A risk analyst is predicting the variability in returns of a stock index for the next trading day using a model known as GARCH (1,1). The GARCH (1,1) model employed is represented by the following equation: $\sigma_t^2 = \alpha_{t-1} + \beta \sigma_{t-1}^2 + \epsilon_t$ In this model:

• $\sigma_t^2$ represents the index variance on day $t$
• $r_{t-1}$ signifies the return on day $t-1$
• $\sigma_{t-1}^2$ stands for the volatility on day $t-1$

Assuming that the expected return stays constant, which specific values for the parameters $\alpha$ and $\beta$ are necessary to ensure the stability of the GARCH (1,1) model?