C31DE Derivatives
Group Project: Option Portfolio Position Analysis (30% of total course mark)
Project Pre-requisites
Prior to starting this project you should:
1. Watch these videos:
i) Edinburgh Coursework Video 1 - The Greeks
ii) Edinburgh Coursework Video 2_CW Instructions explained and a demo
In conjunction with these slides: The Greeks - Slides from Hull.pdf
{Note: at minute 28.04 into Video 1 I started talking about graphs but the screen did not share them. They are the graphs in slides 35 and 36 of the lecture slides on options. So please also have them opened when watching that part of the video}
2. Read the following chapters of Natenberg’s book (also in the list of reading for topics):
i) Chapter 6.pdf
ii) Chapter 8.pdf
iii) Chapter 17.pdf
Project Final Submission
1. Deadline is 11am Friday of Week 9 (14 March 2025)
2. As a group you need to compile a Word Report and an Excel sheet. Appoint one member of the group to make the final submission on behalf of the group. Only THIS PERSON should submit the following two files before the deadline:
i) A Word (.doc or .docx) file of the project report. This is a 2000-word (give or take 100) report of your group’s response to the main requirements. Submit this file to the assignment dedicated to Word files.
The project report should have a cover page that lists the following:
a) identifies the assignment as C31DE Coursework Project Report,
b) your coursework group number (Group X#),
c) the student ID of all group members and
d) the word count of the report excluding figures and tables (no external references needed to be listed unless you use them).
Submit this file using the following file naming convention:
“C31DE_CW_Group #_Word.doc” replacing # with your group number.
ii) An Excel (.xls or .xlsx) file of the project calculations. This file is your group’s calculations that generated the graphs. Submit this file to the assignment dedicated to Excel files. This file verifies your calculations and is assessed in the final criteria of the marking rubric, but do not refer to this file in your Word report. Your Word report should stand alone and not require the reader to refer to the Excel file to follow your textual arguments or narrative presentation of the analysis. It should contain a copy of all the graphs and their interpetations and all what you want to be assessed on.
Use the following convention to name this file:
“C31DE_CW_Group #_Excel.xls” replacing # with your group number.
Some Tips on Working in Groups
Here is a general guide to effective group work that you might find useful:
guide-to-effective-group-work.doc
Specifically:
1. You are expected to actively work within your group BUT NOT across groups, and you are not allowed to interact with anyone outside your group for this coursework.
2. As a group, you are expected to meet (e.g., face-to-face or virtually through a platform. of your choice, such as Teams), assign work as early as possible across members of the group so that all group members are clear about their responsibilities, and meet regularly according to a pre-planned schedule to gauge progress and discuss issues.
3. You are expected to work as a team, be professional in your interactions within the team, attend all scheduled group meetings, communicate effectively and regularly, and be clear about your responsibility within the team and the responsibility of other team members. Keep your team informed of all situations, including Mitigating Circumstances if any. If you expect a delay in attendance of group meetings or unable to progress, then communicate this status to your team without delay. However, if the hinderances you face are due to mitigating circumstances then do not reveal any personal information and just inform. the team that you will be "submitting a Mitigating Circumstances form" to explain your delay or lack of progress, and let the team know in good time to decide on how to rearrange the work and the responsibilities of each member. You need to do this as soon as you expect any Mitigating Circumstances that may affect the group work.
4. The person you assign to submit your group coursework files should be chosen by the group at the outset and is designated as the 'Group Representative'. He or she is NOT expected to take on more work than the other members of the group, except for helping ensure group communication (e.g., emails) reaches every member of the group, and for submitting the final documents required for the assignment(s). ONLY the Group Rep should submit the assignments, but other members should check that this person has submitted before the deadline. In other words, submission before the deadline is the responsibility of all members of the group, but the submission itself should be done by the Group Rep only. If the group rep does not submit ten minutes or so prior to the deadline, other members should take quick action and make the submission before the deadline to avoid the late submission penalty.
5. The hope is that you practice and hone your teamwork skills and contribute effectively, equally, and efficiently as an individual within a team. All members of a group will receive the same group mark if they work effectively with each other without issues. However, should you face continuing difficulties in working with other members of your group (e.g., lack of contribution by others, persistent 'free rider' problem, mitigating circumstances, ... etc) then you have the option to fill in and submit the ‘Peer Assessment Form' in which you outline and document these difficulties. Note that these difficulties are different from mere 'clashes of personalities' which should be minimised or eliminated by having been provided from the outset the flexibility to choose your team members and the group that you sign up to. This form. is available through the link in the instructions above. The described circumstances will be assessed together with information gathered from your other team members and considered in giving you a 'fair' mark taking into account the circumstances and shortfall in teamworking skills. This is the exception, and individuals are expected to conduct themselves professionally as equal contributing members of a group.
Project Requirements
This project requires a fair amount of familiarity with Excel functions and macros, or any similar spreadsheet or software package.
