Forecasting Crashes with a Smile

We derive option-implied bounds on the probability of a crash in an individual stock, and argue a priori that the lower bound should be close to the truth. The lower bound successfully forecasts crashes both in and out of sample. Crucially, our theory-based approach avoids the “crying wolf” problem faced by risk-neutral crash probabilities, which severely overstate crash risk during crisis periods. Despite having no free parameters, the lower bound outperforms elastic net, ridge, and Lasso models that flexibly but atheoretically combine stock characteristics, risk-neutral probabilities and the bound itself, because such models overfit during crisis periods.

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