Assume that the CCIR is 9%. The stock is AAPL is currently trading at $178.97. Assume that there is one European call option with strike price K=200 with delivery in 12 months from now. Assume that there is one European put option with strike price K=200 with delivery in 12 months from now.
a. What is the forward price for delivery 12 months from now?
b. What is the value of the forward price at inception (i.e., today)?
c. What is the (no-arbitrage) spread between the premium of a put and a premium of a call option, both with the same strike price of K=200.
d. If the premium on the put option is $5.05. What is the premium on the call option? Should we expect (on average) the put-call premium to be positive or negative?
The next two questions are meant to help you to understand the put-call parity relationship explained in the slides:
e. Suppose that there is an outstanding forward to deliver the stock at price K at time T (you can think of this forward being entered at time t=-1, so that at time t=0, we can take the forward as “given”). If the spot price is $178.97 and the CCIR is 9%, what is the value of the current forward price? (Hint: compute the reverse position to find the value…)
f. What is the difference in the spread between a put a and call with the strike price K at delivery T based on your answer to e)? Another representation of the put-call parity: g. Draw the payoff of a put option with strike price K and delivery at time T + 1ong stock h. Draw the payoff of a call option with strike price K and delivery at time T + a bond with face value K. i. What must be true for the price of e) and f).