You are an arbitrageur working for Century Arb hedge fund. At 10:30 AM you are observing the following prices/rates. A European put option of XYZ Corp. maturing in 3 months with the strike price of $50 per share is selling for $2 per share, while a European call option on the same stock maturing in 3 months is selling for $4.50 per share. Currently, XYZ Corp's stock price is $54 share and the risk-free rate is 4$ per annum with continuous compounding. 

 

(a) Is there an arbitrage opportunity? Answer yes or no. Use Put-Call parity to prove your answer (5 points).

(b)  If there an arbitrage opportunity identified in part (a), provide a detailed step-by-step description of your trading strategy and calculate your final profit per share