Assignment 6
Problem 8.17.
Consider an exchange-traded call option contract to buy 500 shares with a strike price of $40 and maturity
in four months. Explain how the terms of the option contract change when there is
a. A 10% stock dividend
b. A 10% cash dividend
c. A 4-for-1 stock split
Problem 8.23.
The price of a stock is $40. The price of a one-year European put option on the stock with a strike price of
$30 is quoted as $7 and the price of a one-year European call option on the stock with a strike price of $50
is quoted as $5. Suppose that an investor buys 100 shares, shorts 100 call options, and buys 100 put
options. Draw a diagram illustrating how the investor’s profit or loss varies with the stock price over the
next year. How does your answer change if the investor buys 100 shares, shorts 200 call options, and buys
200 put options?
Problem 8.25.
Use DerivaGem to calculate the value of an American put option on a nondividend paying stock when the
stock price is $30, the strike price is $32, the risk-free rate is 5%, the volatility is 30%, and the time to
maturity is 1.5 years. (Choose Binomial American for the “option type” and 50 time steps.)
a. What is the option’s intrinsic value?
b. What is the option’s time value?
c. What would a time value of zero indicate? What is the value of an option with zero time value?
d. Using a trial and error approach calculate how low the stock price would have to be for the time
value of the option to be zero.
Problem 9.2.
What is a lower bound for the price of a four-month call option on a non-dividend paying stock when the
stock price is $28, the strike price is $25, and the risk-free interest rate is 8% per annum?
Problem 9.7.
The price of a non-dividend paying stock is $19 and the price of a three-month European call option on the
stock with a strike price of $20 is $1. The risk-free rate is 4% per annum. What is the price of a
three-month European put option will a strike price of $20?
Problem 9.14.
The price of a European call that expires in six months and has a strike price of $30 is $2. The underlying
stock price is $29, and a dividend of $0.50 is expected in two months and again in five months. The term
structure is fiat, with all risk-.free interest rates being 10%. What is the price of a European put option that
expires in six months and has a strike price of $30?
Problem 9.18.
Prove the result in equation
.
Problem 9.22.
A European call option and put option on a stock both have a strike price of $20 and an expiration date in
three months. Both sell for $3. The risk-free interest rate is 10% per annum, the current stock price is $19,
and a $1 dividend is expected in one month. Identify the arbitrage opportunity open to a trader.
Problem 10.5.
What trading strategy creates a reverse calendar spread?
Problem 10.10.
Suppose that put options on a stock with strike prices $30 and $35 cost $4 and $7, respectively. How can
the options be used to create (a) a bull spread and (b) a bear spread? Construct a table that shows the profit
and payoff for both spreads.
Problem 10.14.
An investor believes that there will be a big jump in a stock price, but is uncertain as to the direction.
Identify six different strategies the investor can follow and explain the differences among them.
Problem 10.16.
"A box spread comprises four options. Two can be combined to create a long forward position and two
can be combined to create a short forward position." Explain this statement.
Problem 10.19.
Three put options on a stock have the same expiration date and strike prices of $55, $60, and $65. The
market prices are $3, $5, and $8, respectively. Explain how a butterfly spread can be created. Construct a
table showing the profit from the strategy. For what range of stock prices would the butterfly spread lead to
a loss?
Problem 10.22.
Suppose that the price of a non-dividend-paying stock is $32, its volatility is 30%, and the risk-free rate for
all maturities is 5% per annum. Use DerivaGem to calculate the cost of setting up the following positions.
In each case provide a table showing the relationship between profit and final stock price. Ignore the
impact of discounting.
a. A bull spread using European call options with strike prices of $25 and $30 and a maturity of six
months.
b. A bear spread using European put options with strike prices of $25 and $30 and a maturity of six months
c. A butterfly spread using European call options with strike prices of $25, $30, and $35 and a maturity of
one year .
d. A butterfly spread using European put options with strike prices of $25, $30, and $35 and a maturity of
one year.
e. A straddle using options with a strike price of $30 and a six-month maturity.