Consider a European put option on a non-dividend paying stock where the stock price is $49, the strike price is $50, the continuously compounded risk free rate is 5% p.a., the volatility is 35% p.a. and the time to maturity is 6 months.

(a) Determine the theoretical value today of a European put on this stock using a one-period portfolio replication approach (i.e. based on the concept that the payoffs of a put can be replicated by holding/shorting the underlying share and borrowing/lending at the risk-free interest rate). Please keep your answers to 4 dps.

(b) Now suppose the put is selling at $5.00. What opportunities are there for an arbitrageur? Assume the arbitrageur can borrow and lend at the risk-free rate, can short sell shares if necessary, and does not incur any transaction costs. Make sure that you clearly identify the profit accruing to the arbitrageur at the expiration of the arbitrage strategy. Ensure that the cash flow at time 0 is zero.