John Co. stock currently trades for $40 per share. You can buy a call option on

Question

John Co. stock currently trades for $40 per share. You can buy a call option on John's stock with a strike price of $60.00 and a maturity date in exactly 6 months for $6.00. What should the price of a put option with the same strike price and maturity date be? Use a risk-free rate of 2.00% and give the answer to 2 decimal places.

You have written one put on John stock with a strike price of $20, purchased a call on John stock with a strike price of $30, and purchased a put on John's stock with a strike price of $40. What is the payoff to your portfolio of options if John's stock currently trades for $40 per share? Give the answer to 2 decimal places.

Explanation / Answer

1) Using put call parity we have:

Value of call option + PV of the Bond = Value of the Stock + Value of Put Option

6 + 60 / ( 1+ 0.02)6/12 = 40 + P

6 + 59.41 = 40 + P

Thus we get P = 25.41

( Note : The Present Value of the bond is calculated asuming its Face Value if the Strike Price of the Option,

PV of the Bond = Strike Price ( 1 + Risk Free rate )No. of periods in years )

2) The Investor has:

Short Put for a Strike Price= 20

Long Call for a Strike Price = 30

Long Put for a Strike Price= 40

If the current Price of the Stock is 40, the Payoff will be:

Short Put : Zero, as the the Strike Price < the Stock Price thus the investor who is long the Put will not exercise the Option

Long Call : The paoff is 40 - 30 = 10. As the investor has the right to buy the stock at 20, when the Stock Price is 40, he will exercise the Option.

Long Put : Zero, as the Strike Price = Stock Price

Thus the Total Payoff = 0 + 10 + 0 = 10

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