# Constraints by estimating GARCH, EGARCH, GJR-GARCH models

I know that by estimating an GARCH model, given by: $$\sigma_t^2 = \omega + \alpha \epsilon_{t-1}^2 + \beta \sigma_{t-1}^2,$$

$$\omega, \alpha, \beta >0$$ and $$\alpha + \beta <1$$. But what are the constraints and bounds for a EGARCH and GJR-GARCH model, given by:

$$ln(\sigma_t^2) = \omega + \alpha \Big(\frac{|\epsilon|}{\sigma_t} - \sqrt{\frac{2}{\pi}}\Big) +\gamma \frac{\epsilon_{t-1}}{\sigma_{t-1}} + \beta ln(\sigma_{t-1}^2)$$
$$\sigma_t^2 = \omega + \alpha \epsilon_{t-1}^2 + \gamma \epsilon_{t-1}^2 \cdot 1_{\epsilon_{t-1}<0} + \beta \sigma_{t-1}^2$$