Question
The following table shows the daily closing prices (in rand) for the non dividendpaying share of Standard Bank Group Limited (SBK) during the trading period
The following table shows the daily closing prices (in rand) for the non dividendpaying share of Standard Bank Group Limited (SBK) during the trading period from 12 to 27 June 2023. Date Price (Si) 2023-06-12 16.734 2023-06-13 17.000 2023-06-14 17.333 2023-06-15 17.371 2023-06-19 17.378 2023-06-20 17.700 2023-06-21 17.710 2023-06-22 17.550 2023-06-23 17.328 2023-06-26 17.274 2023-06-27 17.350 7.1 Determine the daily log-return (ui)i=1,2, ,10 of the SBKs share prices. (5) Hint: The first log-return will be on the date 2023-06-13, and it is given by u1 = 0.015771. 7.2 Use the GARCH (1,1) model to estimate the daily historical volatility (i) of the SBKs share prices. (17) Hint: The GARCH (1,1) model is given by 2 i = VL + u2 i1 + 2 i1 , where is the weight associated with VL, is the weight assigned to u 2 i1 , and is the weight assigned to 2 i1 . The parameters , and verify the condition + + = 1 and have to be estimated. See the prescribed textbook, Chapter 23 (Estimating volatilities and correlations) for more information. 7.3 Assuming that the current volatility is given on the 27 June 2023, find the expected volatility on 29 June 2023. (2)
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