Dr. Jayanthi Sankaran
Well-Known Member
Hi David,
In the answer below isn't the constraint eg persistence (alpha + beta) < 1 and not (alpha + beta) < 0. Please clarify:
107.3 [This is an exercise to help clarify MLE. Of course the exam cannot ask this question]. Here is a spreadsheet that contains the EUR/USD exchange rate for the last 31 trading days. Use Excel's solver function to apply the MLE method to solve for GARCH(1,1) parameters. What is beta?
a. 0.82
b. 0.86
c. 0.90
d. 0.94
107.3 A. 0.82
Your answer may vary, but notice I maximized the sum of the log function subject to constraints; e.g., persistence (alpha + beta) < 0, or GARCH is unstable. My param estimates are:
Alpha = 0.1058
Beta = 0.8216
Omega = 0.0000010; i.e., implies LR daily volatility = 0.37%
107.4. C. omega = 0.0, beta = lambda, alpha = 1.0 - lambda
As EWMA does not mean revert, the weight (gamma) applied to the long-run variance is zero
Thanks!
Jayanthi
In the answer below isn't the constraint eg persistence (alpha + beta) < 1 and not (alpha + beta) < 0. Please clarify:
107.3 [This is an exercise to help clarify MLE. Of course the exam cannot ask this question]. Here is a spreadsheet that contains the EUR/USD exchange rate for the last 31 trading days. Use Excel's solver function to apply the MLE method to solve for GARCH(1,1) parameters. What is beta?
a. 0.82
b. 0.86
c. 0.90
d. 0.94
107.3 A. 0.82
Your answer may vary, but notice I maximized the sum of the log function subject to constraints; e.g., persistence (alpha + beta) < 0, or GARCH is unstable. My param estimates are:
Alpha = 0.1058
Beta = 0.8216
Omega = 0.0000010; i.e., implies LR daily volatility = 0.37%
107.4. C. omega = 0.0, beta = lambda, alpha = 1.0 - lambda
As EWMA does not mean revert, the weight (gamma) applied to the long-run variance is zero
Thanks!
Jayanthi