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CF963 Computational Models in Economics and Finance

Assignment, 2021/22

  • Answer all (four) questions below. Submit your answers to FASER. You need to submit:
  • one report with your answers to all questions. This should be a .pdf file named according to ‘CF963 RegNumber Report.pdf’, where RegNumber should be replaced by your registration number.
  • all MATLAB (.m) files that you created in the context of this assignment, named according to ‘CF963 RegNumber TaskX.m’, where RegNumber should be replaced by your registration number and X should be replaced by the Task number (1 and 2).
  • Submit them separately (do NOT .zip). Make sure that your code is easy to follow, and copy and paste your code in the report as requested in the specific tasks.
  • Your assignment will be assessed on the quality of the files you submit –correctness, work quality and quality of presentation. Aim for precise and concise answers and explanations. Good luck!

Task 1 [20%]

Consider the following moving average trading strategy:

Let 3MA be the 3-days moving average, and let 7MA be the  7-days  moving average.  If the  3MA crosses the 7MA from below, then buy your entire budget.  If the 3MA crosses the 7MA from above, then sell your entire portfolio.

Your task is to:

  1. (10%) implement the above strategy and test it with MATLAB on the JET.L (JustEat stock 6M) stock’s daily closing prices that are provided on the moodle page of the module (Unit 1). Assume you have £1M available to invest and that only integer quantities of the asset can be traded.

The output of your code should include the following (no particular format is required, as long as the requested information is clearly presented):

  • (4%) when your algorithm buys or sells,
  • (4%) how many assets your algorithm buys or sells in each deal,
  • (2%) what profit/loss your algorithm made in total.

Copy and paste your code and present the requested outputs in the report, in addition to uploading the Matlab file on FRASER. Make sure that your code runs if the JET.L file is in the same folder as the

.m file that you submit, without the need to rename the JET.L file.

Task 2 [30%]

Consider a double auction market where identical copies of a single item are being sold/bought. At each round, every buyer/seller places their limit order, the highest bid is compared with the lowest ask and if the bid is at least as high as the ask, a match of the corresponding traders is made and trade is performed between them (ties can be broken arbitrarily). The same process is repeated until no other match is possible, while each trader can only participate in at most one trade at each round.

Assume 5 buyers and 5 sellers. The cost of each seller at each round is selected uniformly at random from the range [1, . . . , 200]; that cost is that seller’s ask at the corresponding round. Each buyer is

assumed to have a specific valuation v1 = 100, v2 = 125, v3 = 150, v4 = 175, v5 = 200, (this value corresponds to how much the corresponding buyer is willing to spend for one unit of the item). Also, at each round, each buyer places a random bid that is at most equal to the buyer’s valuation; in other words, each buyer I, for i = 1, 2, 3, 4, 5, places a bid selected uniformly at random from the range [1, . . . , vi].

  1. (16%) Program the agent-based simulator in MATLAB for the above setting and run your simulation for 10 rounds.
  2. (7%) Calculate the spread, i.e. the difference of the lowest ask minus the highest bid, at each round, and plot it. If the difference turns out to be negative, consider the spread to be 0.
  3. (7%) Compute how many units of the item were traded in total.

Copy and paste your code and present the requested outputs in the report (in addition to uploading the Matlab file on FRASER). Marks will be awarded for partial answers.

Task 3 [20%]

  1. (13%) Consider the Cournot duopoly model where the inverse demand function and the cost functions are given by

P = 52 2(q1 + q2),            c1 = 7 + 2q1,             c2 = 10,

where qi is the production quantity of firm I, for i = 1, 2. Give the profit functions of the firms and compute the Nash equilibrium defined by the quantity each firm chooses to produce. Compute the profit of each firm, the consumer surplus, and the total surplus at equilibrium. After presenting your calculations, present your answers in a table of the following form:

q1
q2
π1(q1, q2)
π2(q1, q2)
CS
TS
  • (7%) Consider the leader-follower duopoly model with the inverse demand function and the cost functions as defined in Part a. Let the reaction function of firm 2 be

r2(q1) = 16 + 4q1.

Give the profit function of firm 1 and find the equilibrium strategies (production quantities) of the firms. After presenting your calculations, present your answers in a table of the following form:

q1
q2
π1(q1, q2)

Task 4 [30%]

Pick one of the following papers and provide

  1. (10%) a concise summary that reveals the main points addressed in the paper, and
  2. (20%) a critical assessment of the paper.

Focus on the real-life setting that is considered, the modelling choices that were made in an attempt to abstract it and analyse it, and elaborate on the particular computational modelling technique that is applied to it.

Suggestions for points to address: What simplifying assumptions are made? How does computational thinking help us analyze this particular situation? Are the assumptions made and/or the methodology used appropriately? How could this analysis be extended, e.g. can you think of an adaptation to the model that would be meaningful?

Length guide: Your answer should not exceed an A4 page overall. Aim for a half-page summary of the paper and another half-page for criticism on the approach. There is no need to focus on the technical details (mathematical proofs).

Papers:

  • Firms Default Prediction with Machine Learning, by Tesi Aliaj, Aris Anagnostopoulos, and Stefano Piersanti. [link]
    • A Model of Dealer Networks, by Daniele Condorelli, Andrea Galeotti, and Ludovic Renou. [link]
    • Complexity of Stability in Trading Networks, by Tam´as Fleiner, Zsuzsanna Jank´o, Ildik´o Schlotter, Alexander Teytelboym. [link]
    • Personal Finance Decisions with Untruthful Advisors: an Agent-Based Model, by Loretta  Mas- troeni, Maurizio Naldi, and Pierluigi Vellucci. [link]
    • Evolutionary Equilibrium Analysis for Decision on Block Size in Blockchain Systems, by Jinmian Chen, Yukun Cheng, Zhiqi Xu, and Yan Cao. [Link]

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