Subject of Economics
Degree of Quantitative Finance MSc, Data Analytics for Economics and Finance MSc
Degree Exam
Financial Market Microstructure, ECON5074
Wednesday, 4th May 2022, 9:30 – Thursday, 5th May 2022, 9:30
Exam duration: 2 hours
Section A
Answer one question from this section.
1 A variant of the Glosten-Milgrom model. The underlying stock can take on one of three values:
V < V* < V :
with probabilities δV , δV * and δV = 1 - δV - δV * 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 proit, 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? [30 points]
1.2 What is the optimal pricing scheme of the dealer? [30 points]
1.3 If the dealer executes trader with many traders over time, what hap- pens to the bid and ask prices? [40 points]
2 Glosten-Milgrom limit order book. Let V = 0 and V = 5. Suppose that
δ0 = :65, that is, that prior to trading, the probability that V = V is 0:65.
Each trader receives a signal of V or V. The probability that the signal a trader receives is correct is :3. The probability that the signal is noise—a .5 chance of s = V and a .5 chance of V—is .7.
2.1 Suppose that the limit order book is initially empty. An initial trader puts two limit orders in the book using the above information and before he gets a signal. What should the bid and ask prices be? [25 points]
2.2 A second trader receives a signal of V. What is that trader’s updated δ? [25 points]
2.3 Should the second trader buy, sell or put an order into the book? If he enters an order what should the bid and ask prices be? [25 points]
2.4 A third trader enters the market. This trader has received two sepa- rate signals of V. What should he do? [25 points]
Section B
Answer one question from this section.
3 Using information from the limit order book, explain how to measure the degree of informed trading for Amazon equity shares. Suppose the aver- age “slope” of the order book—the value of the diference of the price between the best Bid price and the second-best Bid price, divided by the share quantity of the order associated with the best bid price—is :0012. Suppose that the recent variance of the execution price changes is :0083. Maintaining the assumption that the market behaves as in the static Kyle model,
3.1 Compute the variance of the liquidity trade. [25 points]
3.2 Compute the expected proit of the informed traders for each trading round in this market. [25 points]
3.3 State the variance of the price in the general static Kyle model using covariance algebra. (That is, calculate the general formula for the variance of price starting from λy; this question is separate from the previous questions 3.1 and 3.2.)) You can assume that the mean of the underlying value V is zero. Explain each step. [25 points]
3.4 Can the variance of price add useful information about the information content of trading? [25 points]
4 Kyle model. There is a stock with true value V , which is revealed to all at the end of trade. It is known by all that V is drawn from a distribution that has a mean of zero (that is, p0 is zero) and a variance of Σ0 = 9.6. There are three agent types: (i) a single informed trader who knows V ; (ii) many uninformed but rational market makers who compete with each other; (iii) many noise traders who submit orders totaling u that are Gaussian with mean zero and variance σu(2) = 11.1.
Total order low y is comprised of the informed trader’s trade x and the noise trade u:
y = x + u
4.1 Write down the proit function of the informed trader. [20 points]
4.2 The market makers choose a price impact factor λ and set price equal to
p = λy.
The market maker knows that the informed trader uses a linear strat- egy, that is,
x = βV
The market makers compete with each other. Because there is com- petition, the market makers choose λ so that it is the best prediction of the true value V. What is the market maker’s optimal λ? For full credit, show how λ follows from projection. [20 points]
4.3 Write down the proit function for the informed trader using the pric- ing rule p = λy and state the optimal β. Interpret. [20 points]
4.4 Solve for β , λ and also expected proit in terms of the fundamental variances σu(2) and Σ . [20 points]
4.5 How is liquidity expressed in the model? [20 points]