Please more detail, thanks. (a) Calculate the volatility (?2) of ABC and XYZ Sha

Question

Please more detail, thanks.

(a) Calculate the volatility (?2) of ABC and XYZ Shares. The parameter ? in the exponential weighted moving average (EWMA) ?-? ??.]2 + (1-A) U"n-model is 0.96. Forecast the 2018 Volatility of ABC using the 2016 and 2017 share prices 51.80 and 52.93 and Volatility of XYZ using share prices 67.14 and 67.35 with the aid of estimated volatility (a) and EWMA model? (b) Write the GARCH 1) model. Forecast the 2018 Volatility of ABC and XYZ shares using the 2016 and 2017 prices, estimated volatility and the given parameters of a GARCH (1, 1) model ?= 0.000003, ?=0.04, and -0.82 and ?= 0.000002. a 0.05, and p-0.82.respectively+ (c) Estimate the long-run average volatility of ABC and XYZ and comment on these values

Explanation / Answer

a) From the Covariance matrix (earlier part of the question) the recent estimate of volatility (ABC) ?2 is

0.0000442

The stock return of ABC: 52.93/51.80= 1.0218

Therefore, estimate of ABC volatility for 2018:

?2= 0.96(0.0000442) + (1-0.96) (1.0218)2

    =0.000042432 +0.04176301

    =0.04180

?=0.20436

From the Covariance matrix (earlier part of the question) the recent estimate of volatility (XYZ) ?2 is

0.000815

The stock return of XYZ: 67.35/67.14= 1.003128

Therefore, estimate of XYZ volatility for 2018:

?2= 0.96(0.000815) + (1-0.96) (1.003128)2

    =0.000042432 +0.04176301

    =0.041033

?=0.202566

b) The GARCH model estimate of Volatility:

ABC ?2=0.000003+0.04 (1.003128)2+0.82(0.0000442)

             =0.041802254

            ?= 0.20445

XYZ    ?2=0.000002+0.05 (1.0218)2+0.82(0.000815)

             =0.052874

            ?= 0.229944

c) Long Run estimate of volatility:

ABC = 0.000003/(1-0.82-0.04) = 0.0000214286

XYZ= 0.000002/ (1-0.82-0.05) = 0.0000153846

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