The Relations between Volatilities and the Extreme Stock Price Declines: A Test in the Japanese Equity Markets

The objective of this paper is to examine the predictability of the forecast volatilities for the extreme stock price declines in the Japanese stock markets. Our empirical tests reveal that the forecast volatilities from the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model and the GARCH-in-mean model statistically significantly predict the extreme stock price declines in the Japanese stock markets. Further, we also clarify that the forecast power of the volatilities from the GARCH-in-mean model is stronger than that from the standard GARCH model.