Answer: a=0.075637andβ=0.923363

For a GARCH (1,1) process to be stable, the parameters α (alpha), β (beta), and ω (omega) must be positive and sum to 1. This is because the GARCH (1,1) model is defined as: \[ \sigma_t^2 = \omega + \alpha \epsilon_{t-1}^2 + \beta \sigma_{t-1}^2 \] where: - \( \sigma_t^2 \) is the variance of the return on day t, - \( \omega \) is the constant term, - \( \alpha \) is the coefficient of the lagged squared residual from the previous period, - \( \epsilon_{t-1} \) is the residual from the previous period, - \( \beta \) is the coefficient of the lagged variance from the previous period. In the given options, we are only concerned with the sum of α and β since ω is not provided. The sum of α and β must be less than 1 for the process to be stable. This is because if their sum is equal to or greater than 1, the variance could potentially explode to infinity over time, which is not realistic in financial markets. Analyzing the options: - Option A: \( \alpha = 0.073637 \) and \( \beta = 0.927363 \), their sum is \( 0.073637 + 0.927363 = 1.000999 \), which is greater than 1. - Option B: \( \alpha = 0.075637 \) and \( \beta = 0.923363 \), their sum is \( 0.075637 + 0.923363 = 0.999 \), which is less than 1. - Option C: \( \alpha = 0.084637 \) and \( \beta = 0.916363 \), their sum is \( 0.084637 + 0.916363 = 1.001 \), which is greater than 1. - Option D: \( \alpha = 0.086637 \) and \( \beta = 0.914363 \), their sum is \( 0.086637 + 0.914363 = 1.001 \), which is greater than 1. Only option B has a sum of α and β that is less than 1, making it the correct choice for a stable GARCH (1,1) process.

Author: LeetQuiz Editorial Team