Consider the daily log returns of the GE stock of Exercise 7.1. Obtain estimates ?ˆ(1) b and ?ˆ(3) r

Consider the daily log returns of the GE stock of Exercise
7.1. Obtain estimates _ˆ(1) b and _ˆ(3) r of the extremal index of
(a) the positive return series and (b) the negative return series, using block
sizes k = 5 and 10 and threshold 2.5%.

Exercise 7.1

Consider the daily returns of GE stock from January 2, 1998,
to December 31, 2008. The data can be obtained from CRSP or the file
d-ge9808.txt. Convert the simple returns into log returns. Suppose that you
hold a long position on the stock valued at $1 million. Use the tail
probability 0.01. Compute the value at risk of your position
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Consider the daily log returns of the GE stock of Exercise
7.1. Obtain estimates _ˆ(1) b and _ˆ(3) r of the extremal index of
(a) the positive return series and (b) the negative return series, using block
sizes k = 5 and 10 and threshold 2.5%.

Exercise 7.1

Consider the daily returns of GE stock from January 2, 1998,
to December 31, 2008. The data can be obtained from CRSP or the file
d-ge9808.txt. Convert the simple returns into log returns. Suppose that you
hold a long position on the stock valued at $1 million. Use the tail
probability 0.01. Compute the value at risk of your position for 1-day horizon
and 15-day horizon using the following methods:

(a) The RiskMetrics method.

(b) A Gaussian ARMA–GARCH model.

(c) An ARMA–GARCH model with a Student-t distribution. You
should also estimate the degrees of freedom.

(d) The traditional extreme value theory with subperiod
length n = 21.

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