Iconic British brand Promitte manufactures a yeast-based sandwich paste, sold all over the world. A key ingredient of the product is schlopp, which the British firm imports from Europe. With Britains impending departure from the European Union (Brexit), Promitte is concerned the price of schlopp could riseeven though its supply is expected to rise sharply, and far exceed demand. As a result of its concerns, Promitte is considering entering into an option contract.

Your financial modelling team have studied the price of schlopp and have come to the conclusion that over the next three months the price of schlopp may rise by 20% if there is a hard Brexit (occurring with probability p) or fall by 16.6667% (= 11/1.2, occurring with probability 1p) if there is a soft Brexit. The current price per metric tonne of schlopp is 50. Promitte can borrow money today for any period under six months at the rate of j12 = 5% p.a.

a. What type of option contract would Promitte buy to give it the right to buy schlopp in three months time at a price of 50 per metric tonne? Draw a cash flow diagram setting out the cash flows of such an option contract. (Quote prices to five decimal places.)

b. Consider the replicating portfolio (i.e., the investment strategy which will give identical payoffs, at the end of three months, to the option contract), that involves buying h metric tonnes of schlopp today, and borrowing $B for three months. Find the values of h and B.

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 (premium) for the option contract? Why? Round your answer to three decimal places.

e. The contingent payments method will give the same option value as the arbitrage pricing method, as long as the appropriate value is used for p (the probability of an upward price movement). Find the appropriate value of p in this case.

Your team has just learned that the British government has decided to delay Brexitrather than occurring in three months time, it will occur in six months time. Thus Promitte now needs an option contract with six months to expiry. Your team is confident that your three month modelling above would also apply to the next three month period. That is, over the final three months, prices could either rise or fall again at the same rates and with the same probabilitiesand these changes would apply to the prices in effect at the end of the initial three month period.

f. Draw a contingent cash flow diagram representing the payoffs for this new six month option contract.

g. Calculate the price of the six month option contract.