Question

Spoofer National Bank has created an instrument called a “market participation CD” (MPCD). The CD will mature in one year and at that time will pay either $50 or the value of one share of Megatronics stock, whichever is greater. However, in the fine print of the contract, it specifies that the payoff will never exceed $55, even if the stock price is above that amount. Thus the payoff for the market participation CD is:

State of market:        MPCD pays:

S₁< 50                       50

50 < S₁< 55               S₁

55 < S₁                         55

a. Diagram the payoff function for the MPCD. Be sure to label the critical values on the diagram including: maximum payoff, minimum payout, and the location of any “kinks” in the diagram.

b. Your boss at Spoofer NB has asked you to construct a portfolio that will provide the bank with exactly the amount needed to cover the payments it will be required to make on one MPCD in every state of the market. What instruments would you use to construct the portfolio? Please specify i) the type of instrument ii) including relevant parameters such as strike price, face value, etc., and iii) type of position (long or short).

c. Based on your answer to b, what is the fair marketvalue of an MPCD?

Answer 1

		a	DIAGRAM THE PAYOFF
			S1=Price of Megatronic Stock after one year
			S1	Payoff
			45	50
			46	50
			47	50
			48	50
			49	50
			50	50
			51	51
			52	52
			53	53
			54	54
			55	55
			56	55
			57	55
			58	55
			59	55
			60	55
				b	CONSTRUCTION OF PORTFOLIO
					BULL SPREAD STRATEGY WITH ONE YEAR CALL OPTIONS
				1	Buy Treasury Bond (One year) for 50/(1+i)
					i= annual interest rate on Treasury Bond
				2	Buy (Long) Call on Megatronic Stock with Strike Price =50 , expiring after one year
				3	Sell (Short or Write) Call on Megatronic Stock with Strike Price =55 , expiring at the same time as long Call at strike 50
					Payoff of Long CALL (Strike 50):
					Payoff =Max((S1-50),0)
					Payoff of Short CALL(Strike 55):
					Payoff =Min.((55-S1),0)