1. 1) 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 thanX2, and X2is less than X3 by equal amounts, and all calls have the same expiration date. Graph the payoff diagram to this strategy.
2) A vertical combination is the purchase of a call with exercise price X2and a put with
exercise price X1, with X2greater than X1. Graph the payoff to this strategy.
3) A bearish spread is the purchase of a call with exercise price X2and the sale of a call with
exercise price X1, with X2greater than X1. Graph the payoff to this strategy.
2. Joseph Jones, a manager at Computer science, Inc. (CSI), received 10000 shares of company
stock as part of his compensation package. The stock currently sells at $40 a share. Joseph would like to defer selling the stock until the next tax year. In January, however, he will need to sell all his holding to provide for a down payment on his new house. Joseph is worried about the price risk involved in keeping his shares. At current prices, he would receive $400000 for the stock. If the value of his stock holdings falls below $350000, his ability to come up with the necessary down payment would be jeopardized. On the other hand, if the stock value rises to 450000, he would be able to maintain a small cash reserve even after making the down payment. Joseph considers three investment strategies:
a) Strategy A is to write January call options on the CSI shares with strike price $45. These calls are currently selling for $3 each.
b) Strategy B is to buy January put options on the CSI shares with strike price $35. These calls also sell for $3 each.
c) Strategy C is to establish a zero-cost collar by writing the January calls and buying the January puts.
Evaluate each of these strategies with respect to Joseph’s investment goals. What are the advantages and disadvantages of each? Which would you recommend?
3. The common stock of the C.A.L.L. Corporation has been trading in a narrow range around
$50 per share for moths, and you believe it is going to stay in that range for the next three months. The price of a three-month put option with an exercise price of $50 is $4.
a) If the risk-free interest rate is 10% per year, what must be the price of a three-month call option on C.A.L.L. stock at an exercise price of $50 if it is at the money? ( The stock pays no dividends)
b) What would be a simple options strategy using a put and a call to exploit your conviction about the stock price’s future movement? What is the most money you can make on this position? How far can the stock price move in either direction before you lose money?
c) How can you create a position involving a put, a call, and riskless lending that would have the same payoff strategy as the stock at expiration? What is the net cost of establishing that position now?
4. You are attempting to value a call with an exercise price of $100 and one year to expiration.
The underlying stock pays no dividends, its current price is $100, and you believe it has a 50% chance of increasing to $120 and a 50% chance of decreasing to $80. The risk-free rate of interest is 10%. Calculate the call option’s value using the two-state stock price model. Calculate the value of the put option with exercise price $100 using the same two-state stock price model. Show that put-call parity is satisfied by your solution.
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