ECMT6006 Applied Financial Econometrics Semester 1, 2023
Assignment 3
Due: 11.59PM Sunday 28 May 2023
Academic Honesty
Academic honesty is a core value of the University, and all students are required to act honestly,
ethically and with integrity. The consequences of engaging in plagiarism and academic dishonesty,
along with the process by which they are determined and applied, are set out in the Academic
Honesty in Coursework Policy 2015. Under the same policy, as the unit coordinator, I must report
any suspected plagiarism or academic dishonesty.
Instructions
• This is an individual assignment which accounts for 10% of your final grade. You may
discuss with your classmates, but please ensure that the submitted work is independent.
• You can either hand-write or type your answers, but please compile all your answers
in one PDF file and submit it via a file upload in Canvas. You can only submit your
work once, so please double check before you submit. The page limit of the submission
is 40 pages including appendix (penalty will apply if the page limit is exceeded).
• There are 8 questions (with sub-questions) in this assignment, and please attempt all
questions. Detailed solution to each question will be provided after the assignment is
due.
• I will randomly select 4 questions (same 4 questions for everyone) to grade, and each
question is worth 5 points. The total point of this assignment is 20. The grading will
be based on the completion and general quality of your submission.
• For the analytical questions, please show your derivations. Answers without interme
diate steps will be considered as incomplete.
• For the empirical question, please feel free to use any statistical software to answer
them. Make sure that you present the required results, including figures, and provide
your interpretations if asked. If you use MATLAB live script, you can present your
answers in a document (exported from the live script) which contains your code, output,
and your explanations in texts. If you use separate code, then please attach your code
in an appendix at the end of your submitted PDF file.
• Based on the University late policy, a late submission is subject to a penalty of 5% (of
the total points) per calendar day. Since this is the last assignment and the final exam
of this unit is scheduled on Saturday 10 June, I will post the suggested solutions by
11.59PM Monday 5 June the latest. I will not accept any late submission after
11.59PM Monday 5 June.
• Patton (2019) refers to the reference textbook by Andrew Patton.
Questions
1. Question 4 in Section 5.10.2 of Patton (2019, p. 186).
12. Question 1 in Section 8.6.2 of Patton (2019, p. 302).
3. Question 2 in Section 8.6.2 of Patton (2019, p. 302–303).
4. Question 1 in Section 9.10.2 of Patton (2019, p. 331).
5. Question 2 in Section 9.10.2 of Patton (2019, p. 333).
6. Use the 2010–2015 daily S&P 500 index log returns constructed in the last question of
Assignment 2 to estimate the conditional 5%-VaR using the below two methods.
(i) (Historical Simulation) Use the daily data in the whole year 2010 to obtain the
empirical distribution of the return on the first day of 2011, and compute the
5%-VaR on the first day of 2011. Next, repeat this day after day using a one-year
rolling window, and obtain the daily VaR forecast from 2011 to 2015.
(ii) (Parametric GARCH Model) Assume the daily returns follow the below model
with constant conditional mean and GARCH(1,1) conditional variance:
rt = µ + εt
,
εt = σtνt
, νt ∼ i.i.d. N(0, 1),
σt
2 = ω + αε2
t−1 + βσt
2
−1
.
Estimate the daily conditional 5%-VaR process and make a time-series plot of it.
7. Question 1 in Section 11.7.2 of Patton (2019, p. 408).
8. Question 2 in Section 11.7.2 of Patton (2019, p. 409).
2
