A stock market index is S0 = 95 and the put premium for an option on the index with 1 year to expiry and a strike price of 100 costs 9.29. Short term interest rates with 1 year to maturity are 2% (simple rate).

You work for a retail bank and are asked to structure a guarantee bond using call options written on the stock market index. The guarantee bond has the following features. It guarantees to repay a customer's investment of 100 under any circumstances, but if the stock market increases it passes on the higher value. An administration fee applies which will not be repaid.

(i.) To avoid an arbitrage profit what would the call premium have to be?

(ii.) Explain how you would structure such a guarantee bond using calls.

(iii.) What would your administration fees have to be so that you could structure such a bond and break even?

(iv.) Suppose in one year's time the stock index (S1) is either 85 or 120. What would a customer receive and assuming the retail bank charges an administration fee which allows you to break even what would the return for the investor be?

The Black -Scholes model is :

C=SN(d1)-Ke-rT N(d2)

d1 = [ln(S/K) + (r + 2/2)T] / [ sqrt(T)]

d2 = d1 - sqrt(T)