To offer an illustration of the GJR approach, using monthly S&P500 returns from December 1979 until June 1998, the following results would be obtained, with t-ratios in parentheses

(9.49)

(9.50)

Note that the asymmetry term, γ, has the correct sign and is significant.

To see how volatility rises more after a large negative shock than a large positive one, suppose that and consider If this implies that However, a shock of the same magnitude but of opposite sign, implies that the fitted conditional variance for time t will be