这个作业是设计交易策略并实际应用在股票上

CF963 Computational Models in Economics and Finance

Reassessment II, 2018/19

Lecturer: Maria Kyropoulou

• Answer all (four) questions below. Submit your answers to FASER by noon on the 25th March

2020. You need to submit:

– a single report with your answers to all questions, and

– all MATLAB files that you created in the context of this assignment.

Submit them separately if possible (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– and how clearly you explain what you have done. Aim for precise and

concise answers and explanations. Good luck!

Task 1 [20%]

Your task is to design a trading strategy and test it with MATLAB on any of the FTSE 100 stocks –

daily closing prices that were provided in the module.

In your report, you need to describe your algorithm precisely in words as well as copy and paste

your MATLAB code. You should explain how you evaluate the effectiveness of your strategy, e.g. show

clearly when your algorithm buys and sells, and what profit or loss it makes in each deal (and in total).

You will not be assessed on the profits of your strategy, however, your strategy should be sophisticated

enough to demonstrate some synergy between computation and finance in this context. You should also

briefly elaborate on that synergy.

Task 2 [20%]

a. (13%) Consider the Cournot duopoly model where the inverse demand function and the cost functions

are given by

P = 100 −

Q

2

, c1 = 5q1, c2 =

q

2

2

2

,

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.(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) = 50 −

q1

4

.

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

firms.

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Task 3 [25%]

Consider the following sponsored search auction instance I:

• 3 slots. The top slot has a known click-through rate (CTR) ctr1 = 1, the middle slot has a known

click-through rate ctr2 = 0.55071 and the bottom slot has a known click-through rate ctr3 = 0.4704.

• 3 advertisers. Let the (private) value-per-click of advertiser 1 be 100000 (in some currency), the

(private) value-per-click of advertiser 2 be 52960 and the (private) value-per-click of advertiser 3

be 14583.

• The payoff of bidder i in slot j is ctrj (vi − pj ), where pj is the price charged per-click in slot j.

Under the Generalized Second-Price (GSP) auction rule:

– Advertisers are asked to declare their value per click (this doesn’t mean that their declarations are

truthful!). Advertisers are then ranked according to their declarations and the advertiser with the

highest declaration is assigned to the slot with the highest CTR, the advertiser with the second

highest declaration is assigned to the slot with the second highest CTR, and, finally, the advertiser

with the lowest declaration is assigned to the slot with the smallest CTR. For j = 1, 2, the per-click

payment pj at slot j, is set to be equal to the declaration of the advertiser assigned to slot j + 1,

while p3 = 0.

a. [4% ] Compute the optimal/highest social welfare in I.

b. [21% ] Write MATLAB code that computes a pure Nash equilibrium in I, when advertisers can declare

one of the following: 0, their true value-per-click, half of their true value-per-click.

You can (or not) follow a brute-force approach, i.e. consider all possible combinations of declarations

and for each of them check if it is an equilibrium. Copy and paste your MATLAB code in your report,

and explicitly mention where in your MATLAB code you guarantee that the equilibrium conditions are

satisfied (even if your code doesn’t run or doesn’t compute an equilibrium). If your code successfully

computes an equilibrium, present the equilibrium that you have computed in the report and mention its

social welfare. Marks will be awarded for partially-correct approaches.

Task 4 [35%]

Pick one of the following papers and provide a summary and critical assessment of it, by focusing 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?

Length guide: Your answer should not exceed an A4 page overall. Aim for 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:

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 Mastroeni,

Maurizio Naldi, and Pierluigi Vellucci. [link]

FairLedger: A Fair Blockchain Protocol for Financial Institutions, by Kfir Lev-Ari, Alexander Spiegelman, Idit Keidar, Dahlia Malkhi. [link]

Deep Reinforcement Learning for Trading, by Zihao Zhang, Stefan Zohren, Stephen Roberts. [link]

Please refer to the Student’s handbook on the Departmental

Policy on Plagiarism and Late Submission

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