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