A table below entitled ‘Option Positions’ describes the contents of a number of portfolios of options (spreads) and their underlying stock. You are required to fully analyse the position that relates to your group number along the lines of chapter 17 of Natenberg.
Approach
First read chapters 6, 8 and 17 of Natenberg and the 'The Greek – Slides' (or watch the video). Second, refer to attached table below: 'Option Positions' for required data and the portfolio position that your group should analyse.
Notes
Note that implied volatility of each option is given in the table below, from which you can calculate the actual market prices of the options (by using the implied volatility as the input for sigma in the Black/Scholes). This table replaces Figure 17-5 of Natenberg's handout ‘17 Position Analysis’ for the required data but should be compared to it. You will not need to extract any data from Figure 17-5 for use in analysing your own complex position.
Project
The 'analysis' should be in the form. of a full discussion guided by similar discussions presented in the handouts, particularly, but not exclusively, those in ‘Chapter 17: Position Analysis’. The following calculations should be included and considered as the minimum of tools that you should use to support arguments and discussions of the analysis. They constitute part of the requirement but should be strictly looked at as mere tools, and non-exhaustive at that, to be used in supporting your discussion and analyses. Calculations of these ‘tools’ would attract a small proportion of the marks relative to the discussion requirement.
1. The calculation of the theoretical edge of the position (refer to the bottom of page 353 of Natenberg, which is the first page of Chapter 17).
2. Generate graphs of the theoretical edge of the position and its sensitivities. For this you will need to make extensive and accurate use of Excel to calculate the Greeks for your position, as Natenberg does in chapter 17. Please be aware of, and read below about, Natenberg's convention in expressing the Greeks (multiplies by 100, or divides by 365, …, etc). The equations you require for calculating the Greeks are all in the book by Hull and listed in the table of the Greeks in the slide on the Greeks. Here they are again:
3. Use the graphs to analyse the sensitivity of the theoretical edge of the position to percentage changes in the underlying determinants such as price, volatility, time and interest rates. You should also analyse how these sensitivity measures (Greeks) change with the underlying asset price or with other sensitivity measures. (Here note that Natenberg graphs the 'theoretical edge' rather than the profit or loss, which strictly speaking constitute the intrinsic value at expiration or on immediate exercise only. However, he still vaguely refers to the ‘theoretical edge’ as the 'theoretical profit and loss'. You, however, should be clear of this distinction, but still use the theoretical edge not the profit/loss at expiry (i.e., do not graph profits and loss as defined by intrinsic values of the options, which are values at expiry only.)
4. Fully discuss the aim(s) or objective(s) of the strategy, risks faced by holders of the strategy, and considerations in the mind of the trader as they hold (or monitor) the position till maturity. This point and the following two are the primary requirements of the coursework.
5. Provide a full discussion of hedging aspects of this position that should, at the least, make use of answers to the following questions. You should include a discussion of any trade-offs the trader has to balance.
a) What position in the underlying would make the overall portfolio delta-neutral?
b) A traded option is available with ∆=55, Γ=1.4 and Λ= 0.75. (Note that some 'Greeks' are multiplied by 100 and others not. This is simply a convention. Be consistent in your calculations). What positions should the trader take in this traded option and the underlying asset to make the portfolio both delta- and gamma-neutral?
c) What positions should the trader take to make the portfolio both delta- and vega-neutral?
6. Discuss any other aspect you find important to the institution from holding these portfolios (e.g., the effect of transaction costs, or possible impact on other liabilities)
Things to watch out for
1. Natenberg uses futures as the underlying assets to all options. He prices the futures using the cost of carry model: F = S.ert.
Example
If F = 100 in the primary position, r = 6% and t= 6 weeks, then
S = F.e-rt = 100.e-0.06(6/52) = 99.31008
and this is taken as the price of the underlying asset of the option.
Then using the Black-Scholes with S = 99.31, r= 6%, t= 6/52, E = 100 for March 100 Call options, and s= 20% gives C = 2.69 as the theoretical premium of the call option. This is how the numbers reported in Table 8-20 are calculated (double check it).
2. Natenberg uses 100 as the base number for most Greeks. He basically uses the convention of multiplying option deltas and gammas by 100, he divides option Vegas by 100, and divides the theta by 365 to express it as the rate of time decay per day. For example, given his convention a delta of 100 would be equivalent to holding one share and not 100 shares. This can be confusing when calculating number of options or stocks you need to buy or sell in hedging. Hopefully, however, this warning about this ‘scaling’ convention eliminates this possible source of confusion.
3. Natenberg mistakenly assumes that the downside limit of profit or loss from holding options is infinity. For example, he assumes that the maximum possible profit (loss) one can gain from buying (selling) a put option is infinite, while you obviously know that it is limited to the present value of the exercise price plus or minus the option premium. I presume this misconception is due to the fact that traders often have positions in the underlying assets alongside their derivative portfolios.