# 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 dierent 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 eectiveness of the Binomial Model in pricing call options?

Summarize brie

y what you learned from the experiment.

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