A risk analyst is tasked with calculating the variance of returns for a stock index for the upcoming trading day. To accomplish this, the analyst utilizes a GARCH (1,1) model, which stands for Generalized Autoregressive Conditional Heteroskedasticity, and is essential for predicting future volatility based on past data. The model is represented by the following equation:
on=αrn−1+βon−1+vi,
In this context, on represents the index variance on day n, rn−1 represents the return on day n−1, and on−1 represents the volatility on day n−1. Given that the expected value of the return remains constant over time, identify the combination of values for α and β that would ensure a stable GARCH (1,1) process.