50. 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:
\[ o_n = \alpha r_{n-1} + \beta o_{n-1} + v_i, \]
In this context, \( o_n \) represents the index variance on day \( n \), \( r_{n-1} \) represents the return on day \( n-1 \), and \( o_{n-1} \) 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 \( \alpha \) and \( \beta \) that would ensure a stable GARCH (1,1) process. | Financial Risk Manager Part 1 Quiz - LeetQuiz
Financial Risk Manager Part 1
Get started today
Ultimate access to all questions.
Comments
Loading comments...
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.