Suppose the stock price is $40 and the one-year Treasury rate is 8%. Draw payoff and profit diagrams for the following options:
35-strike put with a premium of $1.53.
40-strike put with a premium of $3.26.
45-strike put with a premium of $5.75.
Consider your payoff diagram with all three options graphed together. Intuitively, why should the option premium (i.e., the option price) increase with the strike price?
Imagine that you are holding 5,000 shares of stock, currently selling at $40 per share. You are ready to sell the shares but would prefer to put off the sale until next year due to tax reasons. If you continue to hold the shares until January, however, you face the risk that the stock will drop in value before year-end. You decide to use a collar (i.e., buying a put and selling a higher-strike price call for each share of stock held) to limit the downside risk without laying out a good deal of additional funds. January call options with a strike price of $45 are selling at $2, and January puts with a strike price of $35 are selling at $3. Assume the Treasury rate is 0%. What would be the value of your portfolio in January (net of the proceeds from the options) if the stock price ends up at (a) $30? (b) $40? (c) $50? Compare these proceeds to what you would realize if you simply continued to hold the shares.
A stock currently sells for $32.00. A 1-year maturity European call option with a strike of
$35.00 has an option premium of $2.27. Assume that the one year Treasury rate is 2%, and the stock does not pay any dividends.
According to the put-call parity, what should be the option premium on the associate put (i.e., a European put on the same stock, same strike price, and same time to maturity)?
Suppose the actual put option price were $2. Is there an arbitrage opportunity? If yes, please describe the arbitrage strategy and calculate your profits.
4. A butterfly spread is the purchase of one call at exercise price X1, the sale of two calls at exercise price X2, and the purchase of one call at exercise price X3. X1 is less than X2, and X2 is less than X3 by equal amounts, and all calls are European and have the same
expiration date. Graph the payoff diagram to this strategy. Also briefly describe the type of investor that would desire this payoff profile. [see next page]
5. The A bull spread is a position in which you buy a call and sell an otherwise identical call with a higher strike price. To see how a bull spread arises, suppose you want to speculate on the stock price increasing. Consider buying a 40-strike European call with 3 months to expiration with a premium of $2.78. You can reduce the cost of the position – and also the potential profit – by selling a 45-strike call with a premium of 0.97.
What is the initial net cost of the two options? Assuming that the 3-month Treasury rate is 2%, what is the future value of the net cost at expiration (i.e., in 3 months)?
Graph the payoff and net profit (i.e., payoff minus future value of the net cost) to this strategy.
Subject | Business |
Due By (Pacific Time) | 11/23/2014 11:00 pm |
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