Charles Schwab once offered investors an equity-linked Certificate of Deposit, issued by First Union National Bank. This product guarantees to repay the invested amount after 5.5 years, plus 70% of the simple appreciation in the S&P 500 over that time.

(a) Suppose the S&P 500 index is 1300 at the time you invest $10,000 in the equity-linked CD. Show that the equity-linked CD is equivalent to a combination of a zero-coupon bond and certain number of call options on the S&P 500 index. What is the face value of the bond? What is the number of the options?

(b) Suppose that the 5.5-year interest rate is 6%, the volatility of the index is 30%, and the dividend yield is 1.5%. What is the value of the equity-linked CD that you invest?

(c) What is the implicit commission you pay to the bank as a percent of your total investment in the equity-linked CD?

(d) Describe in detail how the First Union National Bank should hedge the exposure to the risk in issuing the equity-linked CD, assuming it is possible to buy long-term index options from a broker-dealer.

(e) If the broker-dealer charges a fee, which is 5% of the fair value(i.e.,Black-Scholes value) of the options, how much commission (as a percent of your total investment) the bank can realize after hedging?