1. Suppose someone owns 5,000 shares of a $60 stock. They also have written 25 of the $70 calls, 25 of the $65 calls, and have purchased 75 of the $60 puts.
Write a paragraph about the position risk. That is, explain the consequences of a large market movement up or down.
2. Suppose you wanted to spend $20,000 on a delta neutral 355 straddle with 90-day options. (See the initial conditions above.) Based on Black-Scholes values, how many put and call contracts would you buy?
3. In Problem , suppose that after two days the stock has risen 7/8. Has the position delta increased, decreased, or remained the same?
4. A portfolio contains 125 contracts of XYZ JUN 50 call options (European style), which sell for $3 and have a delta of 0.520. How Many JUN 50 put contracts (selling for $2) must you buy to be approximately delta neutral?
5. A portfolio contains 2,500 shares of ABC common stock. You calculate the following information:
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Option
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Price
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Delta
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Theta
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JUL 40 call
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1 3/4
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0.534
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0.03
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JUL 35 put
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7/8
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-0.312
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0.02
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You decide to write the JUL 40 calls and buy the JUL 35 puts so as to be approximately delta neutral AND so as to have essentially no cash outflow. How may of each option would you buy or write? (You are not concerned about whether the calls are covered or not.)
6. Another portfolio contains 12,000 shares of ABC stock. How many JUL 40 call contracts must the portfolio manager write to remove half of the market risk of ABC stock?
7. Fill in the table with +, -, 0, or inconclusive:
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Delta
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Gamma
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Theta
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Buy 100 shares
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Buy 100 shares, write 1 call
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Buy 100 shares, write 1 put
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Write 1 call, write 1 put
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Buy 100 shares, buy 1 put
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8. A JAN 80 XYZ European call has a delta of 0.550 and a gamma of 0.0180. What are a) the position delta, and b) the position gamma of a long straddle composed of one call contract and one put contract? (No information is missing from this problem.)
9. You hear someone say, “We do not write uncovered options, so our gamma is always positive.” Explain this statement, and state whether you agree or disagree with it.
10. Portfolio A and portfolio B both have a positive delta and a negative gamma, but one is quite conservative while the other is quite speculative. Make up an example showing how this could be the case.
11. State whether the following statement is true or false, and explain: “In the long run, continuously writing covered calls reduces both the expected return and the risk of a stock position.”