Suppose that the risk-free interest rate is r = 0.09. All transactions below are for one share of a certain stock, and all options are European options. Suppose that today, at time t = 0, we short the stock, receiving the amount 50, and buy a call for the strike price 55 and sell a put for the strike price 45, both expiring 4 months from now. The option prices are 2.60 for the call and 2.40 for the put. When answering (b) and (c) take the risk-free interest rate into account. When giving amounts of money as an answer, use two decimals in your answer.

(a) What is the total amount that we receive on this transaction at time t = 0 ? Show your work.

(b) Suppose that we close the entire transaction 4 months from now after the options have expired and change everything to money. What is the maximum profit that we can get and for which range (give the complete range) of stock prices S(T) 0 at expiration is the maximum profit obtained ? (Consider the value of the profit at expiration, not the present value.) Show your work.

(c) Under the assumptions in (b), what is the maximum loss (expressed as a positive number) that we may suffer at expiration and what is the complete range of prices S(T) 0 for which the maximum loss is obtained ?