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?_