Suppose a stock that pays no dividends has current price = 50. The continuously compounded risk-free interest rate is 0.08. The price of a 6-month European call option with strike 48 has price $5, and an equivalent put option has price $3

a) Given that the call option costs $5, using put-call parity, what should the price of the put option be?

b) Given the actual price of the put option $3, is the put option overpriced or underpriced?

c) This means there is an arbitrage opportunity. Depending on your answer to part (b), you want to either buy the actual put option and sell a synthetic one, or sell the actual put option and buy a synthetic one. Find the arbitrage portfolio consisting of one unit of the put option, the call option, the stock, and a bond. Clearly indicate whether you buy or sell each one, and how many units.

d) What is the initial cost of the portfolio? What is the payoff at expiry(regardless of the price of the stock)? What is your profit after 6 months?