Problem 1 Suggest two different portfolios that produce the payoff diagram as in the graph below. Both portfolios may contain any amount of risk-free borrowing or lending, and the underlying stock. Portfolio 1 may contain call options but no put options. Portfolio 2 may contain put options but no call options. Assume the risk-free rate is rf = 10%. 25 20 15 10 5 10 15/20 25 30 35 40 -5 -10 -15

Intermediate Financial Management (MindTap Course List)
13th Edition
ISBN:9781337395083
Author:Eugene F. Brigham, Phillip R. Daves
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Chapter3: Risk And Return: Part Ii
Section: Chapter Questions
Problem 7MC: Write out the equation for the Capital Market Line (CML), and draw it on the graph. Interpret the...
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Problem 1 Suggest two different portfolios that produce the payoff diagram as in the graph below.
Both portfolios may contain any amount of risk-free borrowing or lending, and the underlying stock.
Portfolio 1 may contain call options but no put options. Portfolio 2 may contain put options but
no call options. Assume the risk-free rate is rf = 10%.
25
20
15
10
5
10
15
20
25
30
35
40
-5
-10
-15
Problem 2 Suppose that a stock is currently trading at $60 per share, and the stock price can
only take two possible values one year from now: it can either go up by 25% or down by 20%. The
annual risk-free rate is 4%. Assume that the stock pays no dividends. You are interested in pricing
an European put option on this stock. The option has a strike price of $66, and its maturity date
is exactly one year from now.
a) What is the payoff on the put option if the stock price goes up by 25%?
b) What is the payoff on the put option if the stock price goes down by 20%?
c) What is the price of the put option?
Problem 3
For a two-period binomial model, you are given:
• Each period is one year.
• The current price for a non-dividend paying stock is $20.
• u = 1.2840, where u is one plus the rate of capital gain on the stock per period if the stock
price goes up.
Transcribed Image Text:Problem 1 Suggest two different portfolios that produce the payoff diagram as in the graph below. Both portfolios may contain any amount of risk-free borrowing or lending, and the underlying stock. Portfolio 1 may contain call options but no put options. Portfolio 2 may contain put options but no call options. Assume the risk-free rate is rf = 10%. 25 20 15 10 5 10 15 20 25 30 35 40 -5 -10 -15 Problem 2 Suppose that a stock is currently trading at $60 per share, and the stock price can only take two possible values one year from now: it can either go up by 25% or down by 20%. The annual risk-free rate is 4%. Assume that the stock pays no dividends. You are interested in pricing an European put option on this stock. The option has a strike price of $66, and its maturity date is exactly one year from now. a) What is the payoff on the put option if the stock price goes up by 25%? b) What is the payoff on the put option if the stock price goes down by 20%? c) What is the price of the put option? Problem 3 For a two-period binomial model, you are given: • Each period is one year. • The current price for a non-dividend paying stock is $20. • u = 1.2840, where u is one plus the rate of capital gain on the stock per period if the stock price goes up.
• d = 0.8607, where d is one plus the rate of capital loss on the stock per period if the stock
price goes down.
• The risk-free interest rate is 5%.
Calculate the price of an American call option on the stock with a strike price of $22.
Transcribed Image Text:• d = 0.8607, where d is one plus the rate of capital loss on the stock per period if the stock price goes down. • The risk-free interest rate is 5%. Calculate the price of an American call option on the stock with a strike price of $22.
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