14. Consider the following type of equity related contract. In exactly one years time if the price of BBN Inc. Stock is between $30 and $60, you must pay the then going spot price to buy the stock. If the stocks price is above $60, you must pay an amount given by the formula: 60+.1(S-60) where S is the stocks price (S $60). If the stock is below $30, then you must pay $30.

a. Draw a diagram showing the amount you must pay for the stock when the contract matures. Ignore the initial cost of the contract.

b. You can construct this payoff by buying stock plus different options. Identify the options.

c. Divide the one year time to expiration into two sub-periods of 6 months each. Assume a binomial process for the underlying stock. You have the following information: (i) the annualized (not continuously compounded)risk free rate of interest is 5.85%. (ii) the volatility of the underlying asset (S.D. of its continuously compounded ROR) is 35% per year. (iii) The current price of the stock is $45. What is the value of a contract?

d. How would you redesign this contract so that the net value of the options is zero? (Give a qualitative answer).