Subject of Economics
Degree of Quantitative Finance MSc, Data Analytics for Economics and Finance MSc In-course exam
Financial Market Microstructure, ECON5074
Friday, 4th March 2022, 12:00 - Saturday, 5th March 2022, 12:00
Exam duration: 1 hour
Question 1 - 100%
Glosten-Milgrom. Suppose V= :1, V= 4:5, δ0 = :77 and μ = :23.
(a) Suppose the irst order is a sell order: what is δ1? (25 points)(b) Suppose the second order is a sell order: what is δ2? (25 points)
(c) The dealer knows all of the probabilities but he has no way of distinguishing an uninformed trader from an informed trader. If he wants to use the information of the informed, what should the bid price B2 be so as to accurately predict the value, that is, so that his expected proit (before trading begins) is zero, if the order is a sell?
i. Begin by stating the formula for the dealer’s proit if there is a sell order (20 points)
ii. State the formula for expected proit conditional on a sell order (20 points)
iii. State the formula for the bid price using the numbers you calculate in the previous subsections (10 points)
Question 2 - 100%
Roll model. Download the spreadsheet provided, which contains the index value of the S&P500 index for 2018. Calculate the following using the spreadsheet. Be sure to upload your spreadsheet as your answer.
(i) Calculate the price diferences. You will need to construct inter- mediate columns of data in the spreadsheet. Be sure to treat the beginning and end of the data series correctly: you will lose some of the dates as a result of your calculations. (20 points)
(ii) Calculate the covariance of the price changes and lagged price changes. (20 points)
(iii) Calculate the variance of the price changes (20 points)
(iv) Calculate the parameters c and σ 2 of the Roll model using your previous steps. Be sure to maintain the distinction between σ and σ 2 . (40 points)
Note: You should provide a separate brief description of what you have done in the spreadsheet.