Let the daily return series on Hang Seng Index (HSI) at time t, denoted by y_t, follow a GARCH (1,1) process:

y_t= e_t where e_t~ N(0,²_t)

²_t= 0.00005+ 0.06e²_t-1+ 0.92²_t-1

(i) Assume that the HSI at close of trading at t-2 was 23,000 and the daily standard deviation of the HSI was estimated as 1% at t-1. Ifthe HSI at close of trading at t-1 was 23,100, estimate todays standard deviation. (5 marks)

(ii) What is your estimate of the standard deviation in 100 days? What is the estimate of the standard deviation per year that should be used to price the 100-day option on HSI, assuming 252 days per year? (10 marks)