Question

A call option on Jupiter Motors stock with an exercise price of $45.00 and one-year expiration is selling at $8.37. A put option on Jupiter stock with an exercise price of $45.00 and one-year expiration is selling at $12.04. If the risk-free rate is 3% and Jupiter pays no dividends, what should the stock price be? (Do not round intermediate calculations. Round your answer to 2 decimal places.; Use CONTINUOUS COMPOUNDING)

Stock price $             

Answer 1

Price of call option = c = $8.37, Price of Put option = p = $12.04 and Strike Price = X = $45, Risk free rate = r = 3%

Time to expiration(in year) = t = 1

Let S = Stock price = ?

Then according to put call parity

S + p = c + Xe^-rt

S + 12.04 = 8.37 + 45e^-(3%)(1)

S + 12.04 = 8.37 + 45e^-0.03

S + 12.04 = 8.37 + 45 x 0.9704455

S = 8.37 + 43.6700475 - 12.04 = 40.0000475 = 40.00 (rounded to two decimal places)

Hence the Stock Price = $40.00