代写Homework 1代写留学生数据结构程序
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April 25, 2023
1 Problems
Use the provided data on the SP500 prices from January 1st 2000 to December 31st 2013.
1 Using a qq-plot answer the following two questions:
. Are the log-return unconditionally normally distributed (i.e. are Rt normally dis- tributed)?
. Are the log-return conditionally normally distributed (i.e. are z t = σ(R)t(t) normally dis-
tributed)?
– if σt(2) follows the Risk Metrics model?
– if σt(2) follows a GARCH model?
– if σt(2) is measured by the Realized Variance?
2 Compute the VaRt(0)1(1) and the ESt(0) from January 1st 2011 to December 31st 2013 using:
(a) Historical Simulation with m=200
(b) a normal distribution for the return innovation and the GARCH model for the variance.
(c) a standardized t-student distribution for the return innovation (only for VaR) and the GARCH model for the variance.
(d) Filtered Historical Simulation with m=500 and the GARCH model for the variance.
3 Plot the daily losses along with the VaR and ES measures just computed.
4 Which of the above methods for VaR do you think is better?
5 At the end of the day on December 31st 2010,compute VaRt(0);1 , VaRt(0);2 , ...,VaRt(0);5 and
the same for ES using:
. Monte Carlo simulation with normally distributed innovations and GARCH variance (simulate 500 paths)
. Filtered Historical Simulation with GARCH variance (simulate 500 paths and use the last 500 observations)
2 Upload on Blackboard
Please upload only one Homework per group. Make sure that your submission includes:
. Excel spreadsheet in which you show all the work you have done. You can put comments in order to make more clear your procedure. Please, be clean and precise.
. A short report (pdf ile) with igures, tables and a concise description of the results. Think as if you had to present your results to your boss.
3 Deadline and Solution
. Deadline: before the next class.
. The solution and the Rubric will be posted on Blackboard after the next class: Look for the ile Var_ES.xlsx