# Hull EOC Q&A Question 19

#### Nicole Seaman

##### Director of FRM Operations
Staff member
Subscriber
Posted by @akrushn2 in another thread

Can someone please confirm q19 and whether the answer is correct? I get 1.614% as the answer on my end. the calculations are sqrt( 0.0001 + 0.04*(298/300 -1)^2 + 0.94*0.013^2) = 1.614%.

Question 10.19

Suppose that the price of an asset at close of trading yesterday was $300 and its volatility was estimated as 1.3% per day. The price at the close of trading today is$298. Update the volatility estimate using
• The EWMA model with λ = 0.94
• The GARCH(1,1) model with ω = 0.000002, α = 0.04,and β = 0.94.

The proportional change in the price of the asset is -2/300 = -0.00667.

a) Using the EWMA model the variance is updated to 0.94 x 0.013^2 + 0.06 x 0.00667^2 = 0.00016153 so that the new daily volatility is sqrt 0.00016153 = 0.1275 or 1.271% per day.

b) Using GARCH (1,1) the variance is updated to 0.000002 + 0.94 × 0.013^2 + 0.1275 or 1.275% per day.

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @akrushn2 Please note that ω = 0.0000020 (not 0.0001) such that the given answer looks correct to me. Please see below; XLS is here https://www.dropbox.com/s/0e6u50q43qsl4qk/081219-hull-rmfi-10-19.xlsx?dl=0