Question

1. Draw payoff diagrams for the following option trading strategies. Assume all options have the same expiration date. a. Buy a share and write a call on the stock b. Buy a call with exercise price X1 and write a call with an exercise price X2 on the same stock, with X1 < X2. c. Buy a call with exercise price X1, sell two calls with exercise price X2 and buy a call with exercise price X3 with X1 X2 X3 and X2 halfway between X1 and X3 (i.e. X2 = 1/2 (X1+X3) or 2X2 = X1+X3). 2. A stock has two possible ending prices six months from now: $120 or $90. A call option written on this stock has an exercise price of $110. The option expires in six months. The risk-free rate is 6% per year. The current price of the stock is $100. a. Show how you can create a hedge portfolio using a combination of the stock and call option on this stock. b. What is the equilibrium price of the call option on this stock? 3. A stock has two possible ending prices six months from now: $ 45 or $60. A call option written on this stock has an exercise price of $48. The option expires in six months. The risk-free rate is 4% per year. The current price of the stock is $50. What is the equilibrium price of the call option on this stock? Suppose you find this call option trading at $3.00, describe an arbitrage strategy you can use to take advantage of the mispricing and calculate your arbitrage profit per share used in the strategy.

Answer 1

1]

a]

This is a covered call strategy. The payoff chart of a covered call is as below :

b]

This is a bull call spread strategy. The payoff chart of a bull call spread is as below :

c]

This is a long call butterfly spread strategy. The payoff chart of a long call butterfly spread is as below :