You are observing the following market prices. A put option that expires in six months with an exercise price of $45 sells for $5.80. The stock is currently priced at $40, and the risk-free rate is 3.6% per year, compounded continuously.

What is the price of a call option with the same exercise prices and maturity? (5 marks)

In the above example, suppose you form a portfolio consisting of selling a call option

and buying a put option on the same stock. Is this portfolio risk free? (10 marks)

In the above example, suppose you form a portfolio consisting of buying a share of the stock, selling a call option and buying a put option on the same stock. Is this portfolio risk-free? (5 marks)