A stock that is priced at $3,810 today has an implied volatility of 18.3%. The continuously compounded risk-free interest rate is 6.5% per annum. (a) (i) Determine the theoretical price of a European call option on the stock using the Black-Scholes-Merton (BSM) model. The call option has a strike price of $3,725 and 6 months of remaining life before expiration, (10 marks) You have learned that the European call is now priced at 320 in the market. At the same time, a 6-month European put on the same stock with a strike price of $3,725 is priced at 95. If put-call parity holds, prove that there is an arbitrage opportunity. Explain your arbitrage transactions and determine the arbitrage profit. Assume zero transaction costs and taxes. (10 marks)