COMP0075 [TURN OVER]

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COMP0075: Financial Market Modelling and Analysis
Main Summer Exam Period 2020/21 (A7P)
Suitable for cohorts 2020/21, 2019/20, 2018/19

This assessment consists of THREE questions. Answer ALL parts of ALL questions.

Students should submit typed answers where possible, though it is recognized that scanned
handwritten answers may be necessary for some students.


Marks for each part of each question are indicated in square brackets.
Standard calculators are permitted

1. Three risk-averse market makers must decide whether to run an automated "threshold" strategy
that uses market orders to sell inventory when inventory is too high. If multiple market makers
run this strategy, the algorithms can become coupled and cause oscillatory trading, which loses
money for all those market makers. Assume that:
• if they all use the threshold strategy, each one will lose £0.5m
• if none uses the threshold strategy, each will lose £0.25m when prices fall
• if only one uses the threshold strategy, it will make an estimated profit of £0.2m while
the other two will each lose £0.25m when prices fall
• if any two use the threshold strategy and the third doesn't, then the first two will make an
estimated profit of £0.2m and the third will make an estimated loss of £0.1m.
(i) Give the payoff matrix for the above situation [6 marks]

(ii) Explain the payoff matrix and explain which states are Nash equilibria and which are
not, and why. [6 marks]

(iii) In practice, what advice would you give to each market maker in order to help them to
maximize their profits (or at least to minimize their losses)? [2 marks]

(iv) Would this advice change (and if so how) if a market maker also wanted to minimize the
other market makers’ profits? [2 marks]
[Total 16 marks]


COMP0075 Continued

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2. Consider a computer program whose purpose is to model a central Limit Order Book of a
Continuous Double Auction
(i) Explain the important computer data structures that would be used in such a model, and
for each data structure say in detail what purpose it serves.
[8 marks]
(ii) Give a detailed description of how an order would be added to the two data structures
mentioned above.
[4 marks]



[Total 12 marks]


COMP0075 [TURN OVER]

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3. Consider a market where shares for the fictional company COCO Ltd are traded on two
exchanges (Exchange A and Exchange B) and where an investment fund may purchase these
shares via one or both of two brokers (Broker A and Broker B). The communications latency
between the brokers and the exchanges are given as follows:
Broker A to Exchange A: 150 msec Broker A to Exchange B: 600 msec
Broker B to Exchange A: 500 msec Broker B to Exchange B: 300 msec
Assume that the exchanges are quoting prices for COCO Ltd as follows:
Exchange A: Best Bid = 450 shares @ 330p, Best Ask = 250 shares @ 540p
Exchange B: Best Bid = 310 shares @ 300p, Best Ask = 80 shares @ 520p
A Low Latency Trader (LLT) operates co-located servers at both exchanges, which can
communicate with each other. The relevant latencies are:
LLT (server 1) to Exchange A: 150 nsec LLT (server 2) to Exchange B: 150 nsec
LLT (server 1) to LLT (server 2): 200 msec

(i) Assume an investment fund instructs Broker B to buy 200 shares of COCO Ltd
(a) What are the new depths of the best bids and best asks at both exchanges after the
order has been processed (assuming no activity from the LLT)?
[3 marks]
(b) Can the LLT use low latency to profit from the described order? Give a numeric
inequality that must hold if the LLT is to make a profit and therefore proves your
statement (assume execution times are negligible).
[3 marks]
(c) Private confirmations of receipt and execution are sent. Who sends this information,
and to whom? At what time is each information received relative to the time when
the broker sends its first order (assume execution times are zero)?
[3 marks]
(d) Name three key pieces of information given in the confirmation of execution.
[3 marks]
(ii) Assume the two LLT servers run identical code (since in general they cannot know
whether a broker’s first order will arrive first at Exchange A or Exchange B). Give a
detailed description of what the server code would do, and how, including all
assumptions you make. Assume the server code will only issue orders after it has
determined that it is possible to make a profit by doing so. Include a detailed description
of timing measurements and calculations. Your answer should be carefully structured to
make it as easy as possible to understand, stating clearly, and concisely, what the server
will do and in what order. You may include pseudo-code and bullet points if you wish.
An ideal answer will also consider factors that might frustrate the objectives of the
server code, and possible counter-measures, and will not exceed 1,200 words.
[60 marks]
[Total 72 marks]
[END OF PAPER]






































































































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