Question

Johnson & Johnson (JNJ) is currently trading for $151.30 per share. You see that one month calls and puts with strike prices of $145 have premiums of $15 and $7, respectively. The annual risk free rate is 1%. What is your per share arbitrage profit? Note: Answer in dollars, round to the nearest cent.

Answer 1

According to put-call parity,

Cash Investment + Call Option = Stock + Put Option

{For put-call parity to hold, strike prices and expiry of both call and put options must be same. Also, cash investment must be equal to Present value of strike price of options}

Therefore

Cash Investment + Call Option = 145 / (1 + 0.0/12) + 15

Cash Investment + Call Option = $144.88 + 15

Cash Investment + Call Option = $159.88

Stock + Put Option = 151.30 + 7

Stock + Put Option = 158.30

Therfore I will buy stock and put option and sell call option and take short position in cash market (that is borrow).

Therefore arbitrage gains = $159.88 - $158.30

Therefore arbitrage gains = $1.58