GARCH (1,1) - Scalling Variance

[syaiful]

Hi David, :lol:

The parameters in a GARCH (1,1) model are
w =0.000002
alpha= 0.04
beta =0.95
The current volatility level is 1% per day

(i) What is the long run average variance rate? (ans : 0.0002)
(ii) What is the expected variance in 20 days? (ans : 0.000118)

The part (i) is easy but can you explain the part (ii) ?

Regards,

*Syaiful S

 

[David Harper CFA FRM]

Hi Syaiful

You want Hull 21.13:
E(variance + t) = L.R. Variance + (alpha + beta)^t * (current variance - LR Variance)
in this case, as .000002/(1-.95-.04) = .0002 = LR Variance
= .0002 + (.95+.04)^20*(1%^2 - .002) = 0.00011821

Thanks, David

 

[syaiful]

Ok thanks David.