HOMEWORK.
Assignment 1, due Wednesday, January 18, 2012, in class.
1. Chapter 1, exercise 1.
Using a list of option prices
from the Yahoo Finance website, perform a
similar calculation to that done in the Example in the text, with
Apple (symbol: AAPL) in place of Cisco. For this, use the
first Apple call option expiring during the month of February and for which the
strike price is greater than the current stock price.
You should assume that a European call option for 100 shares of stock is
purchased and that at expiration there are two possible
scenarios for the stock price: it has gone up or down by 10%
since purchase of the option.
Please record the date whose data you used and include all relevant information used.
Including a print-out of the option price table that you use to answer this question is requested.
For those who do not have the book yet, here is the text of the
Example.
Example. On January 4, 2000, a European call option on
Cisco (symbol: CSCO) stock
has a price of $33. The option expires in January, and the strike
price is $70. The price of Cisco
stock on January 4 is $102.
If one bought such an option on 100 shares of Cisco,
the option would cost
$3,300, and
on January 21, 2000 (third Friday of January), one would have
the right to buy 100 shares
of Cisco at a price of $70 per share.
Suppose for simplicity that $1 on January 4 is worth $1 on
January 21, 2000.
Scenario 1: Suppose the price of Cisco stock on January 21 is $120 per share.
This current price of the stock is called the spot price of the stock.
The holder of the option will exercise it and
make a net profit per share of $120 -$70 -$33 (spot price of stock on
January 21 -
price under exercise of option - option price)
and hence a net profit of $1,700. This is a
1700/33 % = 51.5% profit on the $3,300 initial investment.
On the other hand, if the $3,300 had been directly invested in stock,
the investor could have bought 32 whole shares of stock and
the profit would have been $18 times 32 = $576 on an investment
of $ 102 times 32 = $3,264, which is
a 57600/3264 %
= 17.6 % profit.
Scenario 2: Suppose the price of Cisco stock on January 21 is
$67 per share.
The holder of the option will not exercise it
and takes a loss of $33 per share (the cost of the option per
share) and hence a net
loss of $3,300. This is a 100% loss on the $3,300 initial
investment.
On the other hand, if the $3,300 had been invested directly
in stock, the loss would have been $35 times
32 =$1,120 or a 34.3% loss on an investment of $3,264 in stock.
2. Suppose that a stock is currently selling for $30 per share.
A forward contract is to be written committing the holder of the long position in the contract
to buy 100 shares of
stock 3 months from now for $30.50 per share. Suppose that a bank
is charging interest on short term loans at the rate of 6% per annum (continuously compounded)
on a 3-month loan. Describe a strategy for creating an arbitrage
profit and establish the amount of the profit.
3. A combination option called a strangle is obtained by taking a long position in a (European) call and a (European) put option with the same expiration date but differing strike prices, all based on the same underlying asset.
An investor who buys the strangle is betting that
there will be a large movement in the price of the underlying,
but is uncertain whether it will involve an increase or a decrease in the price.
Find a formula for the payoff for a strangle where the put has a strike price of K1 and the call has a strike price of K2 and K1 < K2. Draw a graph of this payoff as a function of the final price of the underlying asset. (Make sure to label your axes on the graph.)
Handout related to Proctor and Gamble/Banker's Trust Swap agreement and Societe Generale trader. (You will need a password to access this page, which will be given out in class.)
Assignment 2, due Wednesday, February 1, 2012, in class.
From Chapter 2,
Exercises 1, 2 (part (d) is optional), 3 (part (d) is optional),
5 (note
that you can use the result from
Exercise 4 if you wish - there is a typo in the book at the end of Exercise
5, it should
read "Exercise 4" rather than "Exercise 3").
Optional problem: Exercise 4.
Assignment 3, due Wednesday, February 15, 2012, in class.
1. Consider the CRR model described in Exercise 2 of Chapter 2 as the model
for a stock and a bond. A forward contract is to be offered under which the holder of a long
position in the forward contract will buy 100 shares of stock at time T=2 for a fixed price F.
(Here F is the total amount to be paid for the 100 shares).
Remember that no money changes hands at time zero when a forward contract is written.
What value should F take in order that there is no arbitrage opportunity for the
investor who holds a long or a short position in the contract?
Explain your reasoning fully (in particular, identify an associated European contingent claim and
derive the value of F using arbitrage pricing for the contingent claim).
2. Exercise 6 (except part (d)) from Chapter 2.
3. Exercise 7 from Chapter 2.
4. This exercise is in a pdf file, click here to access it.
Assignment 4, due Monday, March 5, 2012, in class.
Exercises 2, 3, 4 from Chapter 3.
Assignment 5, due Friday, March 16, 5pm.
Please hand in Exercises 2 (a), (b), 3 from Chapter 4.
Exercises 4, 5 6 from this Chapter 4 are OPTIONAL and do not
need to be handed in.