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Option strategy

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1. 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 the answer change if the investor buys 100 shares, shorts 200 call options, and buys 200 put options?

2. Employ an arbitrage argument to explain why an American option is always worth at least as much as: (a) a European option on the same asset with the same strike price and exercise date, and (b) its intrinsic value. For both parts (a) and (b) clearly state what strategy is employed to make a profit if the condition is not met.

3. Consider an exchange-traded call option contract to buy 1000 shares with a strike price of $50 and maturity in four months. Explain how the terms of the option contract change when there is: (a) a 25% stock dividend, (b) a 10% cash dividend, and (c) a 2-for-1 stock split.

4. The AAAA Company has 100,000 shares outstanding and 20,000 warrants outstanding.
Each warrant has a maturity of one year and gives the holder the right to buy one new share from AAAA Company for $50. Suppose the premium on a call option (on AAAA Co. stock) with a strike price of $50 and maturity of 1 year is $3. What is the market price for one warrant?

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This answer helps to understand the option strategy using call option, put option, and shares.

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Option strategies: straddle, butterfly spread, CONDOR, writing covered calls, writing puts, vertical bull spread

1. Suppose you buy 100 shares of ABC at $79.25 and simultaneously write a March 80 Straddle at the prices given below. Make a spreadsheet and draw a profit/loss diagram and label all significant points for this strategy.

March 80 call at $1.625
March 80 put at $3.50

2. XYZ Inc.'s JUN 300 calls ($4 1/4 each), JUN 305 calls ($2 1/2), and JUN 310 calls ($1) are all available to you. You are required to construct a butterfly spread and show (a) the maximum possible gain and (b) the maximum possible loss and the break-even point. What is the gain or loss if, at expiration, the underlying security sells for exactly $302?

3. Look at the situation in question 2 again. Now assume that you also have a JUN 315 call ($0.50) available to you. If you short a CONDOR using the calls-only strategy, what is (a) the maximum possible gain and (b) the maximum possible loss and the break-even point. What is the gain or loss if, at expiration, the underlying security sells for exactly $302?

4. Explain why writing covered calls and writing puts are generally equivalent strategies. Show with an example.

5. Using the following prices, answer the questions listed below.

CALLS PUTS

EP FEB MAY AUG FEB MAY AUG
JJ 25 3 4 1/4 5 1/2 2 2 1/2 3 3/4
27 1/2 30 1 1 7/8 2 1/2 3 1/8 3 3/4 4 5/8
27 1/2 35 1/8 3/4 1 1/4 7 1/2 8 8

a. Using MAY 30/35 construct a vertical bull spread using calls and puts.
b. Show the maximum profit/loss under both strategies.
c. Suppose at expiration the JJ stock sells for $33 1/4. What is the percentage return on your investment? Ignore transaction costs.

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