Q is a company offering a Buy now pay later (BNPL) service. Q has the credit payment service that allows customers to pay for items by installments. You are thinking of buying a European put option on shares in Q. The current price of one Q share is $50.48 and over the next month the share price will either increase to $60.36 (if there is an increase in customer numbers) or decrease to $42.17 (if there is a decrease in customer numbers). The European put option will expire at the end of one month. The strike price is $57.50. The share will not pay any dividends during the next month. You can borrow money today for one month at the rate of j12 = 6% p.a.

a. Suppose you estimate the probability of a positive market response (an increase in customer numbers) to be 50%. Use the contingent payments method to find the amount you would be willing to pay today (i.e., the option premium) for the put option. (Round your answer to five decimal places.).

b. Consider the replicating portfolio (that is, the investment strategy which will give identical payoffs, at the end of one month, to the put option) that involves buying h shares in Q today, and borrowing $B for one month. Illustrate this model in a carefully labelled contingent cash flow diagram. Find the values of h and B (round your answers to five decimal places).

c. What is the initial cost (net outlay) today of investing in the replicating portfolio? (Round your answer to three decimal places.)

d. What is the fair price (or premium) for the put option, if the arbitrage-free pricing principle is applied? Why? (Round your answer to three decimal places.)