FE-570 F21 Homework #1
Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit
Homework #1 - Due 24 Sep 2021
FE-570 F21
Problem 1.1 (25 pts)
Assume that the limit order book is as shown in the table below.
1) What is the bid-ask spread in cents and basis points of the mid price?
2) If you buy 100 shares with a market order, and immediately sell them also with a market order, what is your P&L?
3) A limit order to buy 150 shares at $33.50 arrives in the market. What transactions occur, and what is the resulting bid-ask spread in cents?
4) A limit order buy order for 2000 shares at $33.53 arrives. List all transactions, and determine the bid-ask spread after the order is executed.
Problem 1.2 (15 pts)
i) Describe the exponential distribution for a random variable. Draw plots of the probability distribution function (pdf) and the cumulative distribution function (cdf) of this distribution.
ii) Compute the mean and variance of an exponentially distributed ran- dom variable.
Problem 1.3 (10 pts)
Rank the following distributions in decreasing order of their heavy tailedness. Justify the answer.
i) Gaussian distribution
ii) Exponential distribution
iii) Student-t distribution with v = 3 degrees of freedom
iv) Student-t distribution with v = 5 degrees of freedom.
Problem 1.4 (50 pts)
Pick a liquidly traded stock (e.g. XOM, IBM, AAPL, etc) and study the validity of the stylized facts of the financial markets for their log-returns computed using daily closing prices.
i) Heavy tailed distributions. Use a qualitative argument based on the QQ-plot, and a more quantitative argument based on a regression of the pdf tails to a functional dependence of the form f (z) = cz−α where z are the log-returns.
ii) Vanishing autocorrelation of returns.
iii) Long-range autocorrelation of the absolute value returns.
Hint. For this analysis you can adapt the R code used in lecture 2. Submit the answer as a R Markdown pdf file.
2021-12-04