Financial Risk Manager Part 1

Get started today

Ultimate access to all questions.

Explanation:

For a GARCH (1,1) process to be stable, the parameters α (alpha) and β (beta) must be positive and their sum must be less than 1. This is because the GARCH model is a way to model financial time series data and estimate the volatility of returns. The stability condition ensures that the variance of the process does not explode or become negative, which would be unrealistic in financial contexts.

In the provided options:

Option A: α = 0.073637 and β = 0.927363, the sum is 1.000000, which violates the stability condition.
Option B: α = 0.075637 and β = 0.923363, the sum is 0.999000, which satisfies the stability condition.
Option C: α = 0.084637 and β = 0.916363, the sum is 1.001000, which violates the stability condition.
Option D: α = 0.086637 and β = 0.914363, the sum is 1.001000, which also violates the stability condition.

Therefore, the correct answer is B, as it is the only combination where the sum of α and β is less than 1, ensuring the stability of the GARCH (1,1) process.

Explanation:

In the provided options:

Option A: α = 0.073637 and β = 0.927363, the sum is 1.000000, which violates the stability condition.
Option B: α = 0.075637 and β = 0.923363, the sum is 0.999000, which satisfies the stability condition.
Option C: α = 0.084637 and β = 0.916363, the sum is 1.001000, which violates the stability condition.
Option D: α = 0.086637 and β = 0.914363, the sum is 1.001000, which also violates the stability condition.

Therefore, the correct answer is B, as it is the only combination where the sum of α and β is less than 1, ensuring the stability of the GARCH (1,1) process.

Comments (0)

No comments yet.

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.

Exam-Like

α = 0.073637 and β = 0.927363

8.1%

α = 0.075637 and β = 0.923363

66.1%

α = 0.084637 and β = 0.916363

16.1%

α = 0.086637 and β = 0.914363

9.7%