Project of Financial Economics

Project 2
UNIVERSITY OF MINNESOTA
ECON 4751 – Financial Economics
Due Tuesday, December 13th, 2016
Instructions: This project is designed to help you apply what you have learned about
optimal portfolio construction. You may use Excel, Stata, Matlab, R, etc. to complete the
project. Regardless of which software you use, you must document with images each step.
Brie
y explain your work throughout the project: what is the purpose of the calculations
you are doing? The main goal of the project is for you to understand the theory behind
the Binomial Model of call option pricing, as well as nd good data sources and become
familiar with using statistical software. Important: The project should look and read
like a short paper. In particular, it should have an Introduction section, a Data
section, a Results section etc. Please do not treat this project as a Problem Set.
1: Before we use the binomial model we need a way to choose reasonable values for the
parameters u and d. The rst step in doing this is estimating , the standard deviation
of the stock’s continuously compounded annual rate of return. Choose ONE stock that
has been traded for more than 15 years and is di erent from one you used in Project
1. Same as in Project 1, given the wide variety of publicly traded stocks, it would
be a tremendous coincidence if two students had the same stock. Use historical price
data from the rst trading day of December in each year to get annual returns for this
stock. Please use all available data (i.e. for stocks that have traded for more years you
should have more observations). Provide a graph of the yearly stock return over time.
In addition to the graph, provide a table of summary statistics on returns, including
the mean, variance, skewness, kurtosis, median, interquartile range, and maximum and
minimum values.
2: We now want to convert the annual returns that we have from above into continuously
compounded annual returns. You may use a formula from the textbook for this, but
please give some intuition as to where that formula is coming from. Find ^ the sample
standard deviation of the continuously compounded annual returns. This is the
unbiased estimate of the standard deviation of the continuosly compounded annual
returns.
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3: The binomial model we will use for this project is a 12-period model. Use the number
of periods together with ^ to calibrate u and d, these are the factors that we will use
to forecast the future possible prices of the stock. Let S0 be the Price of the Stock on
Dec-1-16. Build a 12-period tree for the price of the stock where u and d are used to
forecast the price on Jan-1-17, Feb-1-17, etc. up to Dec-1-17.
4: You need to price a call option on the stock with exercise price S0 and expiration
date Dec-1-16. Build a tree that has C, the option price at the origin vertex and
Cu12 ;Cu11d;;Cu10d2; : : : at the end vertices. Replace the notation for the end vertices
with the option payo given the price forcast on Dec-1-17.
5: In order to use the bionomial model you need a risk-free interest rate. Instead of
giving this exogenously, we would like to use an estimated rate from the data. Find
the returns to one-month T-Bills over the past 10 years. Estimate the average monthly
return of T-Bills given your data. Use this estimate as your monthly risk-free rate and
nd the price of the call option.
6: Find the actual price of the call option on your stock with exercise price roughly S0.
Compare the actual price to the price you computed. In the light of this comparison,
what can you say about the e ectiveness of the Binomial Model in pricing call options?
Summarize brie
y what you learned from the experiment.
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