You're a Banker

Essay

You're a banker. A client wishes to buy a guaranteed note with a 100% indexation to the stock index's growth. In other words, he doesn't want any coupon but requires 100% of the index growth. You wonder about the maturity of such a note. You check the prices of various index calls traded on the market for different maturities. Their strike is the current index level and their price is expressed as a percentage of this level. (For instance if the CAC is worth 3,000, the strike is 3,000 and the one-year maturity call trades at 11% of 3,000. You also check the price of a zero-coupon in percentage for various maturities. The following graph shows, for each maturity, the price of the option, that of the zero-coupon, and 100%-zero. a. What is the maturity of the guaranteed note (coupon =0%, indexation =100%)? Justify.
b. If as a banker, you want to make a profit, should you lengthen or shorten the maturity of that note? Explain why.
c. Everything remaining constant (that is, same volatility and interest rate), should the maturity of the guaranteed note be shorter or longer if the index pays a low dividend rather than a high one? Why?