Market-crash forecasting based on the dynamics of the alpha-stable distribution

This paper investigates on the alpha-stable distribution capacity to capture the probability of market crashes by means of the dynamic forecasting of its alpha and beta parameters. On the basis of the GARCH-stable model, we design a market crash forecasting methodology that involves three-stepwise procedure: (i) Recursively estimation the GARCH-stable parameters through a rolling window; (ii) alpha-stable parameters forecasting according to a VAR model; and (iii) Crash probabilities forecasting and analysis. The model performance for alternative crash definitions is assessed in terms of different accuracy criteria, and compared with a random walk model as benchmark. Our applications to a wide variety of stock indexes for developed and emerging markets reveals a high degree of accuracy and replicability of the results. Hence the model represents an interesting tool for risk management and the design of early warning systems for future crashes.