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Posted: March 26th, 2023

Chapter 8. Option Payo s & Trading Strategies

1.
Draw the payo diagram for
the following portfolio of options, all with the same maturity:

(a) long a call at strike 75, (b) long two calls at strike 80, and (c)
long three calls at strike 85. What is the view of the stock price change
consistent with this portfolio?

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2. You are interested in creating the
following gross payo pro le using an
options portfolio:

Stock price

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Payo

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What options, at what strikes, would you hold in your portfolio?
Assume that the desired payo s are zero for any stock price less than 50 or
greater than 160.

.

3.
(Di cult) Using the principles of the previous question, create a
spreadsheet-based algorithm to generate an option portfolio for any target
gross payo pro le, such as the one in the previous question. Assume, as in the
previous question, that option payo s are provided for stock prices taken at
regular intervals (e.g., intervals of $10). Create a table for the given
problem on a spreadsheet and then use solver to nd the solution.

4. You are managing a separate portfolio dedicated to your retirement
income. You do not wish to take excessive risk, and would prefer to limit the
downside. What common option structure would su ce?

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5. What gross payo pro le do you get if you short a covered call
position and go long a protective put position? Would you pay or receive net
premiums on this position? What is the view taken on the movement of the stock
price if you hold this position? What other options strategy does your
portfolio remind you of? Assume a common strike for all options of $100.

6. If you had a view opposite to that taken in the previous question,
what portfolio structure of options would you choose?

7.
Microsoft is currently trading at $26. You expect that prices will
increase but not rise above $28 per share. Options on Microsoft with strikes of
$22.50, $25.00, $27.50, and $30 are available. What options portfolio would you
construct from these options to incorporate your views?

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8. Suppose your view in the previous question were instead that
Microsoft's shares will fall but a fall below $22 is unlikely. Now what
strategy will you use?

9. Calls are available on IBM at strikes of 95, 100, and 105. Which
should cost more, the 95{100 bullish vertical spread, or the 95{100{105 butter
y spread?

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