Question

2. Assume that an index at close of trading yesterday was 1,040 and the daily volatility of the index was estimated as 1% per day at that time. The parameters in a GARCH(1,1) model are ω = 0.000002, α = 0.06, and β = 0.92. If the level of the index at close of trading today is 1,060, what is the new volatility estimate?

Answer 1

This question asks for new volatility i.e new standard deviation

Price at opening of index = 1040

Price at closing of index = 1060

Profit made =20

U(n-1)= 20/1040 = 0.0192

Variance   = = 0.0001162

Hence, standard deviation = = 0.01078 = 1.078%

Hence, the new volatility estimate is 1.078% per day.