Financial Risk Manager Part 1

Get started today

Ultimate access to all questions.

Explanation:

For a GARCH(1,1) process to be stable, the sum of the parameters $\alpha$ and $\beta$ needs to be less than 1.0.

Let's verify each option:

Option A: $\alpha + \beta = 0.073637 + 0.927363 = 1.001000$ (slightly greater than 1.0)
Option B: $\alpha + \beta = 0.075637 + 0.923363 = 0.999000$ (less than 1.0)
Option C: $\alpha + \beta = 0.084637 + 0.916363 = 1.001000$ (slightly greater than 1.0)
Option D: $\alpha + \beta = 0.086637 + 0.914363 = 1.001000$ (slightly greater than 1.0)

Only Option B satisfies the stability condition where $\alpha + \beta < 1.0$ . This ensures that the GARCH(1,1) process is mean-reverting and stationary over time.

Explanation:

For a GARCH(1,1) process to be stable, the sum of the parameters $\alpha$ and $\beta$ needs to be less than 1.0.

Let's verify each option:

Option A: $\alpha + \beta = 0.073637 + 0.927363 = 1.001000$ (slightly greater than 1.0)
Option B: $\alpha + \beta = 0.075637 + 0.923363 = 0.999000$ (less than 1.0)
Option C: $\alpha + \beta = 0.084637 + 0.916363 = 1.001000$ (slightly greater than 1.0)
Option D: $\alpha + \beta = 0.086637 + 0.914363 = 1.001000$ (slightly greater than 1.0)

Only Option B satisfies the stability condition where $\alpha + \beta < 1.0$ . This ensures that the GARCH(1,1) process is mean-reverting and stationary over time.

Comments (0)

No comments yet.

A risk analyst is estimating the variance of stock returns on day n, given by $\sigma_n^2$ , using the equation,
$\sigma_n^2 = \gamma V_L + \alpha u_{n-1}^2 + \beta \sigma_{n-1}^2,$
where $u_{n-1}$ and $\sigma_{n-1}$ represent the return and volatility on day $n-1$ , respectively.

If the values of $\alpha$ and $\beta$ are as indicated below and the expected value of the return is constant over time, which combination of values is correct for a GARCH(1,1) process?

Exam-Like

$\alpha = 0.073637$ and $\beta = 0.927363$

16.7%

$\alpha = 0.075637$ and $\beta = 0.923363$

33.3%

$\alpha = 0.084637$ and $\beta = 0.916363$

33.3%

$\alpha = 0.086637$ and $\beta = 0.914363$

16.7%