Suppose that a stock index portfolio is currently worth $1,000. A bank can offer clients an $1,000 investment opportunity that consists of (1) a 3-year zero coupon bond with a principal of $1,000 and (2) a 3-year European call options which are at-the-money. The option can be bought for the price c, using funds left over after buying the bond. Any remaining amount of funds will be the banks profit. Assume a 3-year risk-free rate of 3% with continuous compounding.

a) Find the upper limit for the option price c to make the bank profitable.

b) Suppose that the bank could not find any at-the-money call options to create the $1,000 principal-protected note. Suggest two different approaches to increase the feasibility of the principal-protected note. Briefly explain why each approach will work.