Xi’an Jiaotong-Liverpool University
Preface of the CW I:
Suppose we are in the ACF312 economy where there are currently 3 types of financial items traded, including the risk-free bond with 10-year time-to-maturity, the stock of AIHSM Inc. and the associated call option currently with 1-year time-to-maturity and strike price K=110. The public information about these items are summarized in the table below:
Face value: 100
Coupon: 10%
Time to maturity:10 years Close price today: 194
Bond (B)
(Annual- coupon bond)
Additional information:
Based on the empirical data, the (simple compounded) return distribution seems to be a combination of normal distributions. More specifically, the pdf of the return distribution (in terms of loss) is fitted as below by Eddie, who is the famous risk analyst. (The “? ” is missing and only available if you could deduce it or you are a friend of Eddie.)
Stock (S)
AIHSM Inc.
Close price today: 100/share The historical data is available and attached on ICE. (CW_I_data)
Time to maturity:1 year Strike price: 110
Close price today: see task 5 below
Call (C)
(written on one share of stock)
left: ~N(−0.03,0.2^2)
right:
~N(? ,0.4
^2)
Please exploit the additional information as a hint for certain tasks below. You don’t have to use or follow it and please feel free to come up with different alternatives. Moreover, if you would like to exploit this hint, please verify why it is convincing.
Here are the tasks that you need to tackle with:
1. Can you deduce what the risk-free interest rate is? Moreover, try to verify your answer. For example, you can explain how it is calculated, or/and apply alternative techniques to solve this and compare the results, etc.
Hint: Newton’s method may be helpful.
2. Based on the historical data, calculate the volatility of the stock return with GARCH and EWMA scheme. In particular, provide a prediction of the volatility tomorrow.
3. Can you deduce the probability that the call option is in the money at maturity? At least, approximately.
4. Find the theoretical close price of the call option premium today. Please try to calculate it with at least 2 alternative methods. You need to elaborate the methods adopted and make an analytic comparison about the results.
Note that additional rewards may be given if you can get more results obtained by more methods.
PAPER CODE: ACF312/19-20/S2/Coursework Page 2 of 4
Xi’an Jiaotong-Liverpool University
5. If the current close price of the call is selling at 8.88, is this different from your analysis above? How would you interpret this? For example, what may be the possible reason for it?
6. Suppose you plan to buy 1000 shares of stock at today’s close price and would like to have an image about the potential risk. Please calculate the 99% 1-day VaR and Expected Shortfall by Historical Simulation method with Volatility updating scheme incorporated based on the results obtained in task 2. How would you comment about the risk of your portfolio? Is it a risky investment? Please feel free to apply any technique/analysis for this. For example, you can use real stocks/indices as the benchmark.
Please note that you can essentially apply any techniques to solve the tasks but everything needs to be done with MATLAB. In addition, all questions asked should be elaborated.
Detailed guidelines:
1. Marking scheme Written report (70%)
Introduction: It should include critical introduction about your report.
The analysis and results can be elaborated by tasks in structured format. It will be nice if you can demonstrate your results with proper tables or visualize them with appropriate figures. Moreover, you need to explain your ideas about solving the tasks. A critical summary or a step-by-step outline would be enough. You don’t have to review materials covered in this course or standard techniques here. (In CW I, you are not required to write them as a proper report. However, you will exercise how to do it in CW II because I will set it as a requirement. Let’s be super nice this time and nice next time, lol.)
Final discussion: Discuss about the potential strength and weakness when you are solving these tasks. Think about how you can extend the analysis or provide alternative ways even if you don’t know how to program them yet.
Please do not copy and paste your codes in the report. Besides, it is not necessary to explain how the code is designed in the text.
Relevant Codes (30%)
Code will be part of the assessment in order to examine your learning outcomes. Please try to design your codes as best as you can. For example, efficient and well- structured codes with critical comments may be strengths in the context of programming. By contrast, messy lines and redundant loops with no comments in the codes may reflect worse programming capability or habits.
PAPER CODE: ACF312/19-20/S2/Coursework Page 3 of 4
Xi’an Jiaotong-Liverpool University
2. Some requirements for consistency and convenience
Code requirement:
You can program any type of codes you want, e.g. (live) script or functions. However, please prepare a live script named as main_CWI which is able to generate all results by clicking the run button. In addition, all results will be displayed as the output of the live script. (Please recall how I demonstrate the programming via the live script in the MATLAB sessions.)
Note that you may lose mark if the results are not consistent with those in the report or missing when I press the run button of your live script.
Submission requirement:
The submission will be submitted in group and the leader is compulsory for it. Please include everything into a folder named as GROUP_? and compress it as a single file for submission. Note that file name must be formatted as suggested. Please don’t miss the “_”. In addition, please save the report as a pdf file.
Word count limit: 2000 words (excluding listed tasks, Tables, Figures, References, etc.) The word count is not essential, i.e., more is not equivalent to better. It is good to keep everything critical and clear.
Deadline: Submission is no later than 24:00 on 17th May. The submission link will be available on ICE one week before the deadline.
If you have any question, please do not hesitate and feel free to contact me by dropping a message or an email.
— End —
PAPER CODE: ACF312/19-20/S2/Coursework
Page 4 of 4