price movements.

The authors attempt to improve on existing downside risk measurement methods by leveraging research used in the dynamics of earthquake sequences. They note that extremes in financial markets occur more often than expected under normal conditions, which creates challenges when applying traditional statistical models. The authors adopt the epidemic-type aftershock sequence (ETAS) model. With this model, the probability of a shock increases after a shock has occurred, after which the probability declines as a function of time since the last shock—a quality known as being self-exciting. The authors incorporate the ETAS framework into their EWS model.

They test their models using out-of-sample data beginning with the 2008 financial crisis. Their results reveal hit rates that are significantly higher than false alarm rates. In addition, the models perform favorably (i.e., more accurately and quickly) relative to other approaches. The authors’ research confirms that extreme movements in the S&P 500 Index tend to be triggered by previous extreme movements and that crashes are self-enforcing. They also find that larger extremes are observed after the occurrence of more and/or big events than after a tranquil period and that larger events trigger more events than smaller events.

This research will be of particular interest to traders, financial market regulators, and risk management professionals who want to test/apply the authors’ EWS model. It may also have broad appeal given the general interest in the detection and avoidance of market crashes. In addition, those interested in the area of econophysics, including nonfinancial academics, may be interested in how earthquake modeling has been applied to financial markets.

To conduct their research, the authors use S&P 500 data from January 1957 to September 2008 as a model calibration period. They construct 4 primary models with four variations each, for a total of 16 models. The authors focus on negative market shocks and observe 687 events over the 13,738 trading days. According to the models, only 81–113 of the 687 observed events arrived spontaneously, with 76%–85% of the events being triggered by other events.

The authors evaluate their models on an out-of-sample evaluation period: 1 September 2008–1 January 2013. They test each of the 16 models over this period and assess effectiveness using Hanssen–Kuiper skill scores (KSS) for movements above the 95%, 97%, and 99% extremes. The KSS are computed as the hit rate minus the false alarm rate. The KSS for all EWSs are significantly positive.

When they compare the results of EWS models with those of GARCH (generalized autoregressive conditional heteroskedasticity) and ACD (autoregressive conditional duration) models, they find that the ACD models predict too few events, resulting in KSS around zero or even slightly negative. The GARCH models are capable of delivering accurate warning signals, although with slightly lower KSS compared with the EWS. A drawback of the GARCH approach is it takes more than one hour to execute the simulation and deduce alarm signals compared with less than one second for the EWS.

This research does have some limitations, including the relatively limited out-of-sample testing period, which could be addressed in future studies.

Viewing financial market crashes as earthquakes is certainly a novel idea. It is natural to be skeptical that applying techniques used to model seismic activity to financial markets, although interesting, may be a stretch. Earthquakes are a natural phenomenon, whereas market crashes are a human construct with no physical reference. The authors’ argument that the self-exciting nature of both events supports modeling similarities, however, makes intuitive sense. In addition, simulation results indicate that their EWS model has demonstrated some statistical relevance. To increase confidence relative to existing volatility models, it will be important to see how the EWS performs when applied to additional out-of-sample datasets.