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 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
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8568e807-7f6f-46a8-b9cb-7a1d339c7b98%2F4946e283-c3d1-4d1f-9cb0-b76f489447d1%2Ffd2ufr_processed.png&w=3840&q=75)
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8568e807-7f6f-46a8-b9cb-7a1d339c7b98%2F4946e283-c3d1-4d1f-9cb0-b76f489447d1%2Fut2kycd_processed.png&w=3840&q=75)
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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