Submission 4
Instructions:
You are allowed and encouraged to discuss the subject matter
amongst yourselves. Each group submits only one writeup.
Writeup for each group should be their original work.
Submissions will be electronic on canvas. You may use excel,
word, power-point or combinations of all.
There are no limits or constraints on single or double spacing or
font sizes or number of pages for your submission. The write up
should address the questions in a clear manner in a way that
the reader understands your presentation.
1. You have $100,000 to invest. A Stock of company XYZ sells
for $30 today. A European call option to buy a share of
stock XYZ at strike of $25 six months from today sells for
$8. Another European call option to buy a share of stock
XYZ at strike of $30 six months from today sells for $6. You
can go long or short with positions in either of the two
options. In addition, a 6-month riskless zero-coupon bond
with $100 face value sells for $95. You have decided to
limit the number of call options that you buy or sell to at
most 8,000.
You consider three scenarios for the price of stock XYZ six
months from today:
a) the price will be the same as today,
b) the price will go up to $40,
c) or drop to $10.
Your best estimate is that each of these scenarios is
equally likely.
Determine the portfolio of stocks, bonds, and options that
maximize the expected profit.
2. Consider the file called Submission4_Upload_portfolio.xls.
This contains the payoff profile for an equity portfolio that
includes stocks and other derivatives. The payoff depends
on the level of the SPY index. You are allowed to use calls
and puts with strikes of 200, 220, 240,…300,320,…..400. So
you can choose call and put options for all strikes from 200
to 400 with increments of 20. Your task is to add option
positions to your portfolio so that the losses in the
portfolio are eliminated to the greatest extent. Refer to
section of portfolio surgery.
3. Find the implied probability that the Nasdaq index will fall
by 10% in the next six months.
4. Explain the meaning of delta and gamma of an option.
Explain the meaning of theta.
5. A financial institution has the following portfolio of over-
the-counter options on sterling:
Type Position Delta of
Option
Gamma of
Option
Vega of
Option
Call −1,000 0.5 2.2 1.8
Call −500 0.8 0.6 0.2
Put −2,000 -0.40 1.3 0.7
Call −500 0.70 1.8 1.4
A traded option is available with a delta of 0.6, a gamma of 1.5,
and a vega of 0.8.
Another traded option is available with a delta of 0.7, a gamma
of 1.1 and a vega of 0.2.
What position in the traded options would make the new
portfolio both delta, gamma and vega neutral?
