Interpreting GARCH (1,1) model with external regressor in variance equation using rugarch I run a standard GARCH (1,1) model and obtain the following results.

Thereafter, I add an external regressor in the same model and obtain the following results:

The GARCH coefficient (beta1) is zero and the p-value is 1. The coefficient of the external regressor (vxreg1) is 0.415 with p-value of 0.000.
I use the robust standard errors.
How to interpret the result? Should I concur that the external regressor reduces/removes volatility contemporaneously?

Interesting. I would not say the external regressor reduces/removes volatility but it is able to fit/explain it better than the previous period's conditional variance $\sigma_{t-1}^2$ can. This reminds me a bit of the realized GARCH model. There, including lagged realized variance into the conditional variance equation tends to make the lagged squared return term not statistically significant; see slide 36 of Peter R. Hansen's "Lecture 3: Realized GARCH Models" (2016). Meanwhile, in your case the external regressor does the same for lagged conditional variance.
