Reference no: EM133113385

CF963 Computational Models in Economics and Finance - University of Essex

Task 1
Consider the following moving average trading strategy:

Let 7^MA be the 7-days moving average, and let 14^MA be the 14-days moving average. If the 7^MA crosses the 14^MA from below, then buy your entire budget. If the 7^MA crosses the 14^MA from above, then sell your entire portfolio.

Your task is to:

a. 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.

The output of your code should include the following (no particular format is required, as long as ithe requested information is clearly presented):
b. when your algorithm buys or sells,
c. how much your algorithm buys or sells in each deal,
d. 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 FASER).

Task 2
Program the agent-based simulator in MATLAB for the following setting:

There are 20 buyers and 20 sellers and each seller initially owns 30 units of the item that is being traded in a double auction market. Each buyer i 1, . . . , 20 , has a fixed valuation vi that is a random number between 1 and 200 (such random selections have to be implemented by your code); valuations don't change between different rounds of the simulation. At every round, buyers and sellers place their orders that are of the following form: A buyer's order (b, q) is such that
- b (bid) is the maximum amount the corresponding buyer would be willing to spend for one unit of the item and is a random positive integer number that is at most equal to the valuation of the buyer. In other words, the bid is selected uniformly at random from the range [1, . . . , vi]), and
- q (quantity) is the number of units the corresponding buyer would like to buy at this round (for the given price) and is a random integer number between 1 and 5.

Similarly, a seller's order a is such that

- a (ask) is the minimum amount of money the corresponding seller would be willing to get for one unit of the item at this round of the simulation and is is a random integer number that is at least equal to the number corresponding to 10 times the round number, and at most equal to 200.

After all orders have been placed in each round, the maximum number of trades is being implemented while giving priority to high bids and low asks. Note that a buyer's order can be matched to more than one sellers, e.g. if two sellers only have one remaining unit of the item each and a buyer wishes to buy two units. A trade can be performed if the bid is at least as high as the ask. Once a seller sells their 30 units they are no longer considered for trades.

a. Run your simulation for 10 rounds and:
b. Calculate the spread (difference) between the best bid and the best ask at each round and plot it.
c. Compute how many units of the item were traded in total, and
d. Compute the number of units that are available for sale for each possible price after the final round. Copy and paste your code and present the requested outputs, including the plot, in the report (in addition to uploading the matlab file on FASER). No particular format is required, as long as ithe requested information is clearly presented. Marks will be awarded for partial answers.

Task 3

a. Consider the Cournot duopoly model where the inverse demand function and the cost functions are given by

P = 120 - Q, c₁ = 10 + 3q₁, c₂ = 12 + 6q₂,

where Q = q₁ + q₂ is the total production quantity and 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.

b. 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) = 57 - q₁/2.

Give the profit function of firm 1 and find the equilibrium strategies (production quantities) of the firms.

Task 4

Pick one of the following papers and provide
a. a concise summary that reveals the main points addressed in the paper, and
b. 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 appropriate? How could this analysis be extended, e.g. can you think of an adaptation to the model that would be meaningful?

Attachment:- Computational Models in Economics and Finance.rar