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Homework assignment 4
Instruction: Review the class materials, and then go over the detailed step by step example
provided in class. Read carefully the questions and submit the assignment on Blackboard.
1. Consider the price time series for the Amazon stock (AMZN). The sample period is from
January 2, 2004 to May 19, 2017. The data can be downloaded from Yahoo via the quantmod
package. Use the (adjusted) closing prices to compute the daily log returns. For the VaR
calculations, assume that you hold the stock valued at $1 million (long position).
(a). Calculate the VaR of your position for the next trading day using the RiskMetrics
method on May 19, 2017. You must estimate the corresponding IGARCH(1,1)
model. What is the associated expected shortfall? Also, what is the VaR for the
next 10 trading days?
(b). Build a GARCH(1,1) model for the log return series with Gaussian innovations.
What is the VaR based on the fitted model for the next trading day? What is
the corresponding expected shortfall?
(c). Build a GARCH(1,1) model with Student-t innovations for the log return series.
What is the VaR for the next trading day based on the fitted model? What is
the corresponding expected shortfall?
2. Consider the tick-by-tick trade data of Starbucks stock from December 20 to December
31, 2014. The data are in the le taq-t-sbuxdec2031-2014.txt.
(a). Use the data within the normal trading hours only, i.e. from 9:30 am to 4:00 pm
Eastern time, to construct a series of intraday 5-minute log returns. If there is
no trading within a 5-minute interval, assume that the log return is zero. If there
are multiple trades in a 5-minute interval, use the last trade to obtain the price
for that interval. Plot the log return series.
(b). Are there any serial correlations in the intra-day 5-minute log return series? Use
Q(10) to perform the test.
(c). Use 5-minute intraday log returns to compute the realized volatility for each of
the trading days.
(d). Use 1-minute intraday log returns to compute the realized volatility for each of
the trading days.
3. Again, consider the tick-by-tick trade data of Starbucks from December 20 to December
31, 2014.
(a). Construct the series of the number of trades within a 5-minute intervals. Use data
in the normal trading hours only.
(b). Compute the ACF of the constructed time series, say from lag 1 to lag 310. Is
there any evidence of diurnal pattern? [No formal test is needed. Simply comment
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on the ACF plot.]