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Hull EOC Q&A Question 19

Nicole Seaman

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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.

Answer:

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.
 
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