Using the PutCall Parity for the following situation recomme

Using the Put-Call Parity for the following situation recommend a profitable strategy and display the outcome of its payoffs at the time of expiration:

Stock Price = $80

Strike Price = $70 (for both Call and Put)

Risk free rate = 3%;

Call Price = $16 (1 yr expire);

Put Price = $2 (1 yr. expire)

Solution

Answer

If Put Call parity holds then,

Cash + Call = Stock + Put

i.e. Xe^-rt + C = So + P

Where X is Strike price

C is value of call option

So is current market price

P is value of put option

R is rate of interest

T is time period

= 70 e^-0.03*1 + 16 = 80 + 2

= 70 e^-0.03 + 16 = 82

= 70 (0.97045) + 16 = 82

= 67.9315 + 16 = 82

=83.9315 (overvalued - Sell) > 82 (undervalued - Purchase)

Take loan of $ 80 @ 3% for 1 year

Buy stock @ $ 80

Buy the put option - Strike price $ 70, for $ 2

Sell call option – Strike price $ 70, for $ 16

Repay loan with interest: 80 e^0.03*1

= 80 e^0.03

= 80 (1.0305)

= 82.44

Suppose after 1 year stock price is 90, then put option will not be exercised by us but call option will be exercised by the other party.

Gain = [80 (loan taken) – 82.44( loan repaid) ] + [-80(stock purchase price) ] + [16 (call option premium income)-2( put option premium expense) ] + 70 (Proceeds received on exercise of call option by other party)

                                                        = -2.44 + (- 80) + 14 + 70

                                                        = -82.44 + 84

                                                        = $ 1.56