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Market Microstructure, ECON5074

2021

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Section A

You must Answer one question from this section.You must       answer ALL parts of the chosen question. Submit your answer in a (single) separate document.

1  [50% total] A variant of the Glosten-Milgrom model. The underlying stock

can take on one of three values:

V < V*  < V .

with probabilities 6V  , 6V *   and 6V  = 1 · 6V · 6V *   respectively.

● The informed trader can decide whether to buy, sell or make no trans- action.

●  In the event that a trade would yield zero or  negative  profit, the informed trader will not trade.

● The uninformed traders always trade.

● The model is dynamic, that is, traders are repeatedly drawn and are given the opportunity to trade with the dealer.

● The dealer is a monopolist.


Comment on the following:

1.1 What is the optimal strategy of the informed trader? [20%]

1.2 What is the optimal pricing scheme of the dealer?    [20%]

1.3  If the dealer executes trader with many traders over time, what happens to the bid and ask prices?                           [10%]

2  [50% total] We analyzed the case in which there is a monopoly dealer in

the G-M model. What if there is a monopoly dealer (market maker) in the static Kyle model?  (You can assume that the mean of the distribution of the value V is zero, so that pó  = u = 0.)

2.1 How will the market maker’s A differ from the competitive mar-          ket maker case? (You should give an intuitive answer and justification —no calculation should be needed.)                                     [15%]

2.2  How will the informed trader’s trading strategy change?      [15%]

2.3 In the competitive market-maker model, the price reflects the               informed trader’s information. If you calculate the projection of V on total order flow y = z +u in the monopoly market maker situation, is the informativeness of the price bigger or smaller than in the compet- itive market maker situation?  [HINT: The projection will allow you to calculate the forecast error variance; is it bigger or smaller than in the competitive case?  Also, don’t try to fully solve out the model;

just use the information from part 2.1 and 2.2]                  [20%]


Section  B

You must Answer one question from this section.You          must answer ALL parts of the chosen question. Submit your answer in a (single) separate document.

3  [50% total] The government is contemplating imposing a transaction tax

on stock market trades, that is, a fixed cost of e1 would be imposed on each trade.  Comment on the effects of this law should it be adopted, in the context of the material covered in this course.

Specifically, comment on

3.1 The impact on the serial correlation patterns of stocks. Will it be possible to make trading profits from this pattern? [10%]

3.2  How is the learning process affected?                         [10%]

3.3 Will the impact on stocks be uniform across stocks? [10%]

3.4 Analyse the tax using the G-M model. In each round of trading,

either an uninformed trader arrives or an informed trader arrives, just as in the standard G-M model.  Also, trading occurs over multiple periods, so the market maker can learn and adjust 6. The trader pays

the tax.                                                                     [20%]

● Discuss the  range of prices  in which the  informed trader will trade, and the range in which he will not trade. It will be helpful to include schematic diagrams.

● The market maker understands the optimal trading decision of the informed trader, and therefore adjusts his pricing rule accord- ingly. Discuss the pricing rule in each case.


4  [50% total]

Arbitrage via the limit order book.  Suppose that the LOB has the shape in the following figures.  The shallow segment on the right hand part has slope s ī , and the steep part has slope s2 . The kink is at a value ○* , and the short steep segment has width ∆. The values of the parameters are:

Parameter

Value

s ī

s2

*

1.6

7

6

2.4

4.1  In the following figures fully label the relevant points on the

axes with the parameter values and resulting prices (NOTE: the figure is NOT to scale; you must add the correct numbers to the figure). [10%]

4.2  Display the cost and expenditure values for an arbitrage. Label

each of the four figures appropriately with numbers (showing how the

numbers are calculated) and words.                                          [10%]

(i)  In the first figure display the area corresponding to the purchase cost of the first step of the arbitrage.

(ii)  In the second figure display the area corresponding to the pur- chase cost of the second step of the arbitrage.

(iii)  In the third figure display the area corresponding to the revenue of the third step of the arbitrage.

(iv)  In the fourth figure display the area corresponding to the revenue of the fourth step of the arbitrage.

4.3 Calculate the numerical value of the net profit of the arbitrage.     [10%]

4.4 If ∆ is allowed to vary, at what value of ∆ does the profit

become zero?                                                                          [10%]

4.5  Explain why the kink cannot persist using reasoning from the

course (one short paragraph).                                                   [10%]