1 Explain the difference between a forward start option and a package.

Outperformance certificates are offered to investors by many European banks as a way of investing in a company's stock. The initial investment equals to the stock price, S0. If the stock price goes up between time 0 and T, the investor gains k times the increase at time T, where k is, the stock price used to calculate the gain at time T is capped at some maximum level M. If the stock price goes down, the investor's loss is equal to the decrease. The investor does not receive dividends.

a) Show that an outperformance certificate is a package.

b) Calculate the value of a one-year outperformance certificate when the stock price is 50 pounds, k=1.5, M=68 pounds, the risk-free rate is 4.5%, and the stock price volatility is 23%. Dividends equal to 0,5 pounds are expected in 2 months, 5 months, 8 months, and 11 months